The variational piezoelectromagnetic equations for elastic dielectrics

Abstract

The aim of this paper is to extend the variational principles of piezoelectricity [M. C. Dökmeci, IEEE Trans. Ultrason. Ferroelec. Freq. Control UFFC-35(6), 775–787 (1988)] so as to incorporate the magnetic effects. The principle of virtual work is applied to the motions of piezoelectromagnetic medium, and an associated variational principle is derived that yields some of the fundamental equations of the medium and includes its remaining equations as constraints. By use of Lagrange multipliers, the constraints are incorporated into the variational principle and a unified variational principle is derived. Likewise, a variational principle is formulated for an electromagnetic medium with an internal surface of discontinuity. These integral and differential types of variational principles provide a standard basis for generating approximate direct solutions as well as deducing systematically lower order equations of piezoelectromagnetic medium. Also, special cases and the reciprocals of the variational principles are indicated. The results are shown to agree with the earlier variational principles [e.g., M. C. Dökmeci, J. Math. Phys. 19, 109–126 (1978) and P. C. Y. Lee, J. Appl. Phys. 69, 7470–7473 (1991)]. [Work supported in part by The Scientific and Technical Research Council of Turkey.]