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A subspace expanding technique for global zero finding of multi-degree-of-freedom nonlinear systems

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Abstract

A subspace expanding technique (SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom (MDOF) engineering systems by discretizing the space into smaller subdomains, which are called cells. The covering set of the cells is identified by parallel calculations with the root bracketing method. The covering set can be found first in a low-dimensional subspace, and then gradually extended to higher dimensional spaces with the introduction of more equations and variables into the calculations. The results show that the proposed SET is highly-efficient for finding zeros in high-dimensional spaces. The subdivision technique of the cell mapping method is further used to refine the covering set, and the obtained numerical results of zeros are accurate. Three examples are further carried out to verify the applicability of the proposed method, and very good results are achieved. It is believed that the proposed method will significantly enhance the ability to study the stability, bifurcation, and optimization problems in complex MDOF nonlinear dynamic systems.

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Acknowledgement

The first author Zigang LI would like to thank the China Scholarship Council (CSC) for sponsoring his study in the University of California, Merced.

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Authors and Affiliations

  1. Department of Mechanics, School of Science, Xi’an University of Science and Technology, Xi’an, 710054, China

    Zigang Li

  2. State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an, 710049, China

    Jun Jiang & Ling Hong

  3. Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA, 95343, USA

    J. Q. Sun

Authors
  1. Zigang Li
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  2. Jun Jiang
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  3. Ling Hong
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  4. J. Q. Sun
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Corresponding author

Correspondence to J. Q. Sun.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11702213, 11772243, 11572215, and 11332008) and the Natural Science Foundation of Shaanxi Province of China (No.2018JQ1061)

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Li, Z., Jiang, J., Hong, L. et al. A subspace expanding technique for global zero finding of multi-degree-of-freedom nonlinear systems. Appl. Math. Mech.-Engl. Ed. 41, 769–784 (2020). https://doi.org/10.1007/s10483-020-2604-6

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  • DOI: https://doi.org/10.1007/s10483-020-2604-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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