Complex response analysis of a non-smooth oscillator under harmonic and random excitations

doi:10.1007/s10483-021-2731-5

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (5): 641-648.doi: https://doi.org/10.1007/s10483-021-2731-5

Complex response analysis of a non-smooth oscillator under harmonic and random excitations

Shichao MA^1,2, Xin NING^1,2, Liang WANG³, Wantao JIA³, Wei XU³

1. School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. National Key Laboratory of Aerospace Flight Dynamics, Xi'an 710072, China;
3. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China

收稿日期:2020-11-11 修回日期:2021-03-01 出版日期:2021-05-01 发布日期:2021-04-22
通讯作者: Liang WANG, E-mail:liangwang1129@nwpu.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 11872306, 11772256, and 11972289) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (No. CX202003)

Complex response analysis of a non-smooth oscillator under harmonic and random excitations

Shichao MA^1,2, Xin NING^1,2, Liang WANG³, Wantao JIA³, Wei XU³

1. School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China;
2. National Key Laboratory of Aerospace Flight Dynamics, Xi'an 710072, China;
3. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China

Received:2020-11-11 Revised:2021-03-01 Online:2021-05-01 Published:2021-04-22
Contact: Liang WANG, E-mail:liangwang1129@nwpu.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 11872306, 11772256, and 11972289) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (No. CX202003)

摘要/Abstract

摘要： It is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

关键词: non-autonomous system, non-smooth system, random excitation

Abstract: It is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Key words: non-autonomous system, non-smooth system, random excitation

中图分类号:

Shichao MA, Xin NING, Liang WANG, Wantao JIA, Wei XU. Complex response analysis of a non-smooth oscillator under harmonic and random excitations[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 641-648.

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Complex response analysis of a non-smooth oscillator under harmonic and random excitations

Complex response analysis of a non-smooth oscillator under harmonic and random excitations

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