Linear Theory for Small Fields on a Finite Bias

Abstract

The theory of linear piezoelectricity assumes infinitesimal deviations from an ideal reference state of the material in which there are no pre-existing mechanical and/or electrical fields (initial or biasing fields). The presence of biasing fields makes a material apparently behave like a different one, and renders the linear theory of piezoelectricity invalid. The behavior of electroelastic bodies under biasing fields can be described by the theory for infinitesimal incremental fields superposed on finite biasing fields, which is a consequence of the nonlinear theory of electroelasticity when it is linearized around the bias. Knowledge of the behavior of electroelastic bodies under biasing fields is important in many applications including the buckling of thin electroelastic structures, frequency stability of piezoelectric resonators, acoustic wave sensors based on frequency shifts due to biasing fields, characterization of nonlinear electroelastic materials by propagation of small-amplitude waves in electroelastic bodies under biasing fields, and electrostrictive ceramics which operate under a biasing electric field. This chapter presents the linear theory for small fields superposed on finite biasing fields in an electroelastic body.