An analytical three-dimensional solution for free vibration of a magneto-electro-elastic plate considering the nonlocal effect

Abstract

An exact closed-form solution for the three-dimensional free vibrational response of a simply-supported and multilayered magneto-electro-elastic plate considering the nonlocal effect is presented. The solution is derived using the pseudo-Stroh formulation and propagator matrix method. Various numerical examples are presented for a homogeneous elastic plate, piezoelectric plate, magnetostrictive plate, and sandwich plates made of piezoelectric and magnetostrictive materials. The natural frequencies and the corresponding mode shapes of the multilayered plates show the influence of stacking sequence and the important role that the nonlocal effect plays in dynamic analysis of nanostructures. This exact solution is useful for it provides benchmark results to assess the accuracy of nonlocal thin plate models and finite element formulations.