A Dynamic Analysis of Piezoelectric Strained Elements

Abstract : This report is addressed to the dynamic analysis of piezoelectric structural elements under a static mechanical bias. In the first part of the report, the current literature pertaining to the dynamic applications of piezoelectric crystals is reviewed; attention is especially confined to vibrations of structural elements. In the second part, the fundamental equations of piezoelectric media are expressed in variational form as the Euler-Lagrange equations of certain integral and differential types of variational principles. These variational principles are deduced from a general principle of physics by augmenting it through Friedrichs's transformation. In the third part, the system of approximate lower order governing equations of piezoelectric strained elements is systematically and consistently deduced in invariant form from the three dimensional equations of piezoelectricity by means of the variational principles. The governing equations accommodate all the types of extensional, flexural and torsional as well as coupled motions of piezoelectric one- and two- dimensional elements. Also, the uniqueness of solutions is examined and two unified numerical algorithms which are based on Kantorovich's method and the method of moments are described for solutions of the governing equations.