Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect

Based on the Reddyʹs theory of plates with the effect of higher-order shear deformations, the governing equations for nonlinear vibration of orthotropic plates with finite deformations are presented. The nonlinear free vibration is analyzed by the differential quadrature method. The differential quadrature approach suggested by Wang and Bert is extended to handle the multiple boundary conditions of the plate. A new technique is also further extended to simplify nonlinear computations and the harmonic balance method is used in deriving the equation of motion. The numerical convergence and comparison studies are carried out to validate the present solutions. The results show that the presented differential quadrature method is fairly reliable and valid. Influences of geometric and material parameters, transverse shear deformations and rotation inertia, as well as vibration amplitudes, on the nonlinear free vibration characteristics of orthotropic plates are studied.