Chaotic motion of vibro-impact system based on Galerkin-Ivanov transformation

Abstract

Based on the Galerkin-Ivanov transformation, the chaotic motion of a vibro-impact system was investigated. For a general vibro-impact system with one-side rigid, the equivalent smooth system with symmetric structure was obtained by Galerkin-Ivanov transformation. Then, the necessary conditions for threshold of chaos were obtained by employing Melnikov method. A typical single well vibro-impact system was discussed as an illustration. The necessary conditions for onset of Smale horseshoe chaos was approximated. This approximate results were verified by numerical methods such as phase diagram, Poincare section and maximum Lyapunov exponent. The numerical results showed the effectiveness of the proposed method.

Keywords

• vibro-impact system
• galerkin-ivanov transformation
• melnikov method
• chaos motion