Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions

In this paper, we study the free vibration of multilayered magneto-electro-elastic plates under combined clamped/free lateral boundary conditions using a semi-analytical discrete-layer approach. More specifically, we use piecewise continuous approximations for the field variables in the thickness direction and continuous polynomial approximations for those within the plane of the plate. Group theory is further used to isolate the nature of the vibrational modes to reduce the computational cost. As numerical examples, two cases of the lateral boundary conditions combined with the clamped and free edges are considered. The non-dimensional frequencies and mode shapes of elastic displacements, electric and magnetic potentials are presented. Our numerical results clearly illustrate the effect of the stacking sequences and magneto-electric coupling on the frequencies and mode shapes of the anisotropic magneto-electro-elastic plate, and should be useful in future vibration study and design of multilayered magneto-electro-elastic plates.