Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method

In this paper the Fourier series method is introduced to obtain the solution for the displacement response of rectangular plates subjected to a blast loading. Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duffing type nonlinear ordinary differential equations and then solved by adopting the Lindstedt-Poincar'e perturbation method. The complete analysis of square plates was carried out for all-clamped edge conditions. The results of deflection history and stress resultants which uses one perturbation term sufficiently correlated with results coming from both related literature as well as the finite element method.