Nonlinear dynamic buckling of imperfect rectangular plates with different boundary conditions subjected to various pulse functions using the Galerkin method

• The nonlinear dynamic pulse buckling of imperfect rectangular plate subjected to pulse loads is investigated.
• Galerkin method together with trigonometric mode shape functions is applied.
• The nonlinear coupled time integration of governing equation of plate is the solved employing fourth-order Runge–Kutta method.
• The effects of boundary conditions, pulse functions, initial imperfection, force pulse amplitude and geometric parameter on nonlinear dynamic response are investigated.
• The results show that by increasing the restriction in supports, the resistance ability against deformation and stability of plate increases.

In this paper, the nonlinear dynamic pulse buckling of imperfect rectangular plate subjected to sinusoidal, exponential, damping and rectangular pulse functions with six different boundary conditions is investigated. In order to solve the large deformation equations of plate, Galerkin method together with trigonometric mode shape functions is applied. Also, the nonlinear coupled time integration of the governing equation of plate is a solved employing fourth-order Runge–Kutta method. The effects of boundary conditions, pulse functions, initial imperfection, force pulse amplitude and geometrical parameters of the shock spectrum of a plate and deflection histories of plate for impulsive, dynamic and quasi-periodic force loads are studied. In this study, the effects of boundary conditions, pulse functions, initial imperfection, force pulse amplitude and geometric parameter in nonlinear dynamic response are investigated. According to the results for impulsive loading, the displacement response reaches its peak after shock duration and in the dynamic and quasi-static pulse loading, the maximum response of plate occurs during and before shock duration. Moreover, with increasing the loading amplitude, length of the plate and initial imperfection, the maximum displacement of plate increases. Different boundary conditions and various pulse functions have significant influence on the dynamic response of the plate. By increasing the restriction in supports, the resistance ability against deformation and stability of plate increases.