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The South Haven Dory is a one-person rowing boat that is based on lines of the St. Pierre dory, a traditional dory hull shape. The construction method is plywood/epoxy/composite (stitch and glue) with no building mold. It is not an "instant" boat; there are many steps to go through and the result is a strong yet lightweight hull that uses the best properties of plywood and composite construction. This project is an attempt to create a boat with modern construction methods that has beautiful traditional lines. The design can be built out of three sheets of 1/4" plywood with a half sheet or so of 1/2" plywood and 1/2"x2" stock as framing. The wood can be purchased at any building supply store. The bottom is sheathed in a 6 oz fiberglass cloth.
The completed boat is light enough that a strong person can carry the boat a short distance, so the boat can be car-topped or trailered. An estimate for total cost is a little over $300. The boat is very fast under oars and is an excellent introduction to recreational rowing. It is stable if you are used to canoes and kayaks, but not as stable as a fishing boat (for example). I have been able to stand up in it in flat water, but it is a balancing act. The best part about this boat is dropping the anchor and napping in the sun in the front of the boat. You can tell yourself that after rowing, you deserve to relax. I have written these instructions for someone who has had experience with epoxy and stitch and glue techniques, however a beginner could build this boat with help of a book such as "Devlin's Boatbuilding" by Sam Devlin. Another good resource is Martin Reid's My Boat Plans.
If you are considering building this or any boat, I would recommend that you build a model first. I believe that the offsets and information on this page are correct, but I have not built a boat using this document yet, so you might want to make sure the panel shapes fit together before cutting up your ply. I took the information from my notes that I used to build my first dory, so I am fairly certain that the information is correct. I hope to check the lines by building another dory soon.
Completed Dories:
Scarfing - The idea here is to join the two 2'x8' panels to make a 2'x16' panel. Use a long work table (mine was 8' long). Dry fit the panels: Clamp one 2'x8' panel down with the good face up, factory edge toward you, with the 2' edge at the middle of the table. Clamp the other panel next to it, butting the 2' ends tight next to eachother with the good side up and factory edge toward you to make a 2'x16' panel. Take two pins and some thread, and check to make sure that the 16' edge is reasonably straight. When you glue the panels together in the next step, it will be important that there is little space between the 2' ends to avoid a weak point, so if the long side is not straight then you may want to flip one of the panels to see if it works better the other way.
Glue-up - Lay a sheet of saran wrap in the middle of the table under where the joint will be. Cut two 4" strips of glass cloth (a little wider is OK) that are just a little longer than the joint (2'), and mark the middle (with 2" on each side) with a pencil at a few points. Wet out the glass strips, panel ends and the parts of the panel to be covered with cloth with epoxy (don't be epoxy stingy with this joint). Lay the glass strip centered on the saran wrap, wet it out some more with epoxy and set one of the 2'x8' panels on it so that it covers half of the tape (which you have marked at the center). Clamp the first panel down. Put the second panel on the tape, butting it up tight against the other panel, and aligning the long edges exactly. Tap the panels to make sure they are butted up tight against each other and are perfectly aligned on the sides. Clamp the second panel down tightly. Make a small amount of epoxy/filler mix (molasses consistency) and fill the area between the two panels with plenty of goo. Wet out the second glass strip liberally and put it on top of the two panels to be joined. I found it important to lay the top glass strip down immediately after pouring the epoxy/filler mix to avoid any air bubbles in the joint (I do have some air bubbles in the joints, there's probably no way to avoid them completely). Lay another sheet of saran wrap on top of the panels and glass cloth, and put something flat and smooth like a scrap piece of plywood on top of the joint, and weight it down (I used two 5 gallon buckets filled with water).
Wait 24 hours or until the epoxy cures completely. Remove the clamps and weights and inspect the scarf joint. Trim off the excess glass tape and sand lightly. Sanding into the weave of the cloth will reduce the strength of the joint and may result in dramatic failure. Paint on some clear epoxy to fill the weave of the cloth, repeat on the other side after curing. Repeat this procedure for the second hull side panel and the hull bottom panel.
Lines - There are four lines or edges to the completed hull side.
The dimensions are written in boatbuilder's notation, so 1-3-4 means 1 foot, 3 inches, 4 eighths (or 15 1/2"). A "+" means add a sixteenth to the dimension.
|Bottom Line
|Top Line
|Sternmost point, top of transom
|Bottom line is a straight line to next entry
|1-4-6 +
|2 plus 4 1/2"
|Bottom of transom
|0-1-1 +
|1-7-1 +
|Top line corrected, 4/27/01
|1-9-6 +
|0-3-7 +
|1-10-6 +
|0-4-1 +
|0-4-1 +
|1-10-6 +
|0-1-0 +
|1-9-7 +
|See next entry for bottom line
|14 plus 1"
|Bottom of stem, begin stem curve
|14 plus 6"
|Stem curve
|0-7-4 +
|Bottom line is part of stem curve
|15 plus 6"
|Stem curve
|1-7-2 +
|1-7-2 +
|Stem curve and top line meet in bow point
Use a straight edge to draw the transom line, from Station 0 Bottom Line point to Station 2 plus 4 1/2" bottom line point.
Use a batten and clamps to draw the top and bottom line curves. Use a thin batten to draw the stem line curve, from Station 14 plus 1" Bottom Line to Station 16 Bow Point. If some of the points do not fit into a curve well, check your dimensions and if correct, draw the curve fair rather than bending the curve to meet the point. Please report any mistakes in the offset tables to me, Paul VandenBosch.
One word of advice about the curves at the forward bottom corner: if you are going to adjust the curve here, make the hull side panel bigger rather than smaller. Another way to say this is to adjust the curve out rather than in. This point is where the hull bottom and two hull sides come together in front. I have found that curving the bottom of the sides up at this point makes for a weak joint because it bends the hull bottom panel too much. You are better off straightening this part of the line out or even reversing the curve a bit to make the hull side bigger.
Lay the unmarked panel with the good side down. Lay the panel with the lines on top, carefully aligning the edges of the two panels. Clamp them together in a way that you can cut one of the lines with a jigsaw. Cut the line, readjust the clamps and make sure the panels are still aligned correctly, and continue cutting until the hull sides are completed. While the panels are clamped together, you may also drill holes for the wire stitches (see below).
Scarf a 2'x16' panel as described above. You will not need all of this panel, only 2'x12' of it. With the good side up and factory edge facing you, cut off the left 4' of the panel so that what remains of the bottom panel is a four foot section, the scarf, and an eight foot section. (Alternately you could cut a 2'x8' panel in half before you scarf). Using a framing square, mark a centerline exactly one foot from the factory edge, and check to make sure that the centerline splits the panel exactly with one foot on either side, in particular at Stations 5, 6 and 7. With the factory edge facing you and the good side up, mark one foot stations along the factory edge, starting with 0 at the left. If all is well, the scarf should be at station 4 or close to it. Check your centerline; if you run your framing square along the factory edge, the centerline should always show the same distance from the factory edge, and it should be very close to 12".
Take a framing square, and at each station, measure from the centerline (not from the factory edge where the stations are) and mark the offset from the centerline in both directions with a sharp pencil. Keep the framing square square to the factory edge. Note that the aft end of the bottom panel (at Station 0) is 1 1/4" wide, while the forward end comes to a point.
|0-4-4 +
|0-7-2 +
|0-10-6 +
|0-10-4 +
Before you cut out the bottom, add marks on the centerline for the position of the footrest, oarlock, aft seat frame, forward seat frame. Use a heavy marker to mark these positions on the centerline so you don't lose these marks during construction. Label them so you will remember them in a few weeks/months. Note that the footrest is located for a six foot tall person, you may want to adjust it later by getting in the boat and figuring out what is comfortable.
|Bottom Panel Station:
|3 plus 2"
|4 plus 6"
|Aft Seat Frame
|5 plus 8"
|Forward Seat Frame
|6 plus 10"
Use a batten to join the points, and cut out the bottom. Do not drill any wire holes in the bottom until assembly.
I used a thin steel baling wire to wire the boat. It is not particularly thick. A slightly thicker wire might not cut into the plywood as much, but the baling wire did fine. The procedure I suggest is based on experience of having to restitch the boat two or three times to get to the point where I could spread the hull and fillet and tape the interior. You don't have to be this precise, but the way I describe it should work the first time.
Drilling holes for wire should be done symmetrically, so there are the same number of holes in the same places on both sides of the bottom. The best way to do this is to predrill the sides while they are clamped on top of eachother. Choose a drill bit that allows your wire to pass through the hole easily but without too much extra space. The wiring holes should be located as close to the edge of the panel as possible without allowing the wire to rip out the plywood. For the middle of the boat, where stresses are low, drilling the holes a little less than 1/4" from the edge of the plywood is acceptable. Near the corners and on the stem curve, stay about 3/8" from the edges.
Clamp the two hull side panels together and make sure they are aligned perfectly. Starting at the stem top, drill the first hole at the corner, 3/8" from both top and side. Drill a second hole 1/2" down from the first as a reinforcement. Drill the next three holes further down the stem, 1" apart. Then move down the stem and drill two holes 3" apart. Starting at the bottom of the stem, drill a similar pattern of holes moving up, making sure that the first is in the very corner of the stem bottom. Complete the middle of the stem by drilling holes about 3"-4" apart, evenly spaced.
At the transom bottom on the hull side, repeat the pattern, moving up the transom about half way. Repeat the stem top pattern at the transom top on the hull side. DRILL THE HULL SIDE, NOT THE TRANSOM.
Starting on the forward corner of the bottom line of the hull side, drill three holes about 1/2" apart. Drill the next three holes about 1" apart. Drill the next three holes about 2" apart, and then continue to the middle of the panel at about 4"-6" apart. Repeat the pattern starting from the aft corner of the bottom line of the hull side.
Just keep in mind through this process: the bottom fits over the hull side edges and the transom edge. The transom fits over the hull side edges.
Start by wiring three or four holes in the middle of the stem curve. Do not wire the corners at this time. These first stitches are preliminary and should be slightly loose. You will likely remove them and replace them with tighter wire stitches later, because the bending involved in getting the hull to the right shape will stretch and weaken the preliminary stitches. Next, align the transom and drill three or four holes on either side of the transom to match the holes in the hull side exactly. The transom bottom should be even with the hull side bottoms, and the transom fits over the ends of the hull sides. It is very important to position the holes so the wires will pull the parts together with the correct alignment. Wire a few preliminary stitches on both sides of the transom and the hull sides. Check the alignment of the stem bottom, and wire the stem bottom corner reasonably tight but not so tight that the wire will be ripped out when the sides are spread to fit the bottom. Repeat with the stem top, and transom tops and bottoms. Check alignment, drill a few holes, wire them up, and move on until the stem curve and transom are wired up completely.
To add the bottom and turn the flexible mess into a boat, turn the hull upside down on a table, and start at the rear corner where the transom, sides and bottom come together. Drill three holes along the width of the transom bottom. Align the hull bottom with the transom bottom, with the hull bottom over the transom edge and drill the mating holes in the correct position. Putting the holes in the right place is very important! Wire them up tight. Spread the sides out a little so they roughly approximate the shape of the bottom, and put the hull bottom on the edge of the side. Starting at an aft corner, drill a couple of holes in the bottom to match the first few holes on the side panel. Do not drill more than a few holes at a time. Wire them up, and move to the other side, repeat. Continue this process a few holes at a time until you reach the stem. Complete wiring any holes that are not yet complete.
Is the bottom longer than the sides? I drew up the plan so that the bottom should be a little longer than the sides. When you get close to wiring the forward end of the bottom, mark the shape of the sides on the bottom, and use a jigsaw or sander to trim the bottom down so the bottom and sides fit together well. This is the area where you will be able to tell if I did a good job writing down the offsets. Please let me know how this fit for you at firstname.lastname@example.com.
Check alignment, are there any problems? If so, feel free to remove any old stitches that are not holding the hull together correctly and to drill new holes and restitch. Go through all of your stitches and inspect the wire carefully. Hit it lightly with a pliers and if it is loose, tighten it up until it sings. Grab it with the pliers and shake it a little and see if it breaks. Don't cut off the ends yet. Check each one. Everything OK? Then its time to spread the hull.
Turn the hull over (avoid getting jabbed by the thousands of sharp points!) and support it by a couple of cinder blocks (or similar) on the floor, with the blocks near the fore and aft ends of the bottom panel. Put a weight in the middle of the hull (5 gallon pail full of water) and watch the hull assume a beautiful shape. Take a piece of wood and a few clamps and find a way to spread out the hull sides a foot or two aft of the middle of the boat. I fastened a clamp on each side of the hull and cut a batten to the right length to stretch the sides by jamming the batten under the clamps. After admiring it for a while, remove the weight and spreader until you are ready to fillet and tape the inside. You should install the spreader when you tape both the interior and exterior chines.
Taping is a job that you have to do in one shot. Running out of epoxy and running to the store for more halfway through is probably going to be a disaster. So have your workshop organized, prepare for every step of the process, have the stirring sticks, the plastic gloves, the goo squeegee, the silica filler powder, the tape, the cleanup products, plastic bag, trash can, rags and and everything that you will need standing out on display. Go through a dry run and imagine goo dripping everywhere, how do you deal with it?
Check each wire again, replacing any that are broken, loose or are of questionable strength, and when you are satisfied with the wiring and the boat seems ready to be glued together, put the hull back on the blocks and weight the center. Put the spreader in and stretch the boat just a bit further than you want it to be when its done (it will relax a little when the spreader is removed). Look at the alignment of the edges, and at the curves of the sheer (top). Hang a plumb bob and look down the centerline. Does it look pretty fair and balanced, no bulges out to one side? If so you are ready to rock and roll.
Take a large flat screwdriver and gently push each and every wire in towards the joint on the inside of the boat. Take a one inch paintbrush and paint clear epoxy on the plywood about 3" on either side of all the joints. Mix up a pot of thick epoxy/filler (peanut butter consistency) and use a squeegee together with a one inch putty knife to push the filler into the joint. Another way to do this is to use a plastic bag and cut a small hole in the corner and squeeze the epoxy/filler out. Use a rounded stick or squeegee to cove (round) the filler, maybe a 2" radius curve in the middle of the bottom, and 1" or less in the stem. Clean up any extra filler laying outside of the coved (rounded) area. A good cove is about one inch wide (more or less), except for the stem which will be narrow due to the sharp angle. Use a lot of filler in the stem. Have you filled all the joints? Have you cleaned up the extra goo? Good, move on to the tape.
Gently lay the dry tape along the joints centered on the joint. There should be at least an inch or more of tape touching the plywood outside of the filler cove. More is better. Try not to gouge into the filler cove too much, be gentle, no need to push it in or anything. Take the paintbrush and paint clear epoxy over the tape, sticking it down. Keep it centered nicely. Are you getting gooey threads that are a pain to deal with? Me too. If you can get them off with the paintbrush, slobber them on to the wastebasket or a piece of cardboard or something. Otherwise just leave them hanging in the air rather than disturb the rest of the tape. You can get them off after the epoxy cures.
You can cut off the ends of the tape that hang over before you start epoxying it, or you can let them hang over the top of the hull a little and cut them after the epoxy cures. Overlapping the tape at the bottom corners is a good thing, it strengthens the hull at a high stress spot. Keep putting tape down until all the joints are covered. Are you thinking that this will never be strong enough to float your bloat? You could add another layer of filler and tape along the stem. This is the joint that I think needs a little strengthening, although I have not had any problems. I used one layer of tape on the inside joints (except where the tape segments overlap).
When you are done, make a final inspection, then stop poking at it, turn off the light, leave the room, shut the door, and don't let anyone near the boat for 24 hours, including you. Don't try to change it while it is curing, you will only make things worse.
After 24 hours or more, remove the spreader, take out the weight, and clean up the glass that is hanging above the hull top, if any. Don't start cleaning up the inside yet, let it cure at least another day first. Turn the hull over, avoiding the many sharp wire points. Use a wire clipper to clip all the wires off of the outside. If you can pull the wires out, go ahead, but if they won't come out, leave them and just clip them off flush. Use a diagonal wire cutter to get them close to the wood. Sand the all of the outside chines (joint corners), stem and transom joints so they are rounded nicely. They should all have nice round corners, not sharp corners. Now put 4" tape and clear epoxy on all the outside corners. You may have areas where the tape won't lay nicely, try shorter pieces of tape in those areas. Once again, let the epoxy cure a day, lightly sand any rough stuff and then paint another layer of clear epoxy over the tape to fill the weave. Let cure. Flip the boat, lightly sand any rough areas on the tape on the inside of the boat, and paint a layer of clear epoxy over it to fill the weave. Let cure. You now have a hull which will need only minor framing to make it ready to row.
You will need to scarf pieces together to make 15'2" pieces. There will be a lot of stress at the scarf area so make sure you are scarfing ends together with no weak knots or cracks. I used an 6" scarf, trying to get 15' out of two 8' sections and one of my scarfs cracked so you might want to go with a 10" or 12" scarf with two scarfs per batten if you are using 8' stock. I wasn't too concerned about the crack, I just smeared epoxy/filler (molassess consistency) in and outside the crack, put a piece of saran wrap around it, and clamped a piece of furring strip next to it as a sister to make sure it cured with the right curve.
What, you don't know how to scarf? Well, you probably should get a book on boatbuilding, but basically it is cutting an angle into the end of a stick, and cutting the same angle into the end of another stick, and gluing the two sticks together. When I talk about a 10" scarf, it means to start the angle 10" from the end of the stick. I drew a line which showed the area I wanted to cut off to make the angle, and then took a hand saw and cut it off. Then I took the orbital sander and smoothed it out and made sure both angles fit each other OK. Then I glued them with epoxy/filler and clamped them down so they made for a straight 15' stick.
Gluing the outside sheer clamps is a matter of wetting the hull top and sheer clamp with epoxy and clamping the two together. Do one side at a time and have at least 10 clamps (more is better). Sometimes the batten doesn't quite want to follow the curve of the plywood and you have to clamp it hard and bend it hard. If you have to fight it, you might want to let the sheer clamp take it's natural shape and either carve off the additional plywood which sticks up after it cures or fill in the hole with more epoxy/filler and plywood after you add the inner sheer clamps. I had to do both on my boat, which means the top curve should be adjusted, but it wasn't by much. The solution is to use battens that are not very thick. I will use 1/2" battens on my next boat.
Cut the sheer clamps off flush with the hull at the ends, or if you like, you can cut it so the forward end is pointed, which is a little bit more difficult cut, but the boat would probably look better with a pointed sheer clamp. When the first outside sheer clamp has been installed and is cured, stand in the front of the boat and imagine the centerline as it passes through the sheer clamp. Cut the sheer clamp along the centerline. Before installing the second sheer clamp, cut the end to fit the first sheer clamp and use lots of epoxy/filler between the two.
If you don't have enough clamps, there is another way. You will have to start by installing the inside sheer spacers (see below) and put them in to be able to use screws to hold the outside sheer clamp in place.
Are the outside sheer clamps cured? Good, let's move on.
The inner sheer clamp is glued to the spacer blocks. The transom is a little difficult because it is rounded. I just glued straight battens across it and then sanded and ground them down to a rounded shape. Not fine cabinetry work but effective.
The ends and transom corners of the inner sheer clamp will have to be cut to join with an angle. I just look at them and imagein the centerline and maybe mark where I want to cut it and at what angle, and then use a handsaw to cut it. This is not accurate and leaves open spaces, so I put plastic tape around the bottom and side of the joint and try to shape the tape how I want the part to look and then fill the joint with epoxy/filler (molasses consistency). You could also epoxy a piece of fiberglass tape under the forward joint (breasthook?) for strength, or pour some epoxy/filler (molasses consistency) under the joint while the boat is upside down.
The arms are 3" wide 1/2" plywood, and are cut to taper from 3" at the top of the seat base down to the width of the inner sheer clamp, where it touches the sheer clamp. The seat base goes inside the arms and holds up the seat. Install the seat base and arms by painting all mating surfaces with clear epoxy, then join the parts and hull with lots of epoxy/filler (peanut butter consistency). Clamp the seat base and arms together, then cove the joints. I did not use glass tape here, but you could. You can also do this in steps to make sure it fits right, for example epoxy the arms and base together while inside the hull, then install the assembly inside the hull. It should work OK either way. I added a cleat on the inside of the seat base to help hold up the seat and keep it from falling in when I tried to open it, but I am not sure that this is needed. I did not add limber holes. The advantage of limber holes is that you have only one puddle in the boat instead of three, but I personally would rather keep the mud and oar splash in the aft area so the front stays clean and I can lay down in it.
I'm sure that there are many ways to make a foot rest. The advantage of this style is that it serves to strengthen the hull.
My homepage.
Email me at:Paul VandenBosch.


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Fresno State: (2007) Finished 58th with a time of 34:14 at the Cal Poly Invitational ... was 26th in the Hornet Jamboree, finishing with a time of 30:51 ... finished the UC Irvine 8K race with a time of 30:54 (177th) ... was 27th overall with a time of 24:44 in the four-mile race of Watermelon Run.
Prior to Fresno State: A two-year letterwinner in both cross country and track and field at San Lorenzo Valley High.
Personal: Born March 6, 1989 ... Becky and Ron Perry ... sister is Elise ... enjoys playing frisbee ... chose to attend Fresno State because of its academic programs.
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College Hockey:Vermont Regains Momentum
Catamounts Down UML To Go Unbeaten In Five Of Last Six
BURLINGTON, Vt. — Senior goaltender Joe Fallon made 31 saves, helping Vermont to a 3-2 victory over No. 16 Mass.-Lowell, at Gutterson Fieldhouse Sunday.
The Catamounts, who had three different players score, won for the third time in six games after having a four-game unbeaten streak broken Friday against New Hampshire.
Fallon, who is currently rotating with sophomore Mike Spillane, made 22 saves in the final two periods to keep Vermont in front.
"I thought Lowell, from the second period on, really had some great moments of play, and I thought Joe was spectacular tonight for us," said UVM head coach Kevin Sneddon.
"We knew it was going to be this kind of game. Lowell does a tremendous job of keeping the puck to the outside and pressuring you, and it makes it really tough for our defenseman to make clean plays on the breakout. But, I thought our guys did a tremendous job of being poised and using the chip pass if we didn't have a play off the glass and out."
The Catamounts' offense was in high gear to start the game. Reese Wisnowski put the Catamounts up 1-0, just 2:35 into the first, on a wrister from the top of the slot. Chris Atkinson set the play up with a pass out of the corner. Wisnowski's goal was just the senior's second in 92 career games at Vermont.
In the early going, Lowell sophomore goaltender Carter Hutton (18 saves) kept his team in it. He made nine saves in the period, including several good ones, when the Catamounts came out with extra jump.
As the period progressed, though, the River Hawks came on, nearly knotting the game at one, with 5:15 left. Freshman defenseman Maury Edwards rang the left post hard, from above the right circle.
Sneddon and his staff shook up the lines for the game, moving Peter Lenes and Brayden Irwin to the top line while shifting Dean Strong to the wing.
In the second period, the changes paid off. Lenes scored a highlight-reel breakaway-goal for a two-goal advantage. Strong sprung Lenes with a home-run pass, and Lenes came in on Hutton with speed, pulled up, and roofed a backhand at 5:03.
Then, after UML's Ben Holmstrom cut the UVM lead in half to 2-1, with a tip-in, power-play goal at 12:26, UVM's hottest forward line of Viktor Stalberg, Brian Roloff, and Wahsontiio Stacey put together a great rush for a 3-1 lead. Roloff fed Stalberg cutting to the net, who tipped the puck just inside the post at 12:34. The trio has combined for eight goals and 17 points in the last six games.
"[We wanted] to try to spark something between Lenes and Strong. We've got to get those guys scoring goals," explained Sneddon. "When Petey [Lenes] starts scoring goals, his whole confidence level just goes up, and he's playing so well but just not getting any rewards for it. So, it was real nice for him to cash in on that opportunity. He doesn't miss many of those.
"I thought the difference in the game was obviously the Stalberg goal," Sneddon said, "[It was a] textbook, middle-lane drive, offensive play that we work on a lot, and Roloff, with just a beautiful feed. But Viktor, driving that net, just creates a lot of offense with his speed. So, I thought that was the turning point in the game for us."
Lowell had almost four consecutive minutes of power-play time to close the period. Slavomir Tomko took a contact-to-the-head minor at 16:05, and Irwin went off for cross checking at 18:00. The Vermont penalty kill and Fallon did a nice job to keep the River Hawks off the board. Fallon stopped eight power play shots in the period.
"That was big because it allowed us to gain some momentum back," Sneddon said. "We weren't playing great, going into that. They had some great momentum going. They had just scored a power-play goal, not too long [before that]. Now, we were able to gain some momentum back, off some great shot blocks, some great saves, some just really smart puck decisions — textbook Catamount penalty kill there."
Sophomore Kory Falite pulled Lowell within one again, at 10:49 of the third, having poked it home after a scrum in the goalmouth. But that was as close as UML would get, despite a few close calls, as the game wound down.
The River Hawks outshot the Catamounts, 24-12 in the second and third periods, and, 33-21, for the game. Lowell was one-for-three on the power play; Vermont was scoreless in two chances with the man advantage.
"I thought UVM came out in the beginning of the game and showed their speed, skill, grit and determination and really put us on our heels for eight minutes of the game," said UML head coach Blaise MacDonald.
"I thought we did a pretty good job, thanks to Carter Hutton. Then, as the next 52 minutes progressed, I really liked our team," said MacDonald. "The execution wasn't where it needs to be to beat a good team like Vermont, but, all in all, playing on the road with a young team, I just liked the way we competed and hung in there. That locker room is shocked that we didn't score at the end, and that's a good sign."
The Catamounts (7-10-7, 6-6-5 Hockey East) pulled into a tie with Boston University for sixth in Hockey East with 17 points with a game in hand. They are on the road next weekend for two with Providence. The River Hawks (12-9-4, 7-7-4) are fifth in the league with 18 points and host BU Friday.
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COLORADO SPRINGS – After totaling 16 runs and 20 hits in its previous two wins, the NFCA No. 12 Colorado School of Mines softball team needed just one run in the regular season finale Sunday, ending a five-game skid to CSU-Pueblo with 1-0 shutout at Mountain Lion Field in Colorado Springs.
Senior starting pitchers Kelly Unkrich and Justine Bosio went toe-to-toe over the first five innings, yielding no runs and scattering 11 combined singles.
Mines (36-5-1, 27-3 RMAC) finally broke the scoreless stalemate in the sixth behind a trio of juniors as Gianna Duncan singled to left; Sami Springer reached on a fielder's choice and advanced one base on a throwing error by the shortstop and Melissa Marshall tagged a single to right for the go-ahead score and eventual game-winner.
Marshall, sophomore Cassie Ford and senior Molly Thiebaut each went 1-for-3, while Duncan finished 2-for-3, extending her season-high hitting and reached base streaks to six and nine games, respectively.
Freshman Elise Dugwyler reached base for the sixth straight game with an infield single in the second inning, finishing 1-for-2. Sophomore Paige Coufal added a pinch-hit base hit to short in the fifth.
Unkrich went the distance for the 33rd straight start and reestablished the Mines single-season wins mark for the second time, allowing seven singles and four walks, while whiffing three to improve to 22-1. Her 11th shutout, also a single-season record and third-most in Division II entering the weekend, pulled her within four of tying Amanda Kelly (1997-00) of Nebraska-Kearney for the all-time RMAC career mark of 26.
As the RMAC regular season champions and No. 1 seed, the Orediggers will host the conference tournament May 2-4 at both the CSM Softball Field in Golden and nearby Lakewood Park. The eight-team tournament field will be announced later today.


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Wimbledon starts June 23 and how will you be following the action?
While I'm sure you will be tuning in to some of the more than 100 hours of television coverage of one of tennis' biggest events, you will no doubt be checking social media for results, highlights and images.
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Grabyo, a real-time and forward thinking video company announced a major deal in conjunction with The All England Lawn Tennis Club (AELTC) to distribute near-live highlights from Wimbledon to a global digital tennis audience of billions.
The venture will also allow the AELTC share real-time video highlights to sports fans on Facebook, Twitter, Google+ and YouTube.
What's important here is the social media experience created by Grabyo will compliment and enhance the TV experience of Wimbledon.
Social media should not be thought of as a substitute for actually watching a sporting event either live or on television. I think the folks at the AELTC and Grabyo understand that and I'm looking forward to seeing what is offered.
Wimbledon coverage in 2014 will be delivered by a network of broadcasters across 200 territories. Tennis fans are like a sponge and they will soak up more and more coverage so this year, fans can again enjoy Live @ Wimbledon, the AELTC's live video and radio channel, delivered on Wimbledon.com and the official apps.
Wimbledon is right around the corner and now you can follow the tennis in a number of ways.
See more about Grabyo here: http://about.grabyo.com/


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The top commander in Afghanistan, Lt. Gen. Stanley McChrystal, said in a report leaked to the Washington Post that he needs more troops or the war will "likely result in failure." But as pressure to end the war builds, President Obama appears reluctant to commit to raising troop levels and is reportedly exploring other options.
Honduran President Manuel Zelaya, ousted June 28, returned his country Monday and took up residence with some supporters at the Brazilian Embassy in the capital. Roberto Micheletti, who has occupied the presidency since the military coup, declared a round-the-clock curfew.
A new agreement expected to be announced today at the G-20 economic summit in Pittsburgh will make the G-20 the new permanent council on international economic cooperation, replacing the G8. This move highlights the growing economic importance of countries in Asia and Latin America.
The 64th session of the UN General Assembly saw 192 leaders from all over the world come together this week. Secretary-General Ban Ki-moon highlighted the need for global cooperation and the global threat of climate change. President Obama spoke for the first time at the Assembly, stating that the "world must move in a new direction". MADRE Executive Director Vivian Stromberg responded with an open letter to President Obama, stating that the success of his policies hinge on the integration of women's human rights.


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This writer has been in the company of many different artists. Each one is unique and captivating in his/her own way. So I had previously seen this gentle giant with the big voice perform, but had the opportunity to interview him by phone on the evening of February 24, 2014.
His name is Koli Tengella and he is the product of a dysfunctional family as well as a survivor of physical and sexual abuse. He was born on Friday, hence the name Koli. Tengella is the family name, that of a major African king in West Africa - one of the first African kings to stand up to white oppression.
But it is through theater that Tengella has been able to change his destiny. Between the ages of 12 and 18, he was a fan of Lon Chaney, an actor known for his masterful makeup. As a result, he is now known as a performer and an instructor of social justice and positive social change.
Tengella got started as a comic around the age of 18. He went through the phases that most comics go through - that of mimicking comics who were popular at the time. Those modern comics were Eddie Murphy, The Wayans Brothers, Robin Williams, and Steve Martin, all of whom went on to star in movies. Tengella, however, wanted to say more with his humor than just the standard cliched style of comedy. He wanted to be considered more than the comics of the observational humor style and genre.
Of course, he did what most African American comics are/were forced into because that move began to garner work for him, but he was not happy.
In the late 80's, Tengella was named by 4 comedy club owners as most promising comedian in Baltimore Magazine. As he grew in the business, he became more politically and socially conscious. He realized that humor would be one of the most effective and powerful ways to enlighten and educate people as to the suffering and pain that people were going through, of which we might not be aware.
Tengella has been influenced by some of the best of the best, including: Dick Gregory, (for whom he opened twice in Baltimore), Paul Mooney, George Carlin, and Bill Mohr.
He has performed at all the comedy clubs in Baltimore as well as Caesar's Palace in The Poconos. He even did a national college tour for six months, visiting 82 schools during that time. He collected the Do Not Disturb signs from the hotels to keep track.
A native of Baltimore, Tengella attended Springhill Elementary, Dr. Martin L. King Elementary/Middle, Forest Park High, Baltimore City Community College and Morgan State University. His initial goal was to become an attorney, but he was bitten by the acting bug and took a different path.
He studied in an actor apprentice program at Baltimore's Arena Players and attended master classes at Juilliard. He, ultimately, had starring roles in 'A Raisin in the Sun', 'Othello', 'Macbeth', and 'Hamlet'.
Irvin Turner, one of the founders of Arena Players, mentored Tengella and even encouraged him to go to his first audition. Tengella attended an apprentice actor program at Center Stage, where his teacher, Donald Hickens, went on to become the theater teacher at Baltimore School for the Arts.
The six foot plus Tengella has no agent and works independently. He is looking for an agency so that he can perform comedy and travel the speakers' circuit. He has developed his own following in Maryland, as he discusses liberal and social justice issues through humor.
In March, Tengella is schdeuled to do a weekly 3-5 minute segment on Morgan State University's WEAA radio station's Anthony McCarthy Show. It will be a comedic take on national political and pop culture issues called, 'Tengella's Take'.
Tengella has hopes for his future. He says if things go as planned, he will be a regular political pundit on MSNBC or Altrazeera America talking about political issues of black folk, but using humor.
He will then join the ranks of some of the comics with whom he has met or appeared. The list includes DL Hughley, Tracey Morgan, John Witherspoon, Bill Bellamy, Tommy Davidson, Richard Belzer, and the late Shirley Hemphill.
To the up and coming artists, Tengella advises, "Find your truth and stick to it; don't do what is the norm because if it's funny to you, then it will be funny to others. If you can draw people into your perspective of things, it will be funny, too. To use surprise and twisting of stereotypes can be a beautiful thing".
Tengella's goal is just to use comedy/humor to enlighten and empower us all to become better human beings.
Koli Tengella can be reached on Facebook, Twitter and Instagram.
In March, 2014 his website will launch as www.kolitengella.com.


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Active Vibration Suppression of Sandwich Beams using Piezoelectric Shear Actuators: Experiments and Numerical Simulations BRIAN P. BAILLARGEON* AND SENTHIL S. VEL Department of Mechanical Engineering, University of Maine, Orono, Maine 04469, USA ABSTRACT: This article deals with the experimental and numerical assessment of the vibration suppression of smart structures using piezoelectric shear actuators. Experimental results are presented for an adaptive sandwich cantilever beam that consists of aluminum facings and a core composed of two piezoelectric shear actuators and foam. The electric field is applied perpendicular to the poling direction of the piezoelectric actuators to cause transverse shear deformation of the sandwich beam. Active vibration suppression is achieved using either positive position feedback or strain rate feedback. The control system is implemented in realtime using Matlab/Simulink and a dSPACE digital controller. First, the frequency response of the adaptive beam is investigated by using one shear actuator to excite the beam and the other to control its vibration. Parametric studies are conducted to assess the influence of controller parameters on the frequency response of the system. The experimental frequency response function compares well with numerical simulations using the finite element method. Next, the effectiveness of the active vibration suppression system in the time domain is analyzed using a proof-mass actuator that is attached to the tip of the cantilever beam to provide a repeatable vibration input. Experiments and numerical simulations show that the shear actuators can provide significant reduction in tip acceleration and settling time. Key Words: smart/adaptive structure, piezoelectric shear actuator, positive position control, strain-rate control, active vibration suppression INTRODUCTION ORE than a decade of intensive research in the area of smart/adaptive structures has demonstrated the viability and potential of this technology. A class of smart structures, consisting of piezoelectric materials integrated with structural systems, has found widespread use in engineering applications, including active vibration suppression (Bailey and Hubbard, 1985; Garcia et al., 1992; Fuller et al., 1996). Piezoelectric actuators used in adaptive structures are usually thin wafers, which are poled in the thickness direction and bonded to the surfaces of the host structure. The application of an electric field in the thickness direction causes the lateral dimensions of the actuators to increase or decrease, thereby forcing the host structure to deform. These types of actuators, where the electric field is applied parallel to the poling direction to cause normal strains in the piezoelectric material, are known as piezoelectric extension actuators. Piezoelectric extension actuators are usually placed at the extreme thickness positions of a plate-like structure to achieve the most effective actuation. This subjects the M *Author to whom correspondence should be addressed. E-mail: firstname.lastname@example.com JOURNAL OF INTELLIGENT actuators to high longitudinal stresses and may lead to failure, especially when the actuators are made of brittle piezoceramics. Furthermore, surface-bonded actuators are likely to be damaged by contact with surrounding objects. To alleviate these problems, Sun and Zhang (1995) proposed an adaptive sandwich structure consisting of axially poled piezoelectric actuators. The application of an electric field E3 in the thickness direction of a piezoelectric actuator that is poled in the x1-direction, will induce transverse shear strain 13 ¼ d35 E3 , as shown in Figure 1(a). Here d35 is the piezoelectric shear strain coefficient. The axially poled piezoelectric shear actuator, when sandwiched between two elastic facing sheets, will cause transverse deflection of the sandwich structure as depicted in Figure 1(b). Since the shear actuators are placed at the midsurface of the beam, they are subjected to smaller longitudinal stresses than extension actuators. It is noted that for most piezoceramic materials, the piezoelectric shear coefficient d35 , is larger than the other piezoelectric coefficients (Glazounov and Zhang, 1998). For example, typical values of the PZT-5A coefficients, d35 , d13 , and d33 (see Equation (2)) are 584 Â 10À12 , À171 Â 10À12 , and 374 Â 10À12 m/V, respectively (Berlincourt and Krueger, nd). MATERIAL SYSTEMS AND STRUCTURES, Vol. 16—June 2005 1045-389X/05/06 0517–14 $10.00/0 DOI: 10.1177/1045389X05053154 ß 2005 Sage Publications 517 518 B. P. BAILLARGEON E P x3 (a) x1 x3 (b) Foam E PZT Facing Foam Facing x1 Figure 1. (a) Piezoelectric shear actuator and (b) an adaptive sandwich beam containing a piezoelectric shear actuator and foam core. Zhang and Sun (1996) developed a beam theory for a sandwich beam containing shear actuators by modeling the facing sheets as classical Euler–Bernoulli beams and the central core as a Timoshenko beam, which allows transverse shear deformation. Benjeddou et al. (1999) developed a unified finite element (FE) model for extension and shear actuation mechanisms with a detailed formulation of the electric problem. Zhang and Sun (1999) derived an analytical solution for a sandwich plate with a piezoelectric core using the principle of stationary potential energy and the Raleigh–Ritz method. Trindade et al. (2000) performed a parametric study on the active control of a sandwich beam with both shear and extension actuators, using a linear quadratic regulator based on optimal control with state feedback. Vel and Batra (2001a,b) formulated exact three-dimensional solutions for the static electromechanical analysis of sandwich plates with embedded piezoelectric shear actuators. Benjeddou and Deu¨ (2001a,b) derived an exact solution of transverse shear actuation and sensing of simply supported piezoelectric plates using a mixed state-space formulation. A closedform solution of free vibration analysis of simply supported piezoelectric sandwich plates was recently derived by Benjeddou and Deu¨ (2002) using a twodimensional plate theory. Vibration suppression analysis of an adaptive structure with both extension and shear actuators was performed by Raja et al. (2002) using a piezoelectric FE solution. A solution to the deflection of beams containing piezoelectric shear actuators was derived by Aldraihem and Khdeir (2003) using first-order and higher-order beam theories. Recently, Baillargeon and Vel (2004), and Vel and Baillargeon (2004), have presented exact solutions for the free vibration, forced vibration, and active vibration suppression of simply supported adaptive composite plates and cylindrical shells with embedded piezoelectric shear actuators and sensors. AND S. S. VEL Although several different investigations have demonstrated the effectiveness of piezoelectric shear actuators for active vibration suppression in smart structures, the results are based on analytical and/or computational simulations. There has been little experimental work to investigate the effectiveness of the piezoelectric shear mechanism for active vibration suppression. Therefore, it is the goal of the present work to experimentally demonstrate that piezoelectric shear actuators can be utilized for active damping of adaptive structures. An adaptive cantilever sandwich beam consisting of aluminum facings and a core consisting of two shear actuators and foam is fabricated and tested. The analytical procedure presented by Baillargeon and Vel (2005) is not applicable to cantilever beams due to edge effects at the clamped and free edges and the threedimensional stress state near the embedded shear actuators. Therefore, we analyze the vibration suppression of a sandwich cantilever beam using a FE model and compare the numerical results with experiments. Active vibration suppression is implemented using positive position feedback (PPF) (Goh and Caughey, 1985; Fanson and Caughey, 1990; Dosch et al., 1992; Meyer et al., 1998) and strain rate feedback (SRF) (Newman, 1992). In the first part of the study, the frequency response function of the sandwich beam is obtained by using one of the shear actuators to excite the beam and the other shear actuator to suppress the vibrations. The experimentally obtained frequency response function compares well with the numerical results. An experimental parametric study of the PPF controller parameters on the damping of the fundamental and second mode of vibration is performed. It is shown that the simultaneous control of the first two modes of vibration is possible using a single piezoelectric shear actuator. In the second part of the study, the transient response of the adaptive beam is analyzed by subjecting it to a harmonic tip force excitation using a proof-mass actuator. Both piezoelectric shear actuators are used for active vibration suppression. The experiments demonstrate the effectiveness of shear actuators for active vibration suppression. ADAPTIVE SANDWICH BEAM Constitutive Equations We use a rectangular Cartesian coordinate system, shown in Figure 1(b), to describe the infinitesimal deformations of an adaptive sandwich beam. The equations of motion for the piezoelectric material, in the absence of body forces and free charges, are ij, j ¼ u€ i , Dj, j ¼ 0 ði, j ¼ 1, 2, 3Þ, ð1Þ Active Vibration Suppression of Sandwich Beams using Actuators where ij , ui, and Dj are the components of the Cauchy stress tensor, displacement vector, and electric displacement vector, respectively, and is the mass density. A comma followed by index j indicates partial differentiation with respect to the position xj of a material particle, a repeated index implies summation over the range of the index and a superimposed dot indicates differentiation with respect to time t. The constitutive equation for a piezoelectric material poled in the x1-direction, in contracted notation, is 9 2 9 8 38 S11 S12 S13 0 "11 > 0 0 > 11 > > > > > > > 6 > > > > > > > > "22 > 0 0 7 22 > > > > > 7> 6 S12 S22 S23 0 > > > > > > > > 7 6 < " = 6S < 0 0 0 7 33 = 33 13 S23 S33 7 6 ¼6 > 0 0 S44 0 2"23 > 0 7 > > > > 23 > 7> 6 0 > > > > 6 > > > 7> > > > > > > > 5 4 0 0 0 0 S 2" 0 > > > 13 > 55 13 > > > > > ; ; : : 0 0 0 0 0 S66 2"12 12 3 2 d11 0 0 6 d12 0 0 7 78 9 6 7> E1 > 6 6 d13 0 0 7< = 7 E2 , 6 þ6 0 0 7 ; : > 7> 6 0 7 E3 6 5 4 0 0 d35 0 d26 0 9 2 8 3 d11 d12 d13 0 0 0 > = < D1 > 6 7 0 0 0 0 d26 5 D2 ¼ 4 0 > > ; : D3 0 0 0 0 d35 0 9 8 11 > > > > > > > > > 2 38 9 22 > > > > > 11 0 0 > > = < > = < E1 > 33 6 7 þ 4 0 22 0 5 E2 , ð2Þ Â > > 23 > > > ; : > > > 0 0 33 E3 > > > > > 13 > > > > > ; : 12 where "ij are the components of the infinitesimal strain tensor, Ej are the components of the electric field vector, Sij are the elastic compliances, dij are the piezoelectric strain coefficients, and ij are the components of the electric permittivity tensor. The infinitesimal strain tensor and the electric field vector are related to the mechanical displacements uj and the electric potential by 1 "ij ¼ ðui, j þ uj, i Þ, 2 Ej ¼ À, j : ð3Þ Experimental Setup A sandwich cantilever beam consisting of aluminum facings and a core consisting of two piezoceramic shear actuators and foam is fabricated for the experimental studies. The configuration of the sandwich beam used in this study is depicted in Figure 2(a). The facings of 519 the sandwich beam are made of 6061-T6 aluminum. The core consists of two axially poled PZT-5A shear actuators (Morgan Electro Ceramics) and lightweight foam (Baltek Airex R82.80). The components of the beam were firmly bonded together using an adhesive film, placed in a vacuum bag and cured in an autoclave. The beam is 0.305 m (12 in.) in length and 0.0142 m (0.558 in.) in total thickness. The beam is clamped using a thick steel plate bolted to a heavy block of steel. This required the beam to be constructed 0.153 m (6 in.) longer than the cantilever section with a polycarbonate core to withstand the large clamping force of the bolts. The Young's modulus, Poisson's ratio, and density of the aluminum facings are E ¼ 69 GPa, ¼ 0.33, and ¼ 2730 kg/m3 , respectively. The Young's modulus, shear modulus, and density of the Baltek Airex R82.80 foam core are E ¼ 62 MPa, G ¼ 23 MPa, and ¼ 80 kg/m3 , respectively. The PZT-5A is transversely isotropic with its principal material direction oriented along the longitudinal axis of the beam. The electric field is applied through the thickness of the piezoceramic actuators via electrodes at the interface between the actuator and aluminum facings. Due to the lack of published data for PZT-5A poled in the x1-direction (Figure 1(a)), the relevant material properties were inferred through tensor transformations of the fourthorder elastic tensor, third-order piezoelectric tensor, and second-order dielectric permittivity tensor of PZT-5A poled in the x3-direction (Berlincourt and Krueger, nd). The material properties thus obtained are listed in Table 1. The experimental setup of the cantilever beam is depicted in Figure 2(b). The two PZT-5A shear actuators are labeled as P1 and P2 . In the first part of the study, the excitation actuator that is closest to the clamped end, denoted by P1 , is used as a disturbance actuator to excite the beam. Actuator P2 is the control actuator that is used for vibration suppression. Two sensors are attached to the cantilever beam experimental setup, shown in Figure 2(b). A dynamic strain sensor (PCB model 740802) near the clamped edge is used to measure the deformation for the purpose of feedback control, and an accelerometer (PCB model 352A24) at the tip of the beam is used to quantify the effectiveness of the vibration suppression system. The outputs from both sensors are passed through a signal conditioner (PCB model 482A20) before acquisition of the respective signals, as shown in Figure 3. The signal from the accelerometer is acquired through SigLab (model 20-22), which is a dynamic signal and system analyzer that is accessed through a Matlab graphical user interface. The frequency response function of the system is determined using a chirp excitation to shear actuator P1 . The strain at the root of the sandwich beam forces the PPF compensator, and the compensator coordinate , amplified by a gain, is applied to shear actuator P2 for 520 B. P. BAILLARGEON AND S. S. VEL Figure 2. (a, b) Experimental configuration of the adaptive sandwich beam containing two piezoelectric shear actuators and (c) proof-mass actuator constructed using a piezoelectric stack and steel mass. vibration control. Real-time active vibration suppression is implemented using a dSPACE digital control system that consists of a DS1104 controller installed on a PC. The block diagram of the control system, built in Simulink, is converted to C-code using Real-Time workshop, which is then compiled and implemented on the dSPACE hardware to achieve real-time simulation and control. PZT-5A actuators require an electric field intensity of 100–500 V/mm to obtain significant actuation. Since the piezoelectric shear actuators utilized in this study are 4.65 mm thick, it is necessary to use a high-voltage power amplifier to produce large voltages. In this study, a dual channel Trek Piezo Driver (model PZD700) voltage amplifier is used with a gain of 68 V/V for each channel. The input signal to the amplifier from the control system has a magnitude less than Æ10 V, resulting in a maximum voltage of Æ680 V to the piezoelectric actuators. In the second part of the study, a low-voltage piezoelectric stack (Piezo Systems Inc., model TS18H5-202, mass 0.015 kg) and a steel block (mass 0.126 kg) are bonded to the tip of the cantilever beam, as depicted in Figure 2(c), to form a proof-mass actuator that provides a repeatable harmonic disturbance to 521 Active Vibration Suppression of Sandwich Beams using Actuators Table 1. Non-vanishing material properties of PZT-5A shear actuators poled in the x1 direction. Material property S11 S22 S33 S12 S13 S23 S44 S55 S66 À1 ðTPa Þ ðTPaÀ1 Þ ðTPaÀ1 Þ ðTPaÀ1 Þ ðTPaÀ1 Þ ðTPaÀ1 Þ ðTPaÀ1 Þ ðTPaÀ1 Þ ðTPaÀ1 Þ Value Material property Value 18.8 16.4 16.4 À7.22 À7.22 À5.74 44.3 47.5 47.5 À12 374 À171 À171 584 584 150.45 153.1 153.1 7750 À1 d11 ð10 mV Þ d12 ð10À12 mVÀ1 Þ d13 ð10À12 mVÀ1 Þ d26 ð10À12 mVÀ1 Þ d35 ð10À12 mVÀ1 Þ 11 ð10À10 F/mÞ 22 ð10À10 F/mÞ 33 ð10À10 F/mÞ (kg/m3 ) actuator dynamics. Friswell and Inman (1999) have shown that a PPF controller may be formulated as an output feedback controller. The PPF controller consists of a second-order compensator, which is forced by the displacement response of the structure. The output of the compensator, magnified by a gain, is fed back to the structure. The equations that describe the operation of the PPF compensator are € þ 2&n !n _ þ !2n ¼ Gp !2c , where is the modal coordinate that describes the deformation of the structure, !n is the natural frequency of the structure, & n is the damping ratio of the structure, is the compensator coordinate, !c is the compensator frequency, & c is the compensator damping coefficient, and Gp is the feedback gain coefficient. For steady-state vibration, the modal coordinate and controller coordinate are harmonic the beam. The application of a harmonic voltage to the piezoelectric stack induces a harmonic strain in the thickness direction of the stack, resulting in a harmonic force at the tip of the beam due to inertia of the steel block. The embedded piezoelectric shear actuators P1 and P2 are used to suppress the vibration caused by the proof-mass actuator. ¼ 0 ei!t , Two vibration suppression methods, namely PPF and SRF are implemented to control the vibrations of the beam. Positive position feedback (PPF) was introduced by Goh and Caughey (1985). The PPF controller is not sensitive to spillover and it is not destabilized by finite Excitation signal P1 ð5Þ The controller coordinate , magnified by a positive gain, is then fed back as a voltage input ¼ 0 ei!t to a piezoelectric shear actuator, where Gp !4c 0 ¼ ð7Þ 0 : ð!2c À !2 Þ þ 2i&c !c ! Positive Position Feedback Control Strain sensor ¼ 0 ei!t , and the amplitude of the controller coordinate obtained from Equation (4)2 is !2c ð6Þ 0 ¼ 0 : ð!2c À !2 Þ þ 2i&c !c ! Control Design Power amplifier ð4Þ € þ 2&c !c _ þ !2c ¼ !2c , SigLab function generator Signal conditioner PZT shear actuators Accelerometer SigLab data acquisition system P2 Power amplifier Signal conditioner Integrator ADC ξ ω c2 + .. η __ 1/s Integrator . η 1/s 2ζcω c Figure 3. Implementation of active vibration suppression of adaptive sandwich beam using a PPF compensator. ωc2 PPF compensator η Gpωc2 DAC 522 B. P. BAILLARGEON The SRF controller (Newman, 1992) is a secondorder compensator that is forced by the velocity response of the structure. The negative of the output of the compensator, magnified by a gain, is fed back to the structure. The equations that describe the operation of the SRF compensator are € þ 2&c !c _ þ !2c ¼ !2c _, S. S. VEL tions. This resulted in an increase in the number of elements used in the FE model. Strain Rate Feedback Control € þ 2&n !n _ þ !2n ¼ ÀGs !2c , AND ð8Þ where Gs is the SRF feedback gain coefficient. For steady-state vibration, the amplitude of the controller coordinate 0 is obtained by substitution of Equation (5) into Equation (8)2 : i!!2c ð9Þ 0 ¼ 0 : ð!2c À !2 Þ þ 2i&c !c ! The negative of the controller coordinate, magnified by a gain, is then fed back as a voltage input ¼ 0 ei!t to a piezoelectric shear actuator, where ÀGs i!!4c ð10Þ 0 ¼ 0 : ð!2c À !2 Þ þ 2i&c !c ! FINITE ELEMENT MODEL OF ADAPTIVE BEAM The numerical model used in this study utilizes the commercial FE analysis package ABAQUS/Standard 6.3-1 (Hibbitt, Karlsson & Sorensen, Inc., 2002) to analyze the active feedback control of a cantilever beam. A two-dimensional plane stress analysis of the adaptive beam is performed using CPS8R and CPS8RE eightnode biquadratic plane stress elements for the elastic and piezoelectric materials, respectively. Three separate analyses were performed using ABAQUS. The natural frequencies and mode shapes are computed using the FREQUENCY subroutine and the Lanczos method. The frequency response function of the system, without and with active control, is computed using the DIRECT, STEADY STATE subroutine. Finally, the transient response of the system, without and with PPF control, is determined with the IMPLICIT, DYNAMIC subroutine. A mesh convergence study is performed to ensure that the FE model produces solutions that have converged to an acceptable limit. The fourth natural frequency of the system without the proof-mass actuator is used as the convergence criterion. Based on the convergence study, 2754 elements and 8893 nodes are used to model the hybrid cantilever beam. It is noted that the portion of the beam clamped between the steel blocks was also incorporated in the FE model in order to accurately simulate the clamped boundary condi- Frequency Response with Active Damping In the first part of the study, a disturbance potential is applied to shear actuator P1 and the resulting vibration of the beam is controlled using shear actuator P2. The FE frequency response function of the system is obtained by computing the steady-state response of the beam to a harmonic potential applied to the disturbance actuator P1 at discrete frequencies and the ratio of the magnitude of tip acceleration of the beam to the applied disturbance voltage is plotted as a function of the forcing frequency. When performing a closed-loop steady-state analysis using ABAQUS, the control voltage to the actuator P2 is not known a priori since this would depend on the strain at the root of the beam. Computing the frequency response curve of the cantilever beam with feedback control required the development of a custom FORTRAN program that is executed in tandem with the steady-state analysis subroutine in ABAQUS. The frequency and the applied potential to the disturbance actuator P1 are fixed and the program arbitrarily assigns a complex actuation potential V to the control actuator P2 . A steady-state FE solution is computed using this assumed electric potential to the control actuator. The strain near the root of the beam (Figure 2(b)) is determined from the FE solution and the corresponding steady-state feedback control voltage Vc is computed based on either a PPF or SRF control law. The computed value of control potential Vc is compared with the assumed potential V. The procedure is iterated until the difference between the assumed potential V and calculated control potential Vc is zero. This is accomplished by defining a complex function f(V ) ¼ Vc À V, which calculates the difference between the computed and assumed control voltages. The complex zero of the analytic function f(V ) is obtained using Muller's method (Press et al., 1992), which is a generalization of the secant method of root finding using quadratic threepoint interpolation. The root V to the equation f ðVÞ ¼ 0 obtained using the Muller's method is the voltage to the control actuator P2 that satisfies the feedback control law, the equations of motion, and the charge equation. The process is repeated for several discrete frequency values to create a frequency response curve. Transient Analysis with Active Damping In the second part of the study, a transient numerical simulation is performed using the FE method by utilizing an implicit dynamic analysis subroutine and the Newmark- numerical integration scheme in ABAQUS. This analysis is useful for determining the 523 Active Vibration Suppression of Sandwich Beams using Actuators efficacy of the PPF controller in the time domain. The proof-mass actuator is used to induce an excitation at the tip of the cantilever beam and the piezoelectric shear actuators P1 and P2 are used for active vibration suppression. The second-order PPF compensator is modeled directly as second-order spring–mass–damper system in the ABAQUS. The spring stiffness, mass, and damping ratio are determined from chosen values of PPF controller frequency !c and damping coefficient & c. The value of the feedback gain coefficient Gp is set equal to that used in the experimental investigation. At every time step, the strain near the root of the beam is found and multiplied by the square of the compensator frequency and applied as a force to the spring–mass– damper system, and the displacement of the mass, which is the compensator coordinate, is multiplied by the square of the compensator frequency and the PPF gain coefficient and applied as feedback voltage to the control actuator(s). Since the value of the control voltage at the next time increment is determined from the present state of deformation, the algorithm is inherently explicit. A Raleigh structural damping model is incorporated in the FE analysis in order to obtain a realistic transient response for the cantilever beam. In the Raleigh damping model, it is assumed that the damping coefficient depends on the frequency through only two constants that are usually chosen by matching the damping coefficient to the experimental values at two of the system's natural frequencies. For a Raleigh damping model, the damping ratio is related to structural frequency in the following manner: &i ¼ !i þ 2!i 2 ð11Þ where & i and !i are the damping ratio and frequency of the ith mode, respectively, is the mass proportional damping constant, and is the stiffness proportional damping constant. Since we are primarily interested in the damping of the fundamental mode in our transient FE analyses, we have chosen the constants and to match the experimental damping coefficient corresponding to the fundamental frequency !1. It is noted that the choice of constants and to yield a specified value of & 1 is not unique. In the present work, we have arbitrarily chosen to use proportional damping by assuming ¼ 0: With this assumption, the damping parameter is determined from the experimentally measured damping ratio and frequency of the fundamental mode of vibration. The experimentally measured value of the damping ratio computed using the logarithmic decrement (Rao, 1995) is &1 ¼ 0:00584. The piezoceramic stack is modeled as a monolithic piezoelectric material. Due to the lack of reliable properties of the piezoelectric stack from the manufac- turer, the equivalent piezoelectric strain coefficient of the stack was obtained by comparing experimental results with numerical simulations. This resulted in an equivalent piezoelectric strain coefficient of d33 ¼ 7:955 Â 10À8 m/V for the stack. RESULTS AND DISCUSSION In this section, the first four natural frequencies of the beam are determined using the experimental setup and the numerical model. The corresponding FE mode shapes are also presented. Experimental and FE frequency response functions for the system are compared next, followed by an experimental parametric study to determine the effect of PPF controller parameters on system damping. The active vibration suppression of the cantilever beam using SRF control is also examined through experiments and numerical simulations. Last, the transient response of the adaptive sandwich beam is investigated. Natural Frequencies and Mode Shapes of Cantilever Beam The first four experimental and FE natural frequencies of the cantilever sandwich beam without active control are presented in Table 2. The percentage of difference between the two values, with respect to the FE result, is listed in the third column. It is clear that the FE model accurately predicts the natural frequencies of the cantilever beam. The largest error of 2.99% occurs in the fundamental frequency. There is excellent agreement between the experimental and FE values for the second natural frequency with a difference of just 0.12%. The FE mode shapes corresponding to the first four natural frequencies listed in Table 2 are shown in Figure 4. The fundamental mode shape of the adaptive beam is similar to that of a sandwich cantilever beam with a homogeneous core. The mode shapes corresponding to the higher modes of vibration deviate from what would be expected for a sandwich cantilever beam because the piezoceramic actuators have higher stiffness than the foam core. Table 2. Comparison of the first four experimental and numerical natural frequencies. Mode Experimental natural frequency (Hz) Finite element natural frequency (Hz) Difference (%) 1 2 3 4 !1 !2 !3 !4 ¼ 123:06 ¼ 495:71 ¼ 1098:28 ¼ 1538:20 126.85 495.12 1094.6 1558.3 2.99 0.12 0.334 1.29 524 B. P. BAILLARGEON AND S. S. VEL Mode 1 Mode 2 Mode 3 Mode 4 Figure 4. The first four mode shapes of the adaptive sandwich beam using the finite element method. Frequency Response using PPF Control The effect of using PPF control to actively suppress the vibration of a cantilever beam is first examined in the frequency domain. A parametric study is performed to quantify the effect of PPF controller parameters in reducing the resonant peaks of the fundamental mode. The PZT-5A shear actuator P1 acts as the disturbance source, and shear actuator P2 is used for active vibration suppression. As before, the ratio of the tip acceleration to the disturbance potential is plotted as a function of the disturbance frequency. The strain, which is measured by the dynamic strain sensor, is chosen as the measure of the structural position for the PPF compensator. The base PPF compensator utilized in the parametric study has a compensator frequency that is 1.3 times the fundamental frequency (!c ¼ 1:3!1 ¼ 159:98 Hz), a compensator damping coefficient equal to &c ¼ 0:05 and a 40 20 20 log10[a / φ], (dB) The frequency response function of the cantilever beam without active control is compared with experimental results by applying a harmonic potential of constant amplitude to the piezoelectric actuator P1 . The ratio of the steady-state tip acceleration (in m/s2 ) to the excitation voltage (in Volts) applied to P1 is plotted as a function of the forcing frequency in Figure 5. There is good agreement between the experimental and FE results. The FE model predicts the resonance frequencies very well. The amplitude of the resonance peaks of the FE solution are larger than the experimental results since the FE model does not include structural damping. The FE solution yields peaks that tend toward infinity at resonance. At other frequencies, the experimental curves lie below the FE curves. This could be attributed to a number of factors, such as (a) the piezoelectric coefficient d35 may be smaller than the manufacturer's data due to imperfect poling and (b) the plane stress assumption in the numerical model may not be completely correct. 0 −20 −40 Experimental −60 Finite element −80 200 400 600 800 1000 1200 1400 1600 Frequency (Hz) Figure 5. Comparison of the experimental and finite element frequency response functions without feedback control. Here a is the tip acceleration in m/s and is excitation potential in V. feedback gain coefficient Gp ¼ 17 Â 10À6 V s2 . First, the effect of the controller frequency parameter on system damping is investigated while keeping the compensator damping and feedback gain constant. The experimentally measured frequency response functions are shown in Figure 6(a) for the four different controller frequencies of !1 , 1:1!1 , 1:3!1 , and 1:45!1 : The compensator frequencies of 1:1!1 and 1:3!1 produce peak responses of À25:89 and À25:39 dB, respectively, which is a significant reduction from the peak response of À13:23 dB in the absence of active feedback control. The PPF compensator shifts the peak response frequencies from 123.06 to 115.9 Hz when !c ¼ 1:3!1 . This represents a significant shift in system resonance frequency as a result of the compensator. The controller is not very effective when the compensator frequency is equal to the fundamental frequency since the peak response is À18:26 dB. Figure 6(b) depicts the frequency response functions for four different 525 Active Vibration Suppression of Sandwich Beams using Actuators -20 (117.13,-22.65) (115.94,-25.39) (128.50,-25.89) -40 Without control ωc = ω1 ωc = 1.1 ω1 ωc = 1.3 ω1 ωc = 1.45 ω1 -50 -70 80 100 120 140 160 Frequency (Hz) 180 -30 Without control ζc = 0.05 ζc = 0.15 ζc = 0.35 ζc = 0.50 -50 -60 200 -70 80 100 120 140 160 Frequency (Hz) b) 20 log10[a / φ], (dB) -20 (118.94,-23.13) (115.94,-25.39) 200 (123.06,-13.23) (121.19,-19.91) -30 -40 Without control Gp= 3.4×10-6 V s2 Gp = 8.5×10-6 V s2 Gp = 17.0×10-6 V s2 Gp = 34.0×10-6 V s2 -50 -70 c) 180 (111.19,-27.59) -60 controller damping coefficients &c ¼ 0:05, 0:15, 0.35, and 0.5. The optimum compensator damping parameter is 0.15, resulting in a peak response of À29:14 dB. The frequency response curves corresponding to feedback gains Gp ¼ 3:4 Â 10À6 , 8:5 Â 10À6 , 17 Â 10À6 , and 34 Â 10À6 V s2 are shown in Figure 6(c). The peak acceleration decreases as the feedback gain is increased. The peak response reduces from À13:2335 dB without feedback control to À27:5910 dB for Gp ¼ 34 Â 10À6 V s2 . The experimental and FE frequency response curves for !c ¼ 1:1!1 , &c ¼ 0:05, and Gp ¼ 17 Â 10À6 V s2 are compared in Figure 7. The closed-loop resonant frequency from the numerical simulation is smaller than the experimentally obtained value. It is noted that the beam does not possess any damping in the FE model in the absence of feedback control; therefore, the finite peak in the frequency response is due to the PPF compensator. The frequency response function exhibits a sharp decrease (122.63,-27.11) (118.00,-29.14) -40 -10 Figure 6. An experimental parametric study using a PPF controller to actively suppress the fundamental mode of vibration of the beam: (a) &c ¼ 0.05, Gp ¼ 17 Â 10À6 V s2; (b) !c ¼ 1.3!1, Gp ¼ 17 Â 10À6 V s2; and (c) !c ¼ 1.3!1, & c ¼ 0.05. Here a is the tip acceleration in m/s and is excitation potential in V. (123.06,-13.23) (122.81,-25.02) -20 (115.94,-25.39) (125.56,-18.26) -30 -60 a) -10 (123.06,-13.23) 20 log10[a / φ], (dB) 20 log10[a / φ], (dB) -10 80 100 120 140 160 Frequency (Hz) 180 200 in tip acceleration when the forcing frequency nears the target frequency. This shows that the control scheme works well since the control effort is concentrated to reduce the response at that frequency. However, the experiment did not exhibit this trend. The effectiveness of the PPF compensator in suppressing the second mode of vibration is also examined experimentally. Figure 8 contains the results of a parametric study of the effect of PPF compensator parameters on the frequency response functions with Gp ¼ 15:3 Â 10À6 V s2 . The results of the parametric study for different compensator frequencies are given in Figure 8(a). The peak response reduces from À3:6854 to À11:9618 dB when the compensator frequency !c ¼ 1:3!2 . The reduction in peak response is smaller for other choices of compensator frequencies. The compensator damping coefficient &c ¼ 0:30 produces the greatest reduction in peak response, as shown in Figure 8(b). 526 B. P. BAILLARGEON 20 log10[a/φ], (dB) −20 −30 −40 −50 −60 100 120 140 160 180 200 Frequency (Hz) Figure 7. Comparison of experimental and finite element frequency response functions using PPF control with ! ¼ 1:1!1 , &c ¼ 0:05, and Gp ¼ 17 Â 10À6 V s2 : Here a is the tip acceleration in m/s and is excitation potential in V. 0 (495.71,-3.69) -5 20 log10[a / φ], (dB) (503.94,-8.72) -10 (488.88,-10.59) -15 -20 Without control ωc = ω2 ωc = 1.1 ω2 ωc = 1.3 ω2 ωc = 1.45 ω2 -25 -30 400 a) (503.31,-11.75) (493.94,-11.96) 450 500 550 600 Frequency (Hz) In this section, a single shear actuator is used to suppress the first two modes of vibration simultaneously. This is accomplished by using two parallel PPF compensators. The sum of the outputs of two PPF compensators, with parameters equal to the values that exhibited the most reduction in peak response for each individual mode in the previous two parametric studies, is amplified and applied to the shear actuator P2 . The PPF compensator used to target the fundamental mode has a compensator frequency !c ¼ 1:1!1 , damping coefficient &c ¼ 0:15, and feedback gain coefficient Gp ¼ 17 Â 10À6 V s2 . The PPF compensator to control the second natural frequency has a compensator frequency !c ¼ 1:3!2 , damping coefficient &c ¼ 0:3, and a feedback gain coefficient Gp ¼ 15:3 Â 10À6 V s2 . The results are shown in Figure 9. There is good agreement between the FE and experimental values near the first natural frequency. The experimental response at the fundamental frequency is À28.1911 dB at a forcing frequency of 113.125 Hz, which is only slightly more than that when a single controller is used to target the fundamental mode. The experimental and FE frequency response functions near the second natural frequency do not compare as well as that at the fundamental frequency. The FE model produces a larger acceleration than the corresponding experimental values except at the target frequency, where there is a sharp decrease in the numerically obtained acceleration. It is observed that the experimental peak response of À16:4071 dB is smaller than the À11:96 dB peak response when the second mode is targeted by a single PPF compensator (Figure 8). 0 0 (495.71,-3.69) (499.13,-10,10) −10 (498.38,-10.92) -10 (493.94,-11.96) -15 -20 Without control ζc = 0.05 ζc = 0.30 -25 b) −20 −30 −40 ζc = 0.40 −50 ζc = 0.5 -30 400 Experimental Finite element (481.56,-7.80) 20 log10[a / φ], (dB) 20 log10[a / φ], (dB) -5 S. S. VEL Simultaneous Control of the First Two Modes using PPF Control Experimental Finite element 80 AND 450 500 550 600 Frequency (Hz) Figure 8. An experimental parametric study using a PPF controller to actively suppress the second mode of vibration of the beam (a – tip acceleration; – excitation potential): (a) &c ¼ 0.3, Gp ¼ 15.3 Â 10À6 V s2 and (b) !c ¼ 1.3!2, Gp ¼ 15.3 Â 10À6 V s2. Here a is the tip acceleration in m/s and is excitation potential in V. −60 100 200 300 400 500 600 Frequency (Hz) Figure 9. Comparison of experimental and finite element results for the simultaneous control of the first two modes of vibration using actuator P2 and PPF control. Here a is the tip acceleration in m/s and is excitation potential in V. Active Vibration Suppression of Sandwich Beams using Actuators 527 Frequency Response using SRF Control Transient Response using PPF Control This portion of the study focuses on active feedback control using SRF control and to analyze the efficacy of a SRF controller for active vibration suppression. As before, a harmonic disturbance is applied using shear actuator P1, and active vibration suppression is achieved using actuator P2. The results of the parametric study, given in Figure 10 clearly demonstrates that, like PPF control, SRF control can also be used for active vibration suppression using shear actuators. However, unlike the PPF compensator, the resonant frequency does not change much when an SRF compensator is employed. In addition, the peak system response decreases as the compensator damping coefficient is decreased. This trend is different from that for a PPF controller, where the best choice of controller damping parameter was about 0.15. The active feedback control of the cantilever beam in the time domain is the subject of this part of the study. The proof-mass actuator, consisting of a low-voltage piezoelectric stack and steel mass, is attached to the tip of the adaptive sandwich beam to provide repeatable tip excitation, and the two shear actuators are used for active vibration suppression. The addition of the proof-mass actuator causes the experimental fundamental frequency to drop to !1 ¼ 75:66 Hz. The beam is harmonically excited at the fundamental frequency using the proof-mass actuator and allowed to reach a steady state of vibration. At time t ¼ 1 s, PPF control using shear actuator P1 is activated to suppress the vibration. At time t ¼ 2 s, shear actuator P2 is also activated to provide additional vibration suppression. The PPF compensators utilized for this portion of the study have a compensator frequency !c ¼ 1:3!1 and compensator damping coefficient of 0.3. The feedback gain coefficients for both shear actuators P1 and P2 are Gp ¼ 17 Â 10À5 V s2 . The experimental real-time transient response is shown in Figure 11. When only actuator P1 is employed, the tip acceleration reduces from %1:2101 g to 0:2870 g. The tip acceleration reduces even further to 0:0373 g when both P1 and P2 are utilized for vibration suppression. This represents a reduction in amplitude of 30.2 dB or 96:9%. Next, the beam is harmonically excited at the fundamental frequency using the proof-mass actuator until it reaches steady-state. The excitation is stopped at t ¼ 1 s and the vibration is allowed to decay without feedback control. The experiment is repeated again except that this time the PPF controller is activated using both shear actuators as soon as the excitation is stopped. The excitation is precisely controlled in both experiments using Simulink and dSPACE. The same PPF compensator parameters used earlier for the transient experiment are used for this portion of the study. The results are shown in Figure 12. It is found that the settling time, defined as the time required for the tip acceleration to settle to within 2% of the initial steady-state value, in the absence of active control is 1.08 s. The settling time of the adaptive beam with active vibration suppression is 0.23 s, which represents a 78:7% reduction. Lastly, the experimental results are compared with transient numerical simulations. The beam is excited from rest by applying a harmonic potential at the fundamental frequency by the piezoelectric stack for 0.1 s, after which the excitation is switched off and the amplitude of vibration decays either due to natural damping or due to active vibration suppression using PPF control. Raleigh damping is included in the FE model. The transient numerical simulations are depicted −10 20 log10[a /φ], (dB) −20 (123.06,-13.23) w/o control (123.50,-22.42), ω c = 1.3ω1 (123.06,-14.52), ωc = ω1 (123.44,-22.53), ω c = 1.45ω1 (124.19,-24.14), ωc = 1.1ω1 −30 −40 Without control ωc = ω 1 ωc = 1.1ω1 ωc = 1.3ω 1 ω c = 1.45ω 1 −50 −60 −70 (a) 100 120 140 160 180 200 Frequency (Hz) −10 20 log10[a /φ], (dB) 80 (123.06,-13.23),w/o control (123.69,-18.23), ζc = 0.35 (123.69,-16.91), ζ c = 0.50 −20 (123.50,-22.42), ζ c = 0.05 (123.81,-21.28), ζ c = 0.15 −30 −40 Without control ζ c = 0.05 ζ c = 0.15 ζ c = 0.35 ζ c = 0.50 −50 −60 −70 (b) 80 100 120 140 160 180 200 Frequency (Hz) Figure 10. An experimental parametric study using a SRF controller to actively suppress the fundamental mode of vibration of the beam (a – tip acceleration; – excitation potential): (a) &c ¼ 0.05, Gs ¼ 17 Â 10À9 V s3 and (b) !c ¼ 1.3!1, Gs ¼ 17 Â 10À9 V s3 . 528 B. P. BAILLARGEON AND S. S. VEL 2 1.21 g Tip acceleration (g) 1 0.287 g 0.037 g 0 -1 -2 Disturbance - on Disturbance - on Disturbance - on P1 Active P1 Active P1 Inactive P2 Inactive P2 Active P2 Inactive 0 0.5 1 1.5 2 2.5 3 Time (s) Figure 11. The real-time response of the adaptive sandwich beam excited by the proof-mass actuator at the fundamental frequency before and after the PPF controller was initiated. 2 1.5 Without active control Tip acceleration (g) 1 0.5 0 -0.5 PPF control -1 -1.5 -2 Disturbance - off Disturbance - on 0 0.5 1 1.5 Time (s) in Figure 13(a). The PPF controller utilizes both shear actuators and utilizes the same compensator parameters as for the previous studies in this section. The corresponding experimental results are shown in Figure 13(b). The transient numerical simulations compare very well with the experimental results. The settling time decreases from %1.0 to 0.267 s in the numerical simulations when the PPF controller is used. This constitutes a reduction of 73:3% in settling time. In comparison, the experimental settling time decreases from %0.90 to 0.272 s, resulting in a 69:8% reduction. 2 2.5 Figure 12. Experimental comparison of settling time of the adaptive beam before and after the PPF feedback controller was initiated. CONCLUSIONS We have experimentally investigated the active vibration suppression of sandwich beams using piezoelectric shear actuators and compared the results with FE simulations. A sandwich beam consisting of aluminum facings and two piezoelectric shear actuators and foam core was fabricated for the experiments. Active vibration suppression is achieved using either PPF control or SRF control. The control algorithm was implemented in real-time using Matlab/Simulink and a dSPACE digital controller. Active Vibration Suppression of Sandwich Beams using Actuators 0.5 ACKNOWLEDGMENTS Disturbance - off Without active control The authors gratefully acknowledge the support of the Maine Space Grant Consortium under collaborative seed grant No. EP-03-12. 0.25 Tip acceleration (g) 529 0 REFERENCES PPF control -0.25 Disturbance - on -0.5 (a) 0 0.2 0.4 0.6 0.8 1 Time (s) 0.5 Tip acceleration (g) Disturbance - off Without active control 0.25 0 PPF control -0.25 Disturbance - on -0.5 (b) 0 0.2 0.4 0.6 0.8 1 Time (s) Figure 13. (a) Finite element and (b) experimental comparison of the real-time response before and after the PPF controller was initiated. The effectiveness of the shear actuators is first examined in the frequency domain by using one of the shear actuators to excite the beam and the other actuator for active vibration suppression. Parametric studies are performed to investigate the effect of the control parameters on active damping. The experiments demonstrate that the simultaneous control of the first two modes of vibration is possible using a single piezoelectric shear actuator. The experimental and FE frequency response functions compare well. The effectiveness of the shear actuators in the time domain is demonstrated by exciting the beam at its natural frequency using a proof-mass actuator. Active vibration suppression of the beam is achieved using the piezoelectric shear actuators and PPF. It is found that the reduction in steady-state tip acceleration at the fundamental frequency is 30.2 dB. There is good correlation between the experimental and numerical transient response of the adaptive beam. Aldraihem, O.J. and Khdeir, A.A. 2003. ''Exact Deflection Solutions of Beams with Shear Piezoelectric Actuators,'' International Journal of Solids and Structures, 40:1–12. Bailey, T. and Hubbard, Jr., J.E. 1985. ''Distributed Piezoelectric Polymer Active Vibration Control of a Cantilever Beam,'' AIAA Journal of Guidance, Control and Dynamics, 8:605–611. Baillargeon, B.P. and Vel, S.S. 2005. ''Exact Solution for the Vibration and Active Damping of Composite Plates with Piezoelectric Shear Actuators,'' Journal of Sound and Vibration, 282:781–804. Benjeddou, A. and Deu¨, J.-F. 2001a. ''Piezoelectric Transverse Shear Actuation and Sensing of Plates, Part 1: A Threedimensional Mixed State Space Formulation,'' Journal of Intelligent Material Systems and Structures, 12:435–449. Benjeddou, A. and Deu¨, J.-F. 2001b. ''Piezoelectric Transverse Shear Actuation and Sensing of Plates, Part 2: Application and Analysis,'' Journal of Intelligent Material Systems and Structures, 12:451–467. Benjeddou, A. and Deu¨, J.-F. 2002. ''A Two-dimensional Closed-form Solution for the Free-vibration Analysis of Piezoelectric Sandwich Plates,'' International Journal of Solids and Structures, 39:1463–1486. Benjeddou, A., Trindade, M.A. and Ohayon, R. 1999. ''New Shear Actuated Smart Structure Beam Finite Element,'' AIAA Journal, 37:378–383. Berlincourt, D. and Krueger, H.H.A. (nd). Properties of Morgan Electroceramic Ceramics, Revised by C. Near,
(05 August 2002). Dosch, J.J., Inman, D.J. and Garcia, E. 1992. ''Self-sensing Piezoelectric Actuator for Collocated Control,'' Journal of Intelligent Material Systems and Structures, 3:166–185. Fanson, J.L. and Caughey, T.K. 1990. ''Positive Position Feedback Control for Large Space Structures,'' AIAA Journal, 28:717–724. Friswell, M.I. and Inman, D.J. 1999. ''The Relationship between Positive Position Feedback and Output Feedback Controllers,'' Smart Materials and Structures, 8:285–291. Fuller, C.R., Elliott, S.J. and Nelson, P.A. 1996. Active Control of Vibration, Academic Press, San Diego. Garcia, E., Dosch, J. and Inman, D.J. 1992. ''The Application of Smart Structures to the Vibration Suppression Problem,'' Journal of Intelligent Material Systems and Structures, 3:659–667. Glazounov, A.E. and Zhang, Q.M. 1998. ''Piezoelectric Actuator Generating Torsional Displacement from Piezoelectric d15 Shear Response,'' Applied Physics Letters, 72:2526–2528. Goh, C.J. and Caughey, T.K. 1985. ''On the Stability Problem Caused by Finite Actuator Dynamics in the Collocated Control of Large Space Structures,'' International Journal of Control, 41:787–802. Hibbitt, Karlsson & Sorensen, Inc. 2002. ABAQUS Users Manual, Version 6.3. Meyer, J.L., Harrington, W.B., Agrawal, B.N. and Song, G. 1998. ''Vibration Suppression of a Spacecraft Flexible Appendage using Smart Materials,'' Smart Materials and Structures, 7:95–104. Newman, S.M. 1992. ''Active Damping Control of a Flexible Space Structure using Piezoelectric Sensors and Actuators,'' Master's Thesis, U.S. Naval Postgraduate School. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. 1992. Numerical Recipes in C, Cambridge University Press, Cambridge. 530 B. P. BAILLARGEON Raja, S., Prathap, G. and Sinha, P.K. 2002. ''Active Vibration Control Composite Sandwich Beams with Piezoelectric Extension-bending and Shear Actuators,'' Smart Materials and Structures, 11:63–71. Rao, S.S. 1995. Mechanical Vibrations, 3rd Edn, Addison-Wesley, Reading. Sun, C.T. and Zhang, X.D. 1995. ''Use of Thickness-shear Mode in Adaptive Sandwich Structures, Smart Materials and Structures, 4:202–206. Trindade, M.A., Benjeddou, A. and Ohayon, R. 2000. ''Parametric Analysis of the Vibration Control of Sandwich Beams Through Shear-based Piezoelectric Actuation,'' Journal of Intelligent Material Systems and Structures, 10:377–385. Vel, S.S. and Baillargeon, B.P. 2004. ''Analysis of Static Deformation, Vibration and Active Damping of Cylindrical Composite Shells AND S. S. VEL with Piezoelectric Shear Actuators,''Journal of Vibration and Acoustics (submitted). Vel, S.S. and Batra, R.C. 2001a. ''Exact Solution for the Cylindrical Bending of Laminated Plates with Embedded Piezoelectric Shear Actuators,'' Smart Materials and Structures, 10:240–251. Vel, S.S. and Batra, R.C. 2001b. ''Exact Solution for Rectangular Sandwich Plates with Embedded Piezoelectric Shear Actuators,'' AIAA Journal, 39:1363–1373. Zhang, X.D. and Sun, C.T. 1996. ''Formulation of an Adaptive Sandwich Beam,'' Smart Materials and Structures, 5:814–823. Zhang, X.D. and Sun, C.T. 1999. ''Analysis of a Sandwich Plate Containing a Piezoelectric Core,'' Smart Materials and Structures, 8:31–40.
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