Large Amplitude Free Vibration Analysis of Composite Plates with Rotationally Restrained Edges using DQM

Abstract

Large amplitude free vibration analyses of thin-to-moderately thick angle-ply laminated rectangular plates with edges rotationally restrained against rotation are investigated using the differential quadrature method (DQM). The governing equations are based on two different theories: thin or classical plate theory and the first order shear deformation plate theory. In both theories, Green's strain in conjunction with the von Karman assumption is employed. The boundary conditions are implemented precisely at boundary grid points and are built into the equations of motion without any extra efforts. After transforming the governing equations from temporal to frequency domain, a direct iterative method is used to solve the nonlinear eigenvalue system of equations. The convergence of the method is shown and its accuracy is demonstrated by comparing the results with those for limit cases, i.e., laminated plates with classical boundary conditions and also for linear free vibration analysis of laminated plates with restrained edges. Finally, the effects of different parameters on the ratio of nonlinear to linear natural frequency of plates are studied.