首页 > 过刊浏览>2020年第18卷第6期 >38-48. DOI:10.6052/1672-6553-2020-040
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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
作者:
作者单位:

1.河海大学 力学与材料学院工程力学系，南京211100;2.南京理工大学 能源与动力工程学院，南京210094

通讯作者:

E-mail: hy@njust.edu.cn

基金项目:

国家自然科学基金资助项目（11502067）,中央高校基本科研业务费专项资金项目（2018B58014）


STOCHASTIC STABILITY OF A TWO DEGREES-OF-FREEDOM SYSTEM UNDER COMBINED HARMONIC AND GAUSSIAN WHITE NOISE EXCITATION
Author:
Affiliation:

1.Department of Engineering Mechanics， College of Mechanics and Materials， Hohai University， Nanjing 211100， China;2.School of Energy and Power Engineering， Nanjing University of Science and Technology，Nanjing 210094， China

Fund Project:

The project supported by the National Natural Science Foundation of China (11502067) and the Fundamental Research Funds for the Central Universities (2018B58014)

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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.

    Abstract:

    The stochastic stability of a two degrees-of-freedom system under combined harmonic and Gaussian white noise excitation were investigated. Firstly， the non-autonomous system was transformed into an autonomous system by increasing the dimension. Secondly， using both singular perturbation and double Fourier series， the approximate analytical solutions of the moment Lyapunov exponents and the largest Lyapunov exponents were obtained， which agree well with the results obtained by the Monte Carlo simulation. Finally， based on the moment Lyapunov exponents and the largest Lyapunov exponents， the effects of subharmonic resonance and combination additive resonance on the stochastic stability of the two degrees-of-freedom system were discussed.

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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; 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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  • 收稿日期:2019-10-14
  • 最后修改日期:2019-11-18
  • 在线发布日期: 2021-01-05
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