Free Vibrations of Simply Supported Rectangular Mindlin Plate at Higher Modes Using Coupled Displacement Field Method

Abstract: An accurate closed form solution was developed to evaluate the free vibration behaviour of thin and moderately thick isotropic rectangular plates with simply supported boundary condition for all the edges. A novel methodology known as coupled displacement field (CDF) method, proposed by the author was used to study the free vibration of the rectangular plate. Here an admissible trial function which satisfies the boundary conditions was assumed for one of the variables (say total rotations) and another variable which is the lateral displacement field is derived in terms of the initial variable by using the coupling equations, where the two independent variables become dependent on one another. The proposed CDF method makes use of the energy formulation and results in only half the number of undetermined coefficients when compared with the conventional Rayleigh-Ritz method. The vibration problem gets simplified significantly due to the reduction in the number of undetermined coefficients. The plate problem was also solved in Rayleigh-Ritz method to show the efficacy and simplicity of the CDF method. The Primary focus was given to the effect of aspect ratio and slenderness ratio on the non-dimensional frequency parameter at higher modes. The numerical results obtained by the present methodology are validated with Rayleigh-Ritz method and results available in the existing literature where ever possible. The analysis of the plate problem is based on Mindlin plate theory and the effect of shear deformation, as well as rotary inertia, were included.

Keywords: coupled displacement field, coupling equation, large amplitude vibrations, moderately thick plates.