Large Amplitude Free Vibration of Simply Supported and Clamped Moderately Thick Square Plates Using Coupled Displacement Field Method

A simple and efficient coupled displacement field method is developed to study the large amplitude free vibration behavior of the moderately thick square plates. A single term trigonometric admissible displacement field is assumed for one of the variables, say, the total rotations (in both X, Y directions). Making use of the coupling equation, the spatial variation for the lateral displacement field is derived in terms of the total rotations. The coupled displacement field method makes the energy formulation to contain half the number of unknown independent coefficients, in the case of a square plate, contrary to the conventional Rayleigh-Ritz method. The lesser number of undetermined coefficients significantly simplifies the vibration problem. The expressions for the linear and nonlinear fundamental frequency parameters for the all edges simply supported moderately thick square plates are derived. The numerical results obtained from the present formulation are in very good agreement with those obtained from the existing literature.