Forced Vibration Analysis of Functionally Graded Plates With Geometric Nonlinearity

Forced vibration analysis has been carried out on functionally graded plates where the material properties vary along axial direction. The geometric nonlinearity is incorporated in the system using nonlinear strain displacement relations. An indirect methodology is adopted in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude, thus reducing the problem to an equivalent static case. The computational points are selected and start functions are generated at those points by satisfying the flexural and membrane boundary conditions of the plate. The start functions are later used for generating higher order functions using Gram-Schmidt orthogonalisation procedure. The mathematical formulation is based on the variational form of energy principles and the governing equations are derived using Hamilton’s principle. The set of nonlinear governing equations is solved using an iterative direct substitution method employing an appropriate relaxation technique. The results are generated for combinations of clamped and simply supported boundary conditions and presented in amplitude-frequency plane. Three dimensional operational deflection shape plots along with contour plots are also provided for some cases. Results are validated with the works available in the literature.