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RESEARCH PAPERS: Vibration and Sound

Trends in Eigenvalues of Straight and Bent Beams on Elastic Supports

[+] Author and Article Information
F. R. Bourne

Harris Government Aerospace Division, Melbourne, FL

M. W. Dixon

Mechanical Engineering Department, Clemson University

J. Vib., Acoust., Stress, and Reliab 109(2), 133-137 (Apr 01, 1987) (5 pages) doi:10.1115/1.3269404 History: Received July 01, 1986; Online November 23, 2009

Abstract

Singular value analysis is used to develop eigenvalue and eigenvector trends for beams supported by periodically-spaced, elastic elements. These trends are illustrated for both straight and bent beams as a function of the number of spans in the system, the boundary conditions, and the ratio of support to beam stiffness. As might be speculated, the effect of boundary conditions decreases as the number of spans increases. Also the effect of a bend becomes more pronounced as the bend is moved nearer the center of the beam. Simplified models are presented which provide excellent approximations of the first natural frequency for certain values of the ratio of support to beam stiffness.

Copyright © 1987 by ASME
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