FREE VIBRATION ANALYSIS OF ORTHOTROPIC RECTANGULAR THIN PLATES USING RAYLEIGH-RITZ METHOD

AUTHOR: AMANZE, CHIBUIKE ABAMARA

AFFILIATION: DEPARTMENT OF CIVIL ENGINEERING, FEDERAL UNIVERSITY OF TECHNOLOGY OWERRI, NIGERIA

This research work, presents the free vibration analysis of orthotropic rectangular thin plates. Energy approach, (Rayleigh – Ritz method) for vibration analysis was used. It involves the derivation of the potential energy functional from the first principles using the theory of elasticity. The Taylor-Mclaurin’s series was used to develop the truncated polynomial shape functions for each of the six plate boundary conditions considered. Upon substitution of the shape functions into the Rayleigh-Ritz total potential energy functional and minimizing the functional, stability equations were established. The fundamental frequencies for Orthotropic rectangular thin plate in vibration were determined for different aspect ratios ranging from 0.1 to 2 at increments of 0.1 and flexural rigidity combination ratios of  The values of the fundamental frequency obtained from this research study, were compared with the values of  fundamental frequency results from previous research studies .The results from the present study showed that for an aspect ratio of 1.0 and flexural rigidity combination ratios of (i.e. isotropic case),the fundamental frequency for a  free vibrating rectangular thin plate, simply supported on all edges,  was 997.57. The corresponding value from the studies made by Pilkey (which is an approximate method), was 996.83 representing a percentage variation of 0.074% .For aspect ratios of 1.0 and 2.0, and the same flexural rigidity combination ratios, the results obtained from present study, were respectively 19.75 and 12.34.The corresponding values obtained by Pilkey were respectively 19.741 and 12.338.These represent percentage variations of 0.03545% and 0.0486% respectively. Similarly, for aspect ratios of 1.0 and 2.0, and flexural rigidity combination ratio of, (i.e. orthotropic case), the fundamental frequency obtained in this study for a free vibrating orthotropic rectangular thin plate clamped on all edges were, 33.923 and 23.899 respectively and the corresponding values from Kantorovich (which is an approximate method), were 33.92 and 23.85.These represent percentage variations of 0.01769%% and 0.2134% respectively.  These differences indicate that the deflection functions formulated using Taylor’s series are good approximations to the deflection functions obtained by Pilkey and Kantorovich for the free vibrating orthotropic rectangular thin plate.

In view of this submission therefore, Taylor-Polynomial series in Rayleigh-Ritz method is strongly recommended for further studies in similar fields.

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