Free Vibration of a Class of Homogeneous Isotropic Solids

[+] Author and Article Information
P. G. Young, S. M. Dickinson

Department of Mechanical Engineering, The University of Western Ontario, London, ON N6A 5B9, Canada

J. Appl. Mech 62(3), 706-708 (Sep 01, 1995) (3 pages) doi:10.1115/1.2897003 History: Received April 12, 1993; Revised November 20, 1993; Online October 30, 2007


A Ritz approach, with simple polynomials as trial functions, is used to obtain the natural frequencies of vibration of a class of solids. Each solid is modeled by means of a segment which is described in terms of Cartesian coordinates and is bounded by the yz , zx , and xy orthogonal coordinate planes as well as by a fourth curved surface, which is defined by a polynomial expression in the coordinates x , y , and z . By exploiting symmetry, a number of three-dimensional solids previously considered in the open literature are treated, including a sphere, a cylinder and a parallelepiped. The versatility of the approach is then demonstrated by considering several solids of greater geometric complexity, including an ellipsoid, an elliptical cylinder, and a cone.

Copyright © 1995 by The American Society of Mechanical Engineers
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