Galerkin-Ivanov变换的碰撞振动系统混沌运动

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

针对一般的单边碰撞振动系统,借助Galerkin-Ivanov变换得到具有对称结构的等价光滑系统,利用Melnikov方法得到系统出现混沌的必要条件,研究了单边碰撞振动系统的混沌动力学特征。以典型的单势阱碰撞振动系统为应用实例,讨论系统出现Smale马蹄混沌的必要条件;结合相图、Poincare截面图和最大Lyapunov指数等数值方法验证了所得近似结果。数值结果表明了该方法的有效性。

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.