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This paper presents a systematic discussion on the variational principles 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, respectively. The one depending on the internal energy is in a positive-definite form which immediately leads to a few important properties of the lowest resonant frequency.

Variational formulations for the vibration of a piezoelectric body