mechanical excitation of tuning fork and electrical readout
Looks you are using one of the HP DSA's .
What you are seeing is probably some stray leaking of the driving signal into your pickup. Ideally you should be using a differential input pre-amplifier, if the piezo is just plugged straight into the DSA, one end of the piezo will be grounded, so the other piezo lead will pick up stray signals. You should also be using a differential driver to the actuator, this will also minimise spurious signal generation.
Instead of seeing a transfer function of (output/input) , you are seeing (k.input + output/input) at some point in the sweep, now k.input and output/input have similar magnitude but opposite phases, creating the dip in the transfer function;
at some other point they are in phase, and add to the real peak, shifting it to the side. Swapping the leads around just changes the + above to a - , so the In-phase and out of phase artifacts swap places.