Dynamic analysis of multilayered magnetoelectroelastic plates based on a pseudo-Stroh formalism and Lagrange polynomials

Abstract

In this article, a semi-analytical three-dimensional modeling of dynamic behavior of the multilayered magnetoelectroelastic plates under simply supported edges boundary conditions is derived. A combination of pseudo-Stroh formalism and the Lagrange polynomials is elaborated for the space and time response. The time domain is subdivided into small intervals that are discretised using the associated Tchybechev points. The layer-time solution is elaborated in time-dependent matrix form. The propagator matrices are used for the laminated multifunctional plates with an arbitrary number of layers. Extended-traction vectors are obtained for mechanical, electrical, and magnetic excitations. To validate the elaborated numerical procedure, the dynamic behavior of the three layered plates made of piezoelectric material $\mathrm{BaTi}{O}_3$ and piezomagnetic material $\mathrm{CoF}{e}_2{O}_4$ is investigated. The lower surface of the plate is assumed to be traction free, whereas the upper surface is subjected to a dynamic sinusoidal loading. The obtained results are in good agreement with the available ones based on the Layer wise and the state-space approaches. These results demonstrated that a magnetoelectric coupling coefficient is time-independent but depends strongly on the kind of imperfect interfaces and the taking sequences of the multilayered plates. Furthermore, it is established that the imperfect interfaces have a strong influence on the dynamic behavior of the laminated structures.