Waves and vibrations in multilayer poroelastic plates.

Abstract

In view of a recent extensive review concerning wave propagation in porous media [M. Y. Corapcioğlu, in Transport Processes in Porous Media (Kluwer, Dordrecht, 1991), pp. 373–469], this paper presents a theory for the dynamic response of a multilayer plate within the frame of Biot′s theory of elasticity and consolidation for a porous anisotropic solid [M. A. Biot, J. Appl. Phys. 26, 182–185 (1955)]. The multilayer plate may comprise any number of bonded layers, each with a distinct but uniform thickness and anisotropic elastic properties. A differential variational principle [G. A. Altay and M. C. Dökmeci, J. Acoust. Soc. Am. 95, 3007 (A) (1994)] for Biot’s theory together with Mindlin’s plate kinematics for each layer is used to derive the two-dimensional approximate equations of multilayer plate in invariant differential and variational forms. All the continuity conditions between the interfaces of layers are taken into account. The governing equations are capable of predicting the extensional, flexural, torsional, and coupled vibrations of multilayer poroelastic plates. Special cases involving the geometry, material, and motions of multilayer plates are studied. The results contain some of earlier ones as special cases. [Work supported in part by TÜBA-TÜBİTAK.]