| 谐和与高斯白噪声联合作用下二自由度系统的随机稳定性研究 |
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| 引用本文： | 胡栋梁,黄勇.谐和与高斯白噪声联合作用下二自由度系统的随机稳定性研究[J].动力学与控制学报,2020,18(6):38-48. |
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| 作者姓名： | 胡栋梁 黄勇 |
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| 作者单位： | 河海大学,南京理工大学 |
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| 摘 要： | 主要研究了谐和与高斯白噪声共同作用下二自由度系统的随机稳定性问题.首先,通过扩维的方式将非自治系统转化为自治系统.其次,利用摄动法和双傅里叶级数展开的方法求得了系统的矩Lyapunov指数与最大Lyapunov指数的近似解析结果,并和利用Monte Carlo仿真得到的数值结果进行了比较验证.最后,通过对系统矩Lyapunov指数和最大Lyapunov指数解析结果的研究分析,分别讨论了次谐共振和组合共振对系统随机稳定性的影响.
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| 关 键 词： | 随机稳定性 矩Lyapunov指数 最大Lyapunov指数 次谐共振 组合共振 |
| 收稿时间： | 2019/10/14 0:00:00 |
| 修稿时间： | 2019/11/18 0:00:00 |
STOCHASTIC STABILITY OF A TWO DEGREES-OF-FREEDOM SYSTEM UNDER COMBINED HARMONIC AND GAUSSIAN WHITE NOISE EXCITATION |
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| Hu Dongliang,Huang Yong.STOCHASTIC STABILITY OF A TWO DEGREES-OF-FREEDOM SYSTEM UNDER COMBINED HARMONIC AND GAUSSIAN WHITE NOISE EXCITATION[J].Journal of Dynamics and Control,2020,18(6):38-48. |
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| Authors: | Hu Dongliang Huang Yong |
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| Affiliation: | Hohai University,Nanjing University of Science and Technology |
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| Abstract: | In this paper, the stochastic stability of a two degrees-of-freedom system under combined harmonic and Gaussian white noise excitation are investigated. First, the non-autonomous system is transformed into an autonomous system by increasing the dimension. Secondly, applying the methods of singular perturbation and double Fourier series, the approximate analytic solution of the moment Lyapunov exponents and Largest Lyapunov exponents are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, based on the results of the moment Lyapunov exponents and Largest Lyapunov exponents, the effects of subharmonic resonance and combination additive resonance on the stochastic stability of the two degrees-of-freedom system are discussed. |
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| Keywords: | Stochastic stability Moment Lyapunov exponent Largest Lyapunov exponent subharmonic resonance combination additive resonance |
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