Dynamics of a Simple Model for a Wind-Loaded Nonlinear Structure: Bifurcations of Codimension One and Two

[+] Author and Article Information
K. Yagasaki

Department of Mechanical and Systems Engineering, Gifu University, Gifu, Gifu 501-1193, Japan

J. Appl. Mech 65(2), 505-512 (Jun 01, 1998) (8 pages) doi:10.1115/1.2789083 History: Received May 07, 1997; Revised November 15, 1997; Online October 25, 2007


The motion induced by vortex shedding of a structure with nonlinear restoring force is investigated. In particular, a conclusion about nonexistence of bounded motions obtained for a similar problem in the previous study is improved by taking into account the nonlinear restoring force characteristic. The vortex shedding frequency is assumed to be close to the natural frequency of the cross-wind oscillation and the along-wind oscillation is not excited, so that a single-degree-of-freedom model representing the cross-wind motions is obtained. The averaging method is applied to the single-degree-of-freedom system, and the normal form and center manifold theories are used to discuss bifurcations of codimension one, saddle-node and Hopf bifurcations. Moreover, it is shown that a multiple bifurcation of codimension two, called the Bogdanov-Takens bifurcation, occurs in the averaged system. The implications of the averaging results on the dynamics of the original single-degree-of-freedom system are described. Numerical examples are also given with numerical simulation results for both the averaged and original systems to demonstrate our theoretical predictions.

Copyright © 1998 by The American Society of Mechanical Engineers
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