Nonlinear Vibration Response of Shear Deformable Functionally Graded Plate Using Finite Element Method

AbstractThis paper presents the free vibration behavior of functionally graded (FG) plate with von Karman nonlinearity. Hamilton principle is employed to establish the governing equation of motion of FG plate using higher order shear deformation theory (HSDT). The established governing equation also satisfied the traction free boundary conditions on the top and bottom faces of the plate. The gradation of material properties in the thickness direction of functionally graded plate is assumed according to a power law distribution. Results are obtained by employing an efficient C0 finite element with seven degrees of freedom (DOFs) per node. Convergence and comparison studies with analytical and numerical techniques reported in literature are carried out to establish the high accuracy and reliability of the solutions. The effect of nonlinear kinematics, thickness ratio, amplitude ratio and the volume fraction ratio on the vibration characteristics of FGM plate is investigated. It is noticed that the nonlinear frequency ratio is greatly influenced by geometric configuration and nonlinearity exist in stress-strain relationship