An improved stochastic averaging method based on Jacobian elliptic function

被引：0
|
作者：
Xu W.-J. [1 ]
Zheng L.-W. [1 ]
Ma P.-K. [2 ]
机构：
[1] Mechanical and Electrical Engineering Institute, School of Mechatronic Engineering, Quzhou College of Technology, Quzhou
[2] Institute of Superplasticity and Plastic, Jilin University, Changchun
来源：
Zhendong Gongcheng Xuebao/Journal of Vibration Engineering | 2019年 / 32卷 / 03期
关键词：
Bounded noise; Hardening stiffness; Softening stiffness; Stochastic averaging; Stochastic vibration;
D O I：
10.16385/j.cnki.issn.1004-4523.2019.03.009
中图分类号：
学科分类号：
摘要：
A novel stochastic averaging technique is proposed to evaluate the random responses of nonlinear systems with cubic stiffness to bounded noises. By introducing a transformation based on the Jacobian elliptic functions, the stochastic differential equations with respect to the system amplitude and the phase difference between the imposed excitation and the system response are derived. Applying the stochastic averaging principle yields the associated Itô stochastic differential equations. Then, the stationary joint probability density of the amplitude and the phase difference is obtained by solving the corresponding Fokker-Planck-Kolmogorov equation. Numerical results for a representative example with hardening and softening stiffness are given to verify the feasibility and accuracy of the proposed procedure. Compared to the stochastic averaging method based on generalized harmonic functions, the present procedure is of higher accuracy as it is based on the exact solution of the associated conservative nonlinear system. © 2019, Nanjing Univ. of Aeronautics an Astronautics. All right reserved.
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页码：444 / 451
页数：7
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