Nonlinear Vibration Analysis of Clamped Skew Plates by a Variational Method

Nonlinear free vibration analysis of clamped isotropic skew plates has been presented. The large amplitude of vibration is imparted statically by subjecting the plate under uniform transverse pressure. The mathematical formulation is based on the variational principle in which the displacement fields are assumed as a combination of orthogonal polynomial or transcendental functions, each satisfying the corresponding boundary conditions of the plate. The large amplitude dynamic problem is addressed by solving the corresponding static problem first and subsequently with the resultant static displacement field, the dynamic problem is formulated. The vibration frequencies are obtained from the solution of a standard eigenvalue problem. Entire computational work is carried out in a normalized square domain obtained through an appropriate domain mapping technique. Results of the reduced problem revealed excellent agreement with other studies and a typical comparison of the actual problem is also carried out successfully. Results are furnished in dimensionless amplitude-frequency plane, in the form of backbone curves, and pictorial representations of some vibration mode shapes are made.