Chaotic Dynamics of a Quasi-Periodically Forced Beam

[+] Author and Article Information
K. Yagasaki

Department of Mechanical Engineering, Tamagawa University, Machida, Tokyo, 194, Japan

J. Appl. Mech 59(1), 161-167 (Mar 01, 1992) (7 pages) doi:10.1115/1.2899422 History: Received April 03, 1990; Revised January 18, 1991; Online March 31, 2008


A straight beam with fixed ends, forced with two frequencies is considered. By using Galerkin’s method, the equation of motion of the beam is reduced to a finite degree-of-freedom system. The resulting equation is transformed into a multi-frequency system and the averaging method is applied. It is shown, by using Melnikov’s method, that there exist transverse homoclinic orbits in the averaged system associated with the first-mode equation. This implies that chaotic motions may occur in the single-mode equation. Furthermore, the effect of higher modes and the implications of this result for the full beam motions are described.

Copyright © 1992 by The American Society of Mechanical Engineers
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