I am building a ultrasonic transducer like this (with double-exponential (75%-25%) match and 2 ring PZT8 50x20x6.5 (for the moment I do not take account of pre-stress on bolt) :
When I simulate the 2 piezo ring I got 33kHz resonant frequency. So in my mind, to get a maximum of z-displacement on the matching of the transducer, I thought it was a good idea to tweak the length of the matching to get 33khz resonant frequency for the transducer (solid - without piezo effect being simulated). After doing this, I make a simulation with solid + piezo effect and I get no 33kHz resonant frequency :
I done some other simulation for other length and get same thing :
So it seems that if solid & piezo ring are both at 33kHz, I got effectively a maximum z-displacement but not at 33 kHz...
Here is how I polarized thr rings :
So my question is : Why I don't get a 33kHz resonant frequency with piezo effect when solid + piezzo ring are both at 33 kHz resonant frequency?
Here are some other simulated result for displacement & stress :
Is there something wrong with it or can someone explain me what happen?