GLOBAL ANALYSIS FOR A NONLINEAR VIBRATION ABSORBER WITH FAST AND SLOW MODES
- 1 August 2001
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Bifurcation and Chaos
- Vol. 11 (08), 2179-2194
- https://doi.org/10.1142/s0218127401003334
Abstract
A two-degree-of-freedom model of a nonlinear vibration absorber is considered in this paper. Both the global bifurcations and chaotic dynamics of the nonlinear vibration absorber are investigated. The nonlinear equations of motion of this model are derived. The method of multiple scales is used to find the averaged equations. Based on the averaged equations, the theory of normal form is used to obtain the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues by Maple software program. The fast and slow modes may simultaneously exist in the averaged equations. On the basis of the normal form, the global bifurcation and the chaotic dynamics of the nonlinear vibration absorber are analyzed by a global perturbation method developed by Kovacic and Wiggins. The chaotic motion of this model is also found by numerical simulation.Keywords
This publication has 8 references indexed in Scilit:
- Vibration analysis on a thin plate with the aid of computation of normal formsInternational Journal of Non-Linear Mechanics, 2001
- Global Bifurcations in Parametrically Excited Systems with Zero-to-One Internal ResonanceNonlinear Dynamics, 2000
- Dynamics of a Cubic Nonlinear Vibration AbsorberNonlinear Dynamics, 1999
- A Nonlinear Vibration Absorber for Flexible StructuresNonlinear Dynamics, 1998
- On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with brokenO(2) symmetryZeitschrift für angewandte Mathematik und Physik, 1993
- On the response of the non-linear vibration absorberInternational Journal of Non-Linear Mechanics, 1989
- Chaotic Motions of a Torsional Vibration AbsorberJournal of Applied Mechanics, 1988
- Optimization of a non-linear dynamic vibration absorberJournal of Sound and Vibration, 1985