RESEARCH PAPERS: Basic Vibrations Papers

Large Amplitude Elliptical Plate Vibration With Transverse Shear and Rotatory Inertia Effects

[+] Author and Article Information
M. Sathyamoorthy

Department of Mechanical and Industrial Engineering, Clarkson College of Technology, Potsdam, N. Y. 13676

J. Mech. Des 104(2), 426-431 (Apr 01, 1982) (6 pages) doi:10.1115/1.3256363 History: Received May 22, 1981; Online November 17, 2009


An improved nonlinear vibration theory is used in the present analysis to study the effects of transverse shear deformation and rotatory inertia on the large amplitude vibration behavior of isotropic elliptical plates. When these effects are negligible the differential equations given here readily reduce to the well-known dynamic von Kármán equations. Based on a single-mode analysis, solutions to the governing equations are presented for immovably clamped elliptical plates by use of Galerkin’s method and the numerical Runge-Kutta procedure. An excellent agreement is found between the present results and those available for nonlinear bending and large amplitude vibration of elliptical plates. The present results for moderately thick elliptical plates indicate significant influences of the transverse shear deformation, axes ratio, and semi-major axis-to-thickness ratio on the large amplitude vibration of elliptical plates.

Copyright © 1982 by ASME
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