How to calculate the amount of pressure generated by the ultrasonic transducer (single element or multi-phased transducer) after applying a certain voltage to it? I want to use this pressure field as the initial condition for longitudinal wave propagation simulation.
A pizoelectric transducer produces displacement proportional to voltage, not pressure directly. If you know the displacement and the impedance you can work out the pressure.
Alternatively, if you know the power and efficiency of the transducer, you can work out the power in the wave and its area and so its power density and get the pressure and displacement if you know the impedance of the working fluid.
Thank you, Malcolm White, for your answer.
could you please suggest some good articles related to this topic?
you could read the second part of this as a a start
https://en.wikipedia.org/wiki/Acoustic_impedance
If you don't understand waves that you will need to do some more reading about waves.
https://www.feynmanlectures.caltech.edu/I_47.html
I don't know where you will find the best material you need.
Knowing voltage is not enough. You must also know the frequency (or the shape of excitating pulse) and the impedance of transducer material and the surrounding medium. Additionally you must know, that no plate is vibrating in a way as a piston, but in a more complicated way.
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