Vibration frequencies and mode shapes of CCFF rectangular plates simply supported at the free corner. Application to large vibration amplitudes.

Abstract

The linear flexural vibration of a thin isotropic rectangular plate simply supported at the free corner has been investigated by the symplectic superposition method by Rui.Li and al. The purpose of the present study was to establish the efficiency of the Rayleigh-Ritz method (RRM) applied to similar plate problems. Due to its numerical and systematic character, the RRM has many practical advantages compared to the classical laborious analytical approaches and can be extended to investigate the case of geometrically nonlinear vibrations. The trial plate functions used were obtained as products of beam functions with appropriate end conditions in each direction and the point support was modeled by a translational spring with an infinite stiffness. Different cases have been dealt with corresponding to different edge conditions, different aspect ratios, and for several modes. The comparisons made of the solutions obtained with the known solutions of isotropic rectangular plates with one or more point supports show a satisfactory agreement. The nonlinear vibration of various plates with a with point support at one corner have been also examined. The backbone curves based on the SMA have been calculated by Matlab code. The systematic and straightforward method presented can be readily extended to plates with inside point corners.