RESEARCH PAPERS: Vibrations Papers

A Strain Energy Comparison of Discrete Modeling for Vibrating Continuous Systems

[+] Author and Article Information
S. K. Tolani, R. D. Rocke

Department of Mechanical and Aerospace Engineering, University of Missouri—Rolla, Rolla, Mo.

J. Eng. Ind 94(1), 23-30 (Feb 01, 1972) (8 pages) doi:10.1115/1.3428117 History: Received May 11, 1971; Online July 15, 2010


Lumped parameter models commonly used to describe continuous one-dimensional and Bernoulli-Euler beam vibration problems have been compared on the basis of maximum system strain energy. The consistent mass matrix approach has been included in the comparison. Standard matrix techniques have been employed to mathematically obtain desired solutions. Closed form solutions and solutions via the models to the system strain energy were obtained for all systems in three dynamic states: Free vibrations, constant base acceleration, and half sine base acceleration. Behavior of the strain energy errors, in general, were found to be similar to those of the frequency root errors.

Copyright © 1972 by ASME
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