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Extension of dual equivalent linearization to analysis of deterministic dynamic systems. Part 1: single-parameter equivalent linearization

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Abstract

The paper develops the dual equivalent linearization with one weighting coefficient to nonlinear deterministic dynamic systems. The problem of equivalent replacement of a nonlinear function by a linear function is briefly revised using the dual approach that involves two forward and backward replacements. Further selecting a weighting coefficient connecting two objective functions is investigated using a semi-analytical analysis. The dual equivalent linearization with the selected weighting coefficient is then applied to the frequency analysis of nonlinear free vibrations, and some case studies are subsequently carried out in order to verify the accuracy and influence of nonlinearities on the effectiveness of the proposed technique. It is shown that the dual equivalent linearization provides the lowest maximal errors among the solutions obtained from several approximate methods for the rather large nonlinearities considered.

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Data availability: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

The support from Vietnam Academy of Science and Technology (VAST), project VAST01.09/20-21 is acknowledged.

Funding

The authors declare that no funds, grants, or other support was received during the preparation of this manuscript, except for authors Nguyen Dong Anh, Nguyen Cao Thang.

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Authors and Affiliations

  1. Institute of Mechanics, VAST, 264, Doi Can Str, Ba Đình, Hanoi, Vietnam

    N. D. Anh, Tran Tuan Long & Nguyen Cao Thang

  2. Faculty of Mechanical Engineering, Thuyloi University, Đong Đa, Vietnam

    Nguyen Ngoc Linh

  3. Department of Mechanical Engineering, Northwestern University, Evanston, USA

    Anh Tay Nguyen

  4. Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, USA

    I. Elishakoff

Authors
  1. N. D. Anh
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  2. Nguyen Ngoc Linh
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  4. Nguyen Cao Thang
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  5. Anh Tay Nguyen
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  6. I. Elishakoff
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Contributions

1. Nguyen Dong Anh helped in conceptualization; data curation; formal analysis; project administration; resources; supervision; roles/writing–original draft, funding acquisition; 2. Nguyen Ngoc Linh performed conceptualization; data curation; formal analysis; project administration; resources; supervision; roles/writing –original draft; 3. Tran Tuan Long was involved in investigation; validation; visualization; 4. Nguyen Cao Thang helped in investigation; validation; visualization, funding acquisition; 5. Nguyen Tay Anh contributed to investigation; validation; visualization; 6. Isaac Elishakoff helped in investigation; writing—review & editing.

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Correspondence to I. Elishakoff.

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Anh, N.D., Linh, N.N., Long, T.T. et al. Extension of dual equivalent linearization to analysis of deterministic dynamic systems. Part 1: single-parameter equivalent linearization. Nonlinear Dyn 111, 997–1017 (2023). https://doi.org/10.1007/s11071-022-07894-6

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  • DOI: https://doi.org/10.1007/s11071-022-07894-6

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