Piezoelectric coupled with a shunt circuit for vibration damping

Hi, everyone! I am simulating the effect of a shunt circuit on the vibration of a piezoelectric device. Theoretically, with a shunt circuit connected (a resistor and a inductor in parallel with the pzt), the vibration of the device will be further damped. This is because the mechanical energy generated by the vibration of the pzt will be converted to electric energy and further consumed by the shunt circuit in the form of Joule heating. However, when I connect a shunt circuit to the two electrodes of the pzt, the vibration amplitude is unchanged. I bet the circuit and the pzt is not coupled well and the circuit does not back-affect the pzt module.

To make the problem clearer, I list the main boundary setup of my model:

For the PZD module: 1. one end of the pzt beam is fixed and a harmonic loading is applied on the other end;
2. the lower face of the beam is grounded; the upper face is set as floating potential; the other faces are set as zero charge;

For the electric circuit module:
1. ground node is 0;
2. a resistor node is added between 1 and 0;
3. a inductor is added between 1 and 0;
4 "External I vs.U" is added between 1 and 0 and is connected the PZD module and the voltage is the floating potential on the upper face of the pzt beam.


So the question is: 1. will the "electric circuit " module response back to the pzd module?
2. will the "electric circuit" module consider the conservation of energy and thus can consume the mechanical energy in the form of joule heating?
3. any comment on this model and any suggestions?

Thank you in advance for any comment and help!!

Rock