Large amplitude flexural vibration analysis of tapered plates with edges elastically restrained against rotation using DQM

The large amplitude free vibration analysis of tapered rectangular thin plates with edges elastically restrained against rotation is investigated using a differential quadrature method (DQM). The governing equations are based on the thin plate theory using Green’s strain in conjunction with von Karman assumption. In order to better recognize the nonlinearity effects, the in-plane immovable conditions are assumed along the edges of the plate. The boundary conditions are exactly implemented at the boundary grid points and are conveniently built into the equations of motion using a DQ methodology recently developed by the authors to solve fourth-order governing differential equations. The harmonic balance method is used to transform the resulting differential equations from temporal to frequency domain. Consequently, a direct iterative method is used to solve the nonlinear eigenvalue system of equations. The convergence of the method is verified and the solution accuracy is demonstrated by comparing the results with those for limiting cases, i.e., the free vibration of tapered plates under classical boundary conditions. Furthermore, the effects of different parameters on the nonlinear to linear natural frequency ratio of plates with linearly or bi-linearly varying thickness and with edges elastically restrained against rotation are studied and the results are compared with those of DQ solution based on the first-order shear deformation plate theory.