具有高次项非线性振动系统的分岔与混沌分析

Bifurcation and chaos analysis of vibration system with high-power nonlinear resilience

对含有5次项非线性恢复力的振动系统在简谐激励作用下的动态特性进行了渐近分析,得到了系统的主共振曲线方程式;并对系统的分岔和混沌特性进行了数值研究,发现此类非线性振动系统具有倍周期分岔、阵发性分岔、倍周期倒分岔和混沌等复杂的动力学行为.

In this paper,the dynamics characte ristics were studied about the nonlinear forced vibration equation with five-power nonlinear resilien ce,using asymptotic method.The main resonance curve equation was gained.The numerical method was also applied to analysis the bifurcation and chaos o f the system,and existence of period ical motion,explosive bifurcation,dou bling-periodic converse bifurcati on and chaoas were graphically given.