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The free and forced nonlinear vibration of a fixed orthotropic annular plate with elastic ring is studied. By use of Ritz-Kantorovich averaging method the governing nonlinear partial differential equations for ax symmetric vibration of the annular plates are converted to a set of ordinary differential equations which form a nonlinear Eigen value problem. Solution of the related initial value problem is obtained by applying parallel shooting method. The results show the effect of stiffness
coefficient on the dynamic response of
orthotropic plate. The method utilized in this paper can be applied to many
differential eigenvalue problems with piecewise continuous functions.