两自由度非线性振动系统主参数激励下的分岔分析

本文给出了参数激励作用下两自由度非线性振动系统,在1:2内共振条件下主参数激励低阶模态的非线性响应.采用多尺度法得到其振幅和相位的调制方程,分析发现平凡解通过树枝分岔产生耦合模态解,采用Melnikov方法研究全局分岔行为,确定了产生Smale马蹄型混沌的参数值.     

BIFURCATION IN A PARAMETRICALLY EXCITED TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEM WITH 1∶2 INTERNAL RESONANCE

ＩｎｔｒｏｄｕｃｔｉｏｎＰａｒａｍｅｔｒｉｃａｌｙｅｘｃｉｔｅｄｖｉｂｒａｔｉｏｎｓｈａｖｅｂｅｎｅｘｔｅｎｓｉｖｅｌｙａｐｐｌｉｅｄｔｏｉｎｅｎｇｉｎｅｒｉｎｇｓｙｓｔｅｍｓ［１］,ｓｕｃｈａｓｔｈｅｖｉｂｒａｔｉｏｎｏｆｍａｃｈｉｎｅｓ,ｄｙｎａ...     

参激屈曲梁的倍周期分岔和混沌运动的实验研究

本文对一端固定一端滑动承受轴向简谐载荷的屈曲梁的非线性响应进行了实验。研究了其基本参数共振和主参数共振两种情况，揭示了系统的倍周期分岔和混沌运动等复杂动力学行为。在某些情况下，混沌吸引子和周期吸引子共存，另一些则存在间歇混沌。给出了响应的时间历程、相图、频率谱和Ｐｏｉｎｃａｒｅ映射     

高速对称刚性转子的碰摩运动

本文分析了高速对称刚性转子圆柱形碰摩运动和圆锥形碰摩运动，给出了发生圆柱形碰摩运动时系统的稳定范围，对于圆形碰摩运动，给出了其涡动角速度的一阶近似表达式，这可为转子系统的故障诊断提供一定的理论基础。     

Bifurcation in a parametrically excited two-degree-of-freedom nonlinear oscillating system with 1∶2 internal resonance

The nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first-order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steadystate solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos. Project supported by the National Natural Science Foundation of China (19472046)