VARIATIONAL FORMULATIONS FOR THE VIBRATION OF A PIEZOELECTRIC BODY

This paper presents a systematic discussion on the variational princip les for the vibration of a piezoelectric body. It is shown that there exist four types of variational formulations depending on the internal energy, electric enthalpy, mechanical enthalpy, and enthalpy, respect ively. The one depending on the internal energy is in a positive-defin ite form which immediately leads to a few important properties of the lowest resonant frequency.