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The effects of initial geometric imperfection and pre- and post-buckling deformations on vibration of isotropic rectangular plates under uniaxial compressive in-plane load have been studied. The differential equations of plate motions, using the Mindlin theory and Von-Karman stress-strain relations for large deformations, were extracted. The solution of nonlinear differential equations was assumed as the summation of dynamic and static solutions. Due to a large static plate deflection as compared with its vibration amplitude, the differential equations were solved in two steps. First, the static equations were solved using the differential quadrature method and the arc-length strategy. Next, considering small vibration amplitude about the deformed shape and eliminating nonlinear terms, the natural frequencies were extracted using the differential quadrature method. The results for different initial geometric imperfection and different boundary conditions reflect the impact of the mentioned factors on the natural frequencies of plates.

Differential quadrature method (DQM) for studying initial imperfection effects and pre- and post-buckling vibration of plates