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.

► Nonlinear vibration of plates studied using Homotopy Perturbation Method (HPM). ► Exact solutions given for a square plate with all sides hinged in first mode. ► Extensive computations conducted for both first and second modes. ► Benchmarking of amplitude oscillation with shooting quadrature included. ► Visualization of the second mode shape for different times is included.