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Linear and nonlinear stiffness compensation for low-frequency vibration isolation: a comparative study

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Abstract

Quasi-zero stiffness (QZS) vibration isolators show great advantages in low frequency vibration isolation and often developed by compensating the negative stiffness of the bistable structure by linear spring. To overcome the limitation of the bistable property, this paper utilizes linear stiffness (linear spring) and nonlinear stiffness (repulsive magnets) respectively to compensate the general negative stiffness (rhombus structure), and realizes two types of vibration isolators, the QZS-L and QZS-N isolator. Static models are established to characterize the stiffness property and reveal two basic principles for realizing QZS. The realization of QZS in the QZS-L isolator requires large deformation, but it can be achieved under small deformation in the QZS-N system. Both the QZS-L isolator and QZS-N isolator have weak asymmetry in stiffness, which leads to bias in steady-state response. And the former has stronger asymmetry and greater bias. The adjustment method of the QZS-L and QZS-N isolators for different loads is also elaborated separately. A unified dynamic model is established and the displacement transmissibility is derived to evaluate the vibration isolation performance of the two system. The QZS-L isolator is a softening system with a left-shifted resonance peak, while the QZS-N behave as a hardening system with a right-shifted resonance peak. Both isolators have a low resonant frequency and a wide isolation frequency band. Moreover, the initial isolation frequency can become lower when adjusted for larger loads. Comprehensive comparisons and discussions of static characteristics, isolation band, and zero offset are instructive in designing low frequency vibration isolators.

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Data availability

The data that support the findings of this study are available from the corresponding author [Wenming Zhang], upon reasonable request.

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Funding

The authors gratefully acknowledge the support by the National Natural Science Foundation of China (12032015, 12121002), Science and Technology Innovation Action Plan of Shanghai (Grant No. 21190760100), and the China Postdoctoral Science Foundation (Grant No. 2022M722095).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Ge Yan, Jia-Jia Lu, Wen-Hao Qi, Lin-Chuan Zhao, Zhi-Yuan Wu & Wen-Ming Zhang

  2. Shanghai Aerospace Control Technology Institute, 1555 Zhongchun Road, Shanghai, 201109, China

    Feng-Rui Liu

  3. Aerospace System Engineering Shanghai, 3888 Yuanjiang Road, Shanghai, 201108, China

    Han Yan

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  1. Ge Yan
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Yan, G., Lu, JJ., Qi, WH. et al. Linear and nonlinear stiffness compensation for low-frequency vibration isolation: a comparative study. Nonlinear Dyn 112, 5955–5973 (2024). https://doi.org/10.1007/s11071-024-09367-4

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