Study on Effects of Initial Imperfection and Pre & Post-buckling Deformations on Vibration of Plates

Effects of initial geometric imperfection and pre- & post-buckling deformations on vibration of isotropic rectangular plates under uniaxial compressive in-plane load have been studied. Vibration equations of a plate, using Mindlin theory and Von-Karman stressstrain relations for large deformations, have been extracted. The response of nonlinear differential equations was assumed as the summation of dynamic and static responses. Due to the large static deflection of a plate in comparison with its vibration amplitude, the differential equations have been solved in two steps. First, the static equations have been solved using the differential quadrature method and the Arc-length strategy. Next, considering small vibration amplitude about the deformed plate (the first step result) and eliminating nonlinear terms, natural frequencies have been calculated using the differential quadrature method and solving the obtained eigenvalue problem. The results for different initial geometric imperfection and different boundary conditions reflect the impact of the mentioned factors on the natural frequencies of plates.