A NORMAL MODE EXPANSION METHOD FOR THE UNDAMPED FORCED VIBRATION OF LINEAR PIEZOELECTRIC SOLID

A normal mode expansion method for the vibrational responses of non-homogeneous linear piezoelectric materials without damping is presented. It can be applied directly to arbitrary piezoelectric composites, which are widely used in vibrational and acoustic sensor/actuator/transmitter applications. In the present article it is shown that if the normal modes are given, the displacement field can be expanded as the linear superposition of normal modes, while the modal coefficients can be represented in terms of surface and volume integrals directly over the six types of distributed excitations without solving the quasi-static solution explicitly. The present treatment is a modification of an earlier work by Liu [11] using a different definition of the so-called quasi-static solution, and the damping effect has been neglected for simplicity. A simple example is given to exemplify the application of the present formulation.