High-frequency vibrations of a piezomagnetic plate

Abstract

This paper deals with a consistent derivation of the hierarchic system of two-dimensional approximate equations of a piezomagnetic plate at high frequency where the wavelength is of the order of magnitude or smaller than the plate thickness. To begin with, a generalized variational principle is reported for piezomagnetism, and the field variables are represented by the power series expansions in the thickness coordinate. Next, with the aid of the variational principle together with the series expansions, the system of plate equations is derived in invariant, differential and fully variational forms. The system of equations that may be readily expressed in a particular coordinate system most appropriate to the plate geometry is capable of predicting all the types of vibrations at both low and high frequency. Also, the uniqueness is investigated in solutions of the system of plate equations, and the conditions are enumerated for the uniqueness. Further, certain cases involving special geometry, material properties and types of vibrations are indicated. The resulting equations agree with and generalize some of earlier plate equations [cf. the authors, Int. J. Solids Struct. 40, 4699–4706 (2003)]. [Work supported by TUBA.]