Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM

Large amplitude free vibration analyses of tapered Mindlin rectangular plates with elastically restrained against rotation edges are investigated using different differential quadrature method (DQM). The governing equations are based on the first-order shear deformation plate theory in conjunction with Greenʹs strain and von Karman assumption. The spatial derivatives are discretized using DQM and the harmonic balance method is used to transform the resulting differential equations into frequency domain. A direct iterative method is used to solve the nonlinear eigenvalue system of equations. The convergence of the method is shown and their accuracy is demonstrated by comparing the results with those of the limiting cases, i.e. nonlinear free vibration analysis of plates with classical boundary conditions and also linear free vibration analysis of tapered plates. The effects of the elastic restraint coefficient at the edges and the geometrical parameters on the ratio of the nonlinear natural frequency to linear natural frequency of plates with linearly and bi-linearly varying thickness are studied.