Nonlinear electroelastic equations for small fields superposed on a bias

Abstract

The nonlinear differential equations and boundary conditions in small-field variables, for small fields superposed on large static biasing states, are obtained from general rotationally invariant nonlinear electroelastic equations derived previously. The small-field equations are directly applicable in the consistent description of parametric effects in high-coupling piezoelectric materials in terms of the fundamental material parameters. The application of the equations to homogeneously polarized ferroelectrics reveals that in the linear limit the electroelastic equations are identical with the equations of linear piezoelectricity for the symmetry of the polarized state. The influence of a thickness directed homogeneous biasing electric field on the thickness vibrations of a piezoelectric plate, to second order in the biasing field, has been determined. To first order in the biasing field the results indicate that the effective fifth-rank tensor assumed in earlier quasilinear work on the subject did not have correct symmetry properties because the influence of the homogeneous static deformation under the biasing field was ignored.