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A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism

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Abstract

A quasi-zero-stiffness (QZS) vibration isolator is an ideal device for low-frequency vibration isolation. However, its stiffness increases steeply against the displacement, which renders a QZS isolator to be less effective in an ultra-low-frequency range. Aiming at solving this issue, a new nonlinear ultra-low-frequency vibration isolator with a dual quasi-zero-stiffness (DQZS) mechanism is put forward by combining two subordinate QZS mechanisms with a vertical linear spring in parallel. The subordinate mechanism itself has a QZS feature, which provides negative stiffness along the vertical direction through an oblique link rod. The parameter design of the isolator is carried out to fulfil quasi-zero stiffness, which shows that the stiffness–displacement curve is much lower and more flat than the traditional QZS (TQZS) isolator in a wide displacement range. The dynamic behaviours of the DQZS vibration isolation system (VIS) are determined by employing the harmonic balance method, and the vibration isolation performance is evaluated by using theoretical, numerical and experimental transmissibility. It shows that both the beginning frequency of the vibration isolation and the peak transmissibility of the DQZS VIS are lower than the TQZS isolator, which indicates better vibration isolation performance of this ultra-low-stiffness DQZS VIS.

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Acknowledgements

This research work was supported by China Postdoctoral Science Foundation (2020M672476), the National Natural Science Foundation of China (11572116, 11972152, 11702228), the National Key R&D Program of China (2017YFB1102801) and the Hunan Provincial Innovation Foundation for Postgraduate. The first author, Kai Wang, would like to thank the support from the China Scholarship Council (CSC) which sponsors his visit to the University of Liverpool where this work is conducted.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, People’s Republic of China

    Kai Wang, Jiaxi Zhou, Yaopeng Chang & Daolin Xu

  2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Kai Wang, Jiaxi Zhou, Yaopeng Chang & Daolin Xu

  3. School of Engineering, University of Liverpool, Liverpool, L69 3GH, UK

    Huajiang Ouyang

  4. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Yang Yang

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  1. Kai Wang
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Correspondence to Jiaxi Zhou.

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Appendix

Appendix

The following are the detailed expressions of the trigonometry relationships.

$$ \left\{ {\begin{array}{*{20}l} {\cos^{3} \left( {\varOmega \tau } \right) = \frac{1}{4}\cos \left( {3\varOmega \tau } \right) + \frac{3}{4}\cos \left( {\varOmega \tau } \right)} \hfill \\ {\cos^{5} \left( {\varOmega \tau } \right) = \frac{1}{16}\cos \left( {5\varOmega \tau } \right) + \frac{5}{16}\cos \left( {3\varOmega \tau } \right) + \frac{5}{8}\cos \left( {\varOmega \tau } \right)} \hfill \\ {\cos^{7} \left( {\varOmega \tau } \right) = \frac{1}{64}\cos \left( {7\varOmega \tau } \right) + \frac{7}{64}\cos \left( {5\varOmega \tau } \right) + \frac{21}{64}\cos \left( {3\varOmega \tau } \right) + \frac{35}{64}\cos \left( {\varOmega \tau } \right)} \hfill \\ {\cos^{9} \left( {\varOmega \tau } \right) = \frac{1}{256}\cos \left( {9\varOmega \tau } \right) + \frac{9}{256}\cos \left( {7\varOmega \tau } \right) + \frac{9}{64}\cos \left( {5\varOmega \tau } \right)} \hfill \\ {\quad \quad \quad \quad \quad + \frac{21}{64}\cos \left( {3\varOmega \tau } \right) + \frac{63}{128}\cos \left( {\varOmega \tau } \right)} \hfill \\ {\cos^{11} \left( {\varOmega \tau } \right) = \frac{1}{1024}\cos \left( {11\varOmega \tau } \right) + \frac{11}{1024}\cos \left( {9\varOmega \tau } \right) + \frac{55}{1024}\cos \left( {7\varOmega \tau } \right)} \hfill \\ {\quad \quad \quad \quad \quad {\kern 1pt} + \frac{165}{1024}\cos \left( {5\varOmega \tau } \right) + \frac{165}{512}\cos \left( { 3\varOmega \tau } \right){ + }\frac{231}{512}\cos \left( {\varOmega \tau } \right)} \hfill \\ \end{array} } \right. $$
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Wang, K., Zhou, J., Chang, Y. et al. A nonlinear ultra-low-frequency vibration isolator with dual quasi-zero-stiffness mechanism. Nonlinear Dyn 101, 755–773 (2020). https://doi.org/10.1007/s11071-020-05806-0

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