Abstract
The vast literature dealing with the free vibrations of plates contains virtually no references for plates which are loaded by acceleration fields or gravity forces in their plane. The present paper studies the case of the rectangular cantilever plate. In-plane forces caused by an arbitrarily oriented acceleration field must first be determined by solving a plane problem of the theory of elasticity. The transverse free vibration eigenvalue problem is then analyzed by the Ritz method using mode shapes which are the sum of products of the eigenfunctions for vibrating beams. The in-plane forces are included in this analysis. The resulting matrix eigenvalue problem is solved by standard techniques on the digital computer to obtain numerical results for the vibration frequencies and mode shapes of loaded plates. Results are presented which show the effects of varying the intensity of loading, the angle of acceleration, and the aspect ratio of the plate.
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