摘要
耦合SD振子作为一种典型的负刚度振子,在工程设计中有广泛应用.同时高斯色噪声广泛存在于外界环境中,并可能诱发系统产生复杂的非线性动力学行为,因此其随机动力学是非线性动力学研究的热点和难点问题.本文研究了高斯色噪声和谐波激励共同作用下双稳态耦合SD振子的混沌动力学,由于耦合SD振子的刚度项为超越函数形式,无法直接给出系统同宿轨道的解析表达式,给混沌阈值的分析造成了很大的困难.为此,本文首先采用分段线性近似拟合该振子的刚度项,发展了高斯色噪声和谐波激励共同作用下的非光滑系统的随机梅尔尼科夫方法.其次,基于随机梅尔尼科夫过程,利用均方准则和相流函数理论分别得到了弱噪声和强噪声情况下该振子混沌阈值的解析表达式,讨论了噪声强度对混沌动力学的影响.研究结果表明,随着噪声强度的增大混沌区域增大,即增大噪声强度更容易诱发耦合SD振子产生混沌.当阻尼一定时,弱噪声情况下混沌阈值随噪声强度的增加而减小;但是强噪声情况下噪声强度对混沌阈值的影响正好相反.最后,数值结果表明,利用文中的方法研究高斯色噪声和谐波激励共同作用下耦合SD振子的混沌是有效的.本文的结果为随机非光滑系统的混沌动力学研究提供了一定的理论指导.
As a typical oscillator with negative stiffness,coupled SD oscillator is widely used in engineering.At the same time,Gaussian colored noise exists widely in the external environment and may induce complex nonlinear dynamic behaviors,so its stochastic dynamic is a hot topic and difficult problem in nonlinear dynamics research.In this paper,the chaotic dynamics of bistable coupled SD oscillator under Gaussian colored noise and harmonic excitation are studied.The analytical expression of the homoclinic orbit of the coupled SD oscillator can not be given directly because its stiffness term is a transcendental function,which makes it difficult to analyze the chaos threshold.Firstly,the piecewise linearization approximation is used to fit the stiffness term of the oscillator,and stochastic Melnikov method for nonsmooth system under Gaussian colored noise and harmonic excitation is developed.Based on random Melnikov process,then the chaos thresholds of the oscillator under weak noise and strong noise are obtained by the mean square criterion and the phase space flux function theory respectively,and the effect of noise intensity on chaotic dynamics is discussed.The results show that the chaotic region increases with the increase of noise intensity,that is,the increase of noise intensity is more likely to induce the coupled SD oscillator to produce chaos.When the damping is fixed,the chaos threshold decreases with the increase of noise intensity in the case of weak noise.However,the effect of noise intensity on chaos threshold is opposite for the case of strong noise.Finally,numerical results show that it is effective to study the chaos of coupled SD oscillator under Gaussian colored noise and harmonic excitation by the method in this paper.The results of this paper provide some theoretical guidance for the study of chaotic dynamics of stochastic non-smooth systems.
作者
周碧柳
靳艳飞
Zhou Biliu;Jin Yanfei(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China)
出处
《力学学报》
EI
CAS
CSCD
北大核心
2022年第7期2030-2040,共11页
Chinese Journal of Theoretical and Applied Mechanics
基金
北京市自然科学基金(1222015)
国家自然科学基金(12072025)资助项目。
关键词
随机非光滑梅尔尼科夫过程
分段线性近似
同宿混沌
高斯色噪声
耦合SD振子
stochastic non-smooth Melnikov process
piecewise linearization approximation
homoclinic chaos
Gaussian colored noise
coupled SD oscillator
