Homotopy perturbation study of nonlinear vibration of Von Karman rectangular plates

Based on the Von Karman theory, the equations of motion for a rectangular isotropic plate, considering the effect of shear deformation and rotary inertia, have been derived. For the nonlinear vibration of the plate, a nonlinear coupled equation is obtained with an Airy stress function. Using the Galerkin method, this equation is separated into position and time functions. The Homotopy Perturbation Method (HPM) is employed to solve the nonlinear time function. It is shown that the obtained results demonstrate excellent agreement with numerical solutions obtained using the fourth-order Runge–Kutta method.