Energy analysis of a piezoelectric body under nonuniform deformation

One of the most powerful and clear methods for solving electromechanical transducer problems is the energy method based on the use of the Euler-Lagrange equations. The general expression is developed in a form convenient for applying the energy method to the calculation of the internal energy of a piezoelectric body under nonuniform deformation. The electrical and mechanical variables in this expression are separable under certain conditions and the underlying physics is illustrated with particular examples of bars made of piezoelectric ceramic for the case of transverse and axial polarization. In the case that the electrical and mechanical variables are not separable, the contribution of the mutual energy term to the total internal energy is expressed analytically.