Nonlinear Electroelastlc Equations of Wave Propagation and Vibrations in Quartz Bars

Abstract

SUMMARY This paper presents the nonlinear electroelastic equations of wave propagation and vibrations in a quartz bar of uniform cross-section. To begin with, Hamilton’s principle is stated for a nonlinear elastic continuum with small piezoelectric coupling, and then by carrying out the pertinent variations, a variational principle with certain constraints is formulated. The constraints are incorporated into this principle through the dislocation potentials and Lagrange undetermined multipliers, and hence a generalized variational principle is derived for the motions of nonlinear piezoelectric continuum. Next, the generalized principle together with a series expansions of its mechanical displacements and electric potential, a system of nonlinear equations of the quartz bar is consistently obtained. These one-dimensional equations of higher orders of approximation in which account is taken of only the elastic nonlinearities govern all the types of extensional