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Semi-analytical modeling and analysis of nonlinear vibration of bolted thin plate based on virtual material method

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Abstract

In order to effectively simulate the vibration behavior of bolted structures, it is necessary to consider the non-uniform distribution of pressure and the nonlinear characteristics of variable stiffness and damping at bolted joints. In this paper, the virtual material model is used to simulate the above two characteristics of the bolted lap zone, and a semi-analytical modeling of nonlinear vibration of bolted thin plate is studied. Specifically, the non-uniform distribution of pressure in the bolted lap zone is simulated by making the storage modulus of virtual material satisfy linear, parabolic and sinusoidal distribution forms, respectively. The storage and loss moduli of the virtual material are set as a high-order polynomial with displacement dependence to simulate the variable stiffness and damping characteristics of the bolted lap zone. By integrating the mechanical properties of the thin plate and the bolted lap zone simulated by virtual material with the energy method, the nonlinear dynamic semi-analytical modeling of the bolted thin plate is completed, and then, the process of using incremental harmonic balance method to iteratively solve the nonlinear vibration response of bolted thin plates is described. Finally, a case study is carried out to verify the rationality of the proposed virtual material simulation model of bolted lap zone, and the created semi-analytical model is used to explain the soft nonlinear vibration of bolted thin plate under different excitation levels.

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Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universities of China (Grant No. N180312012).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Xiaofeng Liu, Wei Sun, Honghao Liu, Dongxu Du & Hongwei Ma

  2. Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang, 110819, China

    Xiaofeng Liu, Wei Sun, Honghao Liu, Dongxu Du & Hongwei Ma

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  1. Xiaofeng Liu
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  2. Wei Sun
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  3. Honghao Liu
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  4. Dongxu Du
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Correspondence to Wei Sun.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare no potential conflicts of interest with respect to the research, authorship and publication of this paper.

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The study is funded by the Fundamental Research Funds for the Central Universities of China (Grant No. N180312012).

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Liu, X., Sun, W., Liu, H. et al. Semi-analytical modeling and analysis of nonlinear vibration of bolted thin plate based on virtual material method. Nonlinear Dyn 108, 1247–1268 (2022). https://doi.org/10.1007/s11071-022-07288-8

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  • DOI: https://doi.org/10.1007/s11071-022-07288-8

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