Geometrically nonlinear free vibration analysis of shear deformable magneto-electro-elastic plates considering thermal effects based on a novel variational approach

Abstract

In this article, a variational numerical method is utilized to investigate the nonlinear free vibrations of magneto-electro-elastic (MEE) plates under thermal environment. To this end, first, the basic equations are written based on the first-order shear deformation theory and von Kármán's geometric nonlinearity. Next, the constitutive equations are represented in matrix form. In the context of Hamilton's principle, the quadratic and matricized form of energy functional is derived which is then directly discretized on space domain by a method called Variational Differential Quadrature (VDQ). Periodic time differential operators are also constructed for discretizing on time domain. The final solution is obtained by the pseudo arc-length continuation algorithm. The effects of applied electric voltage, applied magnetic potential, temperature change and geometrical parameters on the response curves of MEE plates with different types of boundary conditions are studied. © 2018 Elsevier Ltd