What should be the amplitude of the AC signal to generate Ultrasonic Waves form PZT having resonant frequency of 40 KHz? If there is some basic relation between the amplitude of signal applied and size of the PZT use, please mention it also.
You tend to use thicker ones for higher power. There is a relationship between thickness and the maximum voltage before the piezo starts to become depolarised which will lead to permanent failure. It only tends to be an issue when you are making ultrasonic cleaners or atomisers where the drive voltage can be several hundred volts. In extreme cases you need to stack them.
Morgan Electroceramics has some good technical papers on PZTs.