Article ID Journal Published Year Pages File Type
1867853 Physics Letters A 2008 6 Pages PDF
Abstract

A three-degree-of-freedom vibratory system impacting symmetrical rigid stops is considered. Dynamics of the vibroimpact system is studied by use of a mapping derived from the equations of motion, supplemented by transition conditions at the instants of impacts. Two-parameter bifurcations of fixed points in the vibroimpact system, associated with 1:31:3 strong resonance, are analyzed. Neimark–Sacker bifurcations of period-1 double-impact symmetrical orbits, near 1:31:3 resonance point, are found, and the transition of quasi-periodic impact motions to unstable period-3 six-impact motions, are obtained numerically. The results conform to 1:31:3 resonance bifurcation theory of maps available. More complicated “tire-like” quasi-periodic attractor and torus bifurcation associated with the transition of the closed invariant curve to torus, near 1:31:3 resonance point, are found to exist in the nonlinear system. The results imply that there exist possibly more complicated bifurcation sequences near 1:31:3 resonance points of nonlinear dynamical systems.

Related Topics
Physical Sciences and Engineering Physics and Astronomy Physics and Astronomy (General)
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