Bifurcation Point Analysis of a Magnetostrictive Sandwich Composite Plate Subjected to Magnetic Field and Axial Force

Abstract

This article studies parametric vibration and dynamic instability of a rectangular and symmetric magnetostrictive sandwich composite plate (MSCP) on a visco-Pasternak medium. The MSCP consists of three layers; a magnetostrictive layer considers the core and composites as its upper and lower faces. The MSCP subjected to temperature change, parametrically exciting force, and magnetic load is studied with consideration to geometrical von Karman nonlinearity. Based on the energy method and first shear deformation theory (FSDT), Hamilton’s principle is used to achieve the system’s governing equations and boundary conditions. In the next step, the partial differential equation is transformed into ordinary differential equations by applying the Galerkin technique. Then the equation of motion is solved using the multiple-scale method. Numerical results illustrate the stability of the sandwich plate is significantly related to the magnetostrictive parameters. In addition, the effects of significant parameters, such as the effect of amplitude response and parametric excitation or detuning parameter, coupled with the effect of foundation, thickness ratio, aspect ratio, and temperature increment on vibration characteristics, bifurcation points behavior and stability of the systems are charted, plotted and discussed. The innovation of this article is the use of magnetostrictive material in sandwich plates and the development of its mathematical relationships. It is anticipated that the results of this research can contribute to the development of future smart structural applications subjected to in-plane axial forces.