Nonlinear Vibrations of Rectangular Plates

A numerical method is developed to determine the nonlinear dynamic responses of thin, elastic, rectangular plates subjected to pulse-type uniform pressure loads. The nonlinear plate theory used in this study may be identified as the dynamic von Karman theory. The numerical method is based on finite-difference approximations of the differential equations using central difference formulations. A special form of Gaussian elimination is used to solve the system of algebraic equation resulting from the finite-difference formulation. A stability criterion is developed and checked empirically. The convergence of the solution is examined. Four sets of boundary conditions are considered. The use of the method is demonstrated by specific example problems and the results are compared with other approximate solutions.