谐和与白噪声激励下碰撞振动系统的混沌运动

Chaos of vibro-impact system under harmonic and white noise excitations

碰撞振动系统轨线的不连续性使得系统表现出强非线性和奇异性的特性.鉴于此,研究谐和与白噪声激励下非线性单边碰撞振动系统的混沌动力学.利用动力系统稳定性理论和Melnikov方法,分析碰撞振动系统的同宿轨,得到系统出现Smale马蹄混沌的阀值.并通过相图、Poincare截面图和安全盆等数值仿真验证该解析阀值的有效性.研究表明,基于Melnikov方法获得的解析结果是系统出现混沌运动的必要条件,也是系统出现安全盆腐蚀的充要条件.

Discontinuity generally induces the characteristic of strong nonlinear and singularity for vibro-impact systems.Chaos in a vibro-impact system under harmonic and white noise excitations is investigated.Based on dynamical theory and Melnikov method,the homoclinic orbits are studied and the critical value of onset of Smale chaos is given analytically.Additively,this analytical results are verified by numerical simulations,including Phase diagram,Poincare section and safe basins.The results reveals that the conclusion via Melnikov method is the necessary condition for onset of chaos motion,and the necessary and sufficient condition for the erosion of safe basin.