Resonant Transducer Damping with Acoustic Load

Hello,

I am trying to understand the effect of mechanical load on the resonant characteristics of a piezoelectric transducer. For that I basically take a rod of PZT-5H. I applied a voltage difference between two ends of the rod. I also put two materials in contact with two ends of the PZT-5H rod. I want to see how the resonant frequency and the quality factor changes as this two load material changes. As a simulation, I do a frequency analysis over a frequency range and I look for the displacement of the center of the top surface of the PZT-5H rod. I see a good resonance. For different materials I see small changes in the resonant frequency and peak displacement. However, I think my system is quite ideal now. My question is how can I add nonidealities to the system like damping or losses?

Thanks for any replies