RESEARCH PAPERS: Vibrations Papers

Nonlinear Vibration of Buckled Beams

[+] Author and Article Information
Gwo-Bao Min

Bendix Corp., Ann Arbor, Mich.; The University of Michigan, Ann Arbor, Mich.

J. G. Eisley

Aerospace Engineering Department, The University of Michigan, Ann Arbor, Mich.

J. Eng. Ind 94(2), 637-645 (May 01, 1972) (9 pages) doi:10.1115/1.3428216 History: Received May 12, 1971; Online July 15, 2010


The steady state response and stability of free and forced vibration of simply supported, axially restrained, buckled beams is investigated. The equations of motion dealing with the buckled state include the effect of an initial displacement either by initial load or by initial temperature. By an assumed mode solution, the response and stability of two types of vibration are determined—snap-through (symmetrical) and one-sided (unsymmetric) vibration. The theoretical results of the response and stability are verified by analog computer simulation. It is concluded that the stability of the unsymmetric vibration is not a problem and that the different orders of parametric response of the rest modes (the modes originally not excited) in symmetric vibration correspond to the instability regions determined for the approximate single mode response.

Copyright © 1972 by ASME
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