Bifurcations and Chaos in Structural Control

by K. Hackl, Univ of Delaware, Newark, United States,
A. Cheng, Univ of Delaware, Newark, United States,
C. Y. Yang, Univ of Delaware, Newark, United States,
M. Chajes, Univ of Delaware, Newark, United States,



Document Type: Proceeding Paper

Part of: Engineering Mechanics

Abstract: We study a harmonically forced oscillator with nonlinear soft spring subjected to a linear feedback control with time delay. This system can be written as a three dimensional dynamical system. First the local and global bifurcations of the autonomous (unforced) system are investigated using normal form and center manifold theory. Based on these results a stability analysis of the system is carried out. This analysis is then extended to the forced system using Melnikov's method. An approximate criterion for the transition from regular to chaotic motion and from smooth to fractal boundary of the stable region is derived.

Subject Headings: Oscillations | Bifurcations | System analysis | Linear functions | Fractals | Domain boundary | Hydraulic structures

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