Effect of forcing frequency on nonlinear dynamic pulse buckling of imperfect rectangular plates with different boundary conditions

• The influence of forcing frequency on nonlinear dynamic pulse buckling of imperfect rectangular plate subjected to pulse loads is investigated.
• Trigonometric and polynomial mode shape functions are applied to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations.
• The numerical study of ordinary nonlinear differential equations is accomplished by Runge Kutta integration methods.
• The convergence of the polynomial and trigonometric mod shape functions are investigated to compute the dynamic response of plate.
• The results show that, by increasing the forcing frequency of impulsive loading, the maximum displacement of plate increases and converge with lower values to response of plate subjected to exponential impulsive loading.

The present study was aimed to investigate the influence of forcing frequency on nonlinear dynamic pulse buckling of imperfect rectangular plates with six different boundary conditions. The Galerkin's approximate method on the basis of polynomial and trigonometric mode shape functions is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations. Moreover a numerical study of these governing equations is accomplished by Runge Kutta integration methods. The convergence of the polynomial and trigonometric mod shape functions are investigated to compute the dynamic response of plate. The effects of frequency of impulse loading and boundary conditions on the deflection histories of plate are studied. The dynamic response of plate subjected to impulsive loading with different forcing frequency is compared to results obtained by exponential impulsive loading. The results show that, by increasing the forcing frequency of impulsive loading, the maximum displacement of plate increases and converge with lower values to response of plate subjected to exponential impulse. Moreover, different boundary conditions and various pulse functions have significant influence on the dynamic response of the plate.