Free vibration response of two-dimensional magneto-electro-elastic laminated plates

An approximate solution for the free vibration problem of two-dimensional magneto-electro-elastic laminates is presented to determine their fundamental behavior. The laminates are composed of linear homogeneous elastic, piezoelectric, or magnetostrictive layers with perfect bonding between each interface. The solution for the elastic displacements, electric potential, and magnetic potential is obtained by combining a discrete layer approach with the Ritz method. The model developed here is not dependent on specific boundary conditions, and it is presented as an alternative to the exact or analytical approaches which are limited to a very specific set of edge conditions. The natural frequencies and through-thickness modal behavior are computed for simply supported and cantilever laminates. Solutions for the simply supported case are compared with the known exact solution for piezoelectric laminates, and excellent agreement is obtained. The present approach is also validated by comparing the natural frequencies of a two-layer cantilever plate with known analytical solution and with results obtained using commercial finite element software.