I am trying to model a piezostack in Abaqus. But the result of force generation I obtained is almost two times the amount mentioned in catalogue. In the analysis I did not specify any initial preload, so, I guess the error in result is due to that.
The transmission ratio is the ratio of the amplitude of output vibration to the amplitude of input vibration say Ao/Ai. This ratio is function of frequency w and it depends on filter characteristics of the material. If it is assumed that the input vibration which is the excitation is uniform and independent of frequency, then the output will characterize the filtering effectiveness of the material.
Since you acquire the vibration waveform in the time domain by a vibration transducer, in order to get its frequency content you can use the Fourier Transform. If the waveform is in digital format you can use DFT or FFT to analyse it in the frequency domain. Whenever you get peaks in the FFT then you have resonance behavior. The largest peak will be the main resonance frequency. The most important issue it that the sampling frequency must be at least double the highest frequency contained in the waveform. Also, the time window of the vibration must be sufficiently large to acquire the lowest possible vibration frequency.
Best wishes.
To measure the transmission coefficient you need to divide the FFT of the output waveform to the FFT of the input waveform as per definition of the transfer ratio.