Numerical Analysis of Nonlinear Forced Vibration of Functionally Graded Rectangular Plates with Various Boundary Conditionsusing3D theory of Elasticity

Researchesdone by researchers on the forced vibration analysis of rectangular plates based on the three-dimensional elasticity theory are limited to the analytical solutions for simply-supported boundary conditions or linear analyses. In this study, by eliminating the previous limitations, the forced vibration of functionally graded rectangular plates with different boundary conditions is examined based on three-dimensional theory of elasticity and taking into account the geometrically nonlinearity.The rectangular plate is made of the aluminum and alumina in which are distributed through the thickness direction according to a power law for functionally graded materials. In order to achieve the governing equations and corresponding boundary conditions in terms of displacements, Green-Lagrange, stress-strain relations and Hamilton's principle are used. The nonlinear coupled governing equations are discretized in the space domain using the generalized differential quadrature (GDQ) method.Then, utilizing the numerical-based Galerkin scheme, one can obtain a time-varying set of ordinary differential equations of Duffing type. The arc-length method is employed to solve the vectorized form of nonlinear parameterized equations. Finally, to have a comprehensive study on the effects of geometrical parameters,forcingamplitude and damping ratio on the frequency-response curve of functionally graded rectangular plateswith different boundary conditions are examined.