Part of the International Centre for Mechanical Sciences book series (CISM, volume 298)
Chaotic and Regular Motion in Nonlinear Vibrating Systems
Studies of phenomena arising in nonlinear oscillators are often modelled by an equation of the form
where and ψ(x) are approximated by finite Taylor series, and represents a dissipative term. Such a system has an extensive literature. A now classical approach to the study of the system behaviour, such as that presented in the popular book by Hayashi , is the theoretical analysis based on approximate analytical methods with experimental verification employing electric circuits or electronic computers. In these studies the system is assumed to tend to steady-state oscillation when started with any initial conditions and steady-state solutions are often the main point of interest. Approximate analytical solutions describing various types of resonances and analysis of local stability of the solutions and their domains of attraction provided us with a great deal of knowledge about the system behaviour. The results show a variety of nonlinear phenomena such as: principal, sub, ultra and subultra harmonic resonances and jump phenomena associated with stability limits on resonance curves, which seem to leave no room for any irregular, random-like and unpredictable solutions in the deterministic systems.
KeywordsPhase Portrait Chaotic Motion Harmonic Component Strange Attractor Resonance Curve
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