Nonlinear free vibration analysis of annular sector plates using differential quadrature method

Abstract

The nonlinear free vibration of isotropic annular sector plates is studied using differential quadrature method. The geometric nonlinearity is used into the strains and based on the first-order shear deformation plate theory, the nonlinear governing equations of motion are obtained. According to differential quadrature analogue, the equations of motion and boundary conditions are discretized. The harmonic balance method is used to obtain the eigenvalue system. The eigenvalue system is solved using an iterative solution. The obtained results are verified for fully clamped annular sector plates and the convergence of results is investigated for some boundary conditions. The effects of some parameters, such as thickness to outer radius ratio, inner to outer radius ratio and sector angle on the nonlinear to linear natural frequency ratio, are also studied. It is shown that the simply supported plate is more sensitive to the geometrical parameters than the fully clamped plate.