The energy analysis of the piezoceramic bodies under nonuniform deformations

Abstract

One of the most powerful and clear methods of solving electromechanical transducer problems is an energy method based on the use of Lagrange equations. To apply this method to piezoceramic transducers one needs to have an expression for internal energy of a piezoceramic body in a convenient form. Such a general expression for energy under arbitrary nonuniform deformations is developed and discussed. It is shown that under certain conditions the electrical and mechanical variables in the expression for internal energy of a piezoceramic body can be separated. The underlying physics for this condition is illustrated with an example of piezoceramic rods with transverse and axial polarization. In the case of electrical and mechanical variables that are not separated, the contribution of mutual terms in the total internal energy is expressed analytically and can be easily treated.