Benchmark solution for multilayer magneto-electro-elastic plates adhesively bonded by viscoelastic interlayer

Abstract

An analytical solution is developed for a simply supported multilayer magneto-electro-elastic plate, which is adhesively bonded by viscoelastic interlayer and subjected to transverse loading. The three-dimensional equations of magneto-electro-elasticity are used to describe the mechanical behavior in each layer of the plate, while the mechanical property of the viscoelastic interlayer is simulated by the standard linear solid model with strain memory effect. The imperfect electric conditions between adjacent layers are considered. Making use of the Fourier series expansion as well as the state-space method, a linear equation system to the solution of the problem considered is derived. By means of the Laplace transformation, the undetermined coefficients contained in the equation system are obtained analytically. The present solution can be used as the benchmark to assess the other numerical solutions. The comparison study shows a trend that the finite element solution converges to the proposed theoretical results as the mesh density increases; in contrast to the theoretical solution, the finite element solution is, however, time-consuming, in terms of mesh division and calculation. In this study, the effects of the time; interlayer thickness; and interlayer electric coefficient on the mechanical, electric, and magnetic fields are also investigated.