Free vibrations of a piezoelectric body

We present a systematic analysis of the eigenvalue problem associated with free vibrations of a finite piezoelectric body. The analysis is based on an abstract formulation of the three-dimensional theory of piezoelectricity. A series of fundamental properties of free vibrations of a piezoelectric body are proved concisely. The problem of free vibrations of a piezoelectric plate governed by the two-dimensional plate equations due to Mindlin is treated in a similar manner.Address after September 1, 1994: Department of Mechanical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.Address after August 16, 1994: Clifton Garvin Professor, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.