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        <h1><a href="../sd_2014.html">Dynamics of Structures</a></h1>
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          <h2>2014-04-29</h2>
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          <h2>MDOF Systems</h2>
          <p class="first">
            Multiple degrees of freedom linear systems are very simple
            to study if we adopt a matrix notation for the equation of
            motion...</p>
          <ul>
            <li>Vectorial equation of dynamic equilibrium.</li>
            <li>Linear relationship between displacement,
              acceleration vector and elastic, inertial force vector
              are written in terms of a matrix product.</li>
            <li>Homogeneous equation of motion, equation of
              frequencies, eigenvalues and eigenvectors, eigenvectors'
              properties.</li>
            <li>Modal superposition.</li>
            <li>A complete example of solution.</li>
          </ul>
          Material available for this class:
          <ul>
            <li>the <a href="06/slides.pdf">slides</a> i used for my
            lesson</li>
            <li>a ready to <a href="06/handout.pdf">print version</a>
              of the slides,</li>
            <li>a <a href="06/response.gp">gnuplot script</a> that you
              could use to produce the last two graphics in the slides
              (from the command line type "gnuplot response.gp").
	      If you don't have the gnuplot program installed on your
	      system (and don't bother to try it out) you could anyway
	      study the source to see how you can write a simple
	      program that computes the response of a 2DOF system.</li>
            <li> an <a href="http://nbviewer.ipython.org/url/boffi.github.io/dati_2014/06/example_MDOF.ipynb">
              IPython notebook</a> that computes the response for the
              same problem as above.</li>
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        <a href="mailto:giacomo.boffi@polimi.it">Giacomo Boffi</a>
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