Long Term Structural Dynamics of Mechanical Systems With Local Nonlinearities

[+] Author and Article Information
R. H. B. Fey

TNO Building and Construction Research, Centre for Mechanical Engineering, P.O. Box 29, 2600 AA Delft, The Netherlands

D. H. van Campen, A. de Kraker

Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

J. Vib. Acoust 118(2), 147-153 (Apr 01, 1996) (7 pages) doi:10.1115/1.2889642 History: Received July 01, 1994; Online February 26, 2008


This paper deals with the long term behavior of periodically excited mechanical systems consisting of linear components and local nonlinearities. The number of degrees of freedom of the linear components is reduced by applying a component mode synthesis technique. Lyapunov exponents are used to identify the character of the long term behavior of a nonlinear dynamic system, which may be periodic, quasi-periodic or chaotic. Periodic solutions are calculated efficiently by solving a two-point boundary value problem using finite differences. Floquet multipliers are calculated to determine the local stability of these solutions and to identify local bifurcation points. The methods presented are applied to a beam system supported by a one-sided linear spring, which reveals very rich, complex dynamic behavior.

Copyright © 1996 by The American Society of Mechanical Engineers
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