AN ANALYTICAL STUDY OF GENERALIZED ASSOCIATED LINEAR EQUATIONS FOR A CLASS OF NONLINEAR SYSTEMS

被引：0
|
作者：
Zhang B. [1 ]
Zhang W. [1 ]
Peng Z. [1 ,2 ]
机构：
[1] School of Mechanical Engineering, Ningxia University, Yinchuan
[2] State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai
来源：
Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics | 2024年 / 56卷 / 03期
关键词：
generalized associated linear equations; generalized frequency response functions; Key words nonlinear output frequency response functions; nonlinear vibration; Volterra series;
D O I：
10.6052/0459-1879-23-481
中图分类号：
学科分类号：
摘要：
The nonlinear output frequency response function, which is suitable for modeling nonlinear system and has been applied for structural damage detection and fault diagnosis, is a generalization of the frequency response function in linear system theory. Based on the Volterra series theory and the recursive formulation of the generalized frequency response function of an SISO (single-input/single-output) nonlinear system described by nonlinear differential equations, this study maps the generalized frequency response function into a one-dimensional frequency domain by means of utilizing property of multiple integration and multi-dimensional Fourier transform. After that, a formula that can be used to solve generalized associated linear equations for a class of nonlinear systems is deduced. It is shown in this work that the nth-order nonlinear output response of this kind of system is the result of a generalized excitation that is a combination of the excitation and the first n−1 orders of nonlinear output response. Letting the above-mentioned generalized excitation be the input of each order of the generalized associated linear equations, the arbitrary order nonlinear output response of this kind of nonlinear system can be obtained by solving a series of linear differential equations; clearly, this presented approach overcomes the shortcoming that accompanying linear equation was not used for solving such nonlinear system. Meanwhile, a coupled computational method is proposed for the numerical calculation of the generalized associated linear equations. It is found out that this method can improve calculation accuracy of nonlinear output response and would be a new alternative for calculating nonlinear output frequency response function. Finally, as examples, emerging causes of nonlinear phenomena of two typical nonlinear systems are investigated by using the generalized associated linear equations and linear operator theory, and the corresponding results offer an effective reference for the analysis and design of some nonlinear systems. © 2024 Chinese Society of Theoretical and Applied Mechanics. All rights reserved.
引用
收藏
页码：832 / 846
页数：14
相关论文
共 32 条
  • [11] Zhu YP, Lang ZQ., Design of nonlinear systems in the frequency domain: an output frequency response function-based approach, IEEE Transactions on Control Systems Technology, 26, 4, pp. 1-14, (2017)
  • [12] Rijlaarsdam D, Nuij P, Schoukens J, Et al., A comparative overview of frequency domain methods for nonlinear systems, Mechatronics, 42, pp. 11-24, (2017)
  • [13] Peng ZK, Lang ZQ, Billings SA., Crack detection using nonlinear output frequency response functions, Journal of Sound and Vibration, 301, 3-5, pp. 777-788, (2007)
  • [14] Peng ZK, Lang ZQ, Wolters C, Et al., Feasibility study of structural damage detection using NARMAX modelling and nonlinear output frequency response function based analysis, Mechanical Systems and Signal Processing, 25, 3, pp. 1045-1061, (2011)
  • [15] Liu Y, Zhao YL, Li JT, Et al., Application of weighted contribution rate of nonlinear output frequency response functions to rotor rub impact, Mechanical Systems and Signal Processing, 136, (2020)
  • [16] Li Zhinong, Li Yunlong, Diao Haiyang, Research on diagnosis method of rotor misalignment-bumping coupling fault based on nonlinear output frequency response function, Journal of Mechanical Engineering, 55, 19, pp. 84-91, (2019)
  • [17] Liu Tianyang, Liang Haiying, Feng Yiming, Et al., Application of the improved NOFRFs weighted contribution rate inthefaultdiagnosisofrotor rub-impact, Machine Design and Research, 38, 3, pp. 93-99, (2022)
  • [18] Luo Zhong, Zhou Guangze, Zhu Yunpeng, Et al., Modelling and analysis of complex system dynamics based on orthogonal matching pursuit algorithm, Journal of Mechanical Engineering, 58, 19, pp. 86-94, (2022)
  • [19] Yu CS, Zhu YP, Luo HT, Et al., Design assessments of complex systems based on design oriented modelling and uncertainty analysis, Mechanical Systems and Signal Processing, 188, (2023)
  • [20] Zhu YP, Zhao YL, Lang ZQ, Et al., Online rotor systems condition monitoring using nonlinear output frequency response functions under harmonic excitations, IEEE Transactions on Industrial Informatics, 18, 10, pp. 6789-6808, (2022)
1234