Electroelastic modeling of the motions of ceramic bars under large driving voltages

Abstract

In relation to electroceramic media subject to large driving voltages, this paper presents the one-dimensional nonlinear equations of a cylindrical ceramic bar. The field variables of the ceramic bar are all expanded in the power series expansions of its cross-sectional coordinates. By means of a unified variational principle, which is formulated through Hamilton’s principle and Legendre’s transformation [e.g., M. C. Dökmeci, IEEE Trans. UFFC 35, 775–787 (1988)] together with the series expansions of field variables, the one-dimensional electroelastic equations are systematically derived in both differential and variational forms. They are capable of predicting the extensional, flexural, and torsional as well as coupled motions of a ceramic bar at low and high frequencies. By a proper truncation of the series expansions, the electroelastic equations incorporate as many higher-order effects as deemed desirable in any case. Special cases are investigated [cf. M. C. Dökmeci, Int. J. Solids Struct. 10, 401–409 (1974) and Proceedingsofthe 40thAnnualSymposiumonFrequencyControl (IEEE, New York, 1986), pp. 168–178]. The uniqueness is examined in solutions of the linearized electroelastic equations. [Work supported in part by The Scientific and Technical Research Council of Turkey.]