CAJ | 학술논문

针对一类具有非线性刚度、非线性阻尼的非线性相对转动系统,应用耗散系统的拉格朗日原理建立在组合谐波激励作用下非线性相对转动系统的动力学方程.构造李雅普诺夫函数,分析相对转动系统的稳定性,研究自治系统的分岔特性.应用多尺度法求解相对转动系统的非自治系统在组合激励作用下的分岔响应方程.最后采用数值仿真方法,通过分岔图、时域波形、相平面图、Poincar′e截面图等研究外扰激励、系统阻尼、非线性刚度对相对转动系统经历倍周期分岔进入混沌运动的影响.
침대일류구유비선성강도、비선성조니적비선성상대전동계통,응용모산계통적랍격랑일원리건립재조합해파격려작용하비선성상대전동계통적동역학방정.구조리아보낙부함수,분석상대전동계통적은정성,연구자치계통적분차특성.응용다척도법구해상대전동계통적비자치계통재조합격려작용하적분차향응방정.최후채용수치방진방법,통과분차도、시역파형、상평면도、Poincar′e절면도등연구외우격려、계통조니、비선성강도대상대전동계통경력배주기분차진입혼돈운동적영향.
Using the Lagrange principle of dissipative system, the nonlinear dynamic equation of a relative rotation with combined harmonic excitation is established, which contains nonlinear stiffness and nonlinear damping. The stability and bifurcation characteristics of autonomous system are analyzed by constructing Lyapunov function. Bifurcation response equation of non-autonomous system under the combined harmonic excitation is obtained by the method of multiple scale. Finally, numerical method is employed to analyze the effects of external excitation, system damping and nonlinear stiffness on the process that the system enter into chaos motion via period-doubling bifurcation by bifurcation diagram, time domain waveform, phase trajectory and Poincar′e map.