Thickness effects in the free vibration of laminated magneto-electro-elastic beams and plates

Abstract

A semi-analytical discrete-layer approach is used to evaluate thickness effects in the free vibration of laminated magneto-electro-elastic beams and plates under various lateral boundary conditions. To match the primary physical phenomenon and simplify the study, piecewise continuous approximations are used through the thickness direction and either continuous global polynomial or trigonometric functions are used to simulate the deflection in axial or planar displacement fields. Thin plate models can be recovered to predict frequency estimation for various boundary conditions and compared with continuum-based theories using more complex approximations. Based on symmetry the natural vibratory modes can be grouped to optimize computation. Numerical examples are used to show the thickness effects, with non-dimensional frequencies computed to multiple plates under six lateral boundary conditions: simply supported, clamped, and four different combinations of free and clamped/simply-supported edges. As the out-of-plate dimension becomes small and two opposite sides are free, this methodology can also be applied to beams under simply-supported, fixed-fixed and cantilever support conditions. Along with the influence of electro-elatstic and magneto-elastic coupling, the results of these analyses clearly illustrate the thickness effects within laminated plates by showing how the results vary with length/thickness ratio. Finding the accurate ratio varied with thickness is expected to provide useful specifications for the further study and design of multilayered magneto-electro-elastic beams and plates.