Clamped-Free Non Homogeneous Magneto Electro Elastic Plate of Polygonal Cross-Sections with Hydrostatic Stress and Gravity

In this article, the influence of hydrostatic stress and gravity on a clamped free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on twodimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal crosssections composed of non homogeneous isotropic material. The frequency equations are obtained by satisfying the boundary conditions along the irregular surface of the polygonal plate using Fourier expansion collocation method. The complex roots of the frequency equations are obtained by secant method. The numerical computations are carried out for triangular, square, pentagon and hexagon cross sectional plates. Graphical representation is given for the various physical variables via gravity and different edge boundaries and its characteristics are discussed. This result can be applied for optimum design of concrete plates with polygonal cross sections.