ScholarLens Back to search
2004•Engineering MechanicsRequires access

STABILITY AND BIFURCATIONS OF PERIODIC MOTION IN A THREE-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

Ding Wangcai

Open publisher page 0 citations

Abstract

A three-degree-of-freedom vibro-impact system is considered in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the six- dimension Poincar maps of n-1 periodic motion are established. The stability of the periodic motion is determined by computing eigenvalues of Jacobian matrix of the maps. If some eigenvalues are on the unit circle, bifurcation occurs as controlling parameter varies. By numerical simulation, Hopf bifurcation and period- doubling bifurcation of 1-1 periodic motion are analyzed. As controlling parameter varies further, the routes from periodic motion to chaos via quasi-periodic bifurcation and period-doubling bifurcation are investigated, respectively. One of the routes is found to be non-typical.

About this research paper

What this paper is about

A three-degree-of-freedom vibro-impact system is considered in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the six- dimension Poincar maps of n-1 periodic motion are established. The stability of the periodic motion is determined by computing eigenvalues of Jacobian matrix of the maps. If some eigenvalues are on the unit circle, bifurcation occurs as controlling parameter varies. By numerical simulation, Hopf bifurcation and period- doubling bifurcation of 1-1 periodic motion are analyzed. As controlling parameter varies further, the routes from periodic motion to chaos via quasi-periodic bifurcation and period-doubling bifurcation are investigated, respectively. One of the routes is found to be non-typical.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

A three-degree-of-freedom vibro-impact system is considered in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the six- dimension Poincar maps of n-1 periodic motion are established. The stability of the periodic motion is determined by computing eigenvalues of Jacobian matrix of the maps. If some eigenvalues are on the unit circle, bifurcation occurs as controlling parameter varies. By numerical simulation, Hopf bifurcation and period- doubling bifurcation of 1-1 periodic motion are analyzed. As controlling parameter varies further, the routes from periodic motion to chaos via quasi-periodic bifurcation and period-doubling bifurcation are investigated, respectively. One of the routes is found to be non-typical.

Key concepts: Bifurcation, Mathematics, Period-doubling bifurcation, Jacobian matrix and determinant, Eigenvalues and eigenvectors, Saddle-node bifurcation, Infinite-period bifurcation, Periodic function

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
STABILITY AND BIFURCATIONS OF PERIODIC MOTION IN A THREE-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM — Research Paper | ScholarLens