Wave propagation in magneto-electro-elastic multilayered plates

An analytical treatment is presented for the propagation of harmonic waves in magneto-electro-elastic multilayered plates, where the general anisotropic and three-phase coupled constitutive equations are used. The state-vector approach is employed to derive the propagator matrix which connects the field variables at the upper interface to those at the lower interface of each layer. The global propagator matrix is obtained by propagating the solution in each layer from the bottom of the layered plate to the top using the continuity conditions of the field variables across the interfaces. From the global propagator matrix, we finally obtain the dispersion relation by imposing the traction-free boundary condition on the top and bottom surfaces of the layered plate. Dispersion curves, modal shapes, and natural frequencies are presented for layered plates made of orthotropic elastic (graphite–epoxy), transversely isotropic PZT-5A, piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄ materials. While the numerical results show clearly the influence of different stacking sequences as well as material properties on the field response, the general methodology presented in the paper could be useful to the analysis and design of layered composites made of smart piezoelectric and piezomagnetic materials.