Skip to main content
Log in

Isolation performances and optimization of triple quasi-zero stiffness isolators

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

In this paper, triple quasi-zero stiffness (QZS) passive vibration isolators whose restoring force curve has a three-stage softening effect are proposed. Multi-coupled SD oscillators with three independent geometrical parameters are used as negative stiffness mechanisms to achieve QZS characteristics at the origin and symmetrical positions on both sides of the origin. Isolation performances of different triple QZS isolators are analyzed to show influences of the selection of QZS regions away from the origin on the range of isolation regions. Pareto optimizations of system parameters are carried out to get a larger range of small restoring force regions and small stiffness regions. Isolation performances of two triple QZS isolators are discussed to show the influence of different Pareto optimization solutions through the comparisons with single and double QZS isolators. Results showed that triple QZS isolators have both the advantages of single and double QZS isolators which results in better isolation performances under both small and large excitation amplitudes. An improvement in isolation performances for triple QZS isolators is found with the decrease in average stiffness due to the appearance of two symmetrical QZS regions away from the origin. Larger displacements of QZS regions away from the origin result in better isolation performances when excitation amplitude is large, and triple QZS characteristics are similar to double QZS isolators at this time. Smaller restoring forces of QZS regions away from the origin lead to better isolation performances when excitation amplitude is small, and triple QZS characteristics are similar to single QZS isolators at this moment. Compared with the decrease in average stiffness, the improvement of isolation performances shows a hysteresis phenomenon due to the difference between static and dynamic characteristics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. A. Ibrahim, J. Sound Vib. 314, 371 (2008).

    Article�� ADS  Google Scholar 

  2. J. C. Ji, Q. Luo, and K. Ye, Mech. Syst. Signal Process. 161, 107945 (2021).

    Article  Google Scholar 

  3. Y. Zhang, and Q. Cao, Int. J. Mech. Sci. 214, 106904 (2022).

    Article  Google Scholar 

  4. W. Zhang, W. Q. Cheng, W. You, X. Chen, J. Zhang, C. Li, and C. Fang, Sci. China-Phys. Mech. Astron. 65, 289604 (2022).

    Article  ADS  Google Scholar 

  5. C. Li, C. Fang, Z. Li, M. D. Ding, P. F. Chen, Y. Qiu, W. You, Y. Yuan, M. J. An, H. J. Tao, X. S. Li, Z. Chen, Q. Liu, G. Mei, L. Yang, W. Zhang, W. Q. Cheng, J. X. Chen, C. Y. Chen, Q. Gu, Q. L. Huang, M. X. Liu, C. S. Han, H. W. Xin, C. Z. Chen, Y. W. Ni, W. B. Wang, S. H. Rao, H. T. Li, X. Lu, W. Wang, J. Lin, Y. X. Jiang, L. J. Meng, and J. Zhao, Sci. China-Phys. Mech. Astron. 65, 289602 (2022), arXiv: 2205.05962.

    Article  ADS  Google Scholar 

  6. W. G. Molyneux, Aircr. Eng. Aerosp. Tech. 30, 160 (1958).

    Article  Google Scholar 

  7. I. Kovacic, M. J. Brennan, and T. P. Waters, J. Sound Vib. 315, 700 (2008).

    Article  ADS  Google Scholar 

  8. A. Carrella, M. J. Brennan, I. Kovacic, and T. P. Waters, J. Sound Vib. 322, 707 (2009).

    Article  ADS  Google Scholar 

  9. G. Gatti, I. Kovacic, and M. J. Brennan, J. Sound Vib. 329, 1823 (2010).

    Article  ADS  Google Scholar 

  10. J. Yang, Y. P. Xiong, and J. T. Xing, J. Sound Vib. 332, 167 (2013).

    Article  ADS  Google Scholar 

  11. Z. Hao, and Q. Cao, J. Sound Vib. 340, 61 (2015).

    Article  ADS  Google Scholar 

  12. L. Meng, J. Sun, and W. Wu, Shock Vib. 2015, 1 (2015).

    Google Scholar 

  13. A. Carrella, M. J. Brennan, T. P. Waters, and K. Shin, J. Sound Vib. 315, 712 (2008).

    Article  ADS  Google Scholar 

  14. J. L. Wu, J. X. Che, X. D. Chen, and W. Jiang, Sci. China Tech. Sci. 65, 2127 (2022).

    Article  ADS  Google Scholar 

  15. Y. Shi, S. F. Xu, Z. L. Li, Y. X. Wang, Y. L. Nie, and Z. B. Sun, Sci. China Tech. Sci. 66, 2013 (2023).

    Article  Google Scholar 

  16. N. Y. P. Vo, M. K. Nguyen, and T. D. Le, Commun. Nonlinear Sci. Numer. Simul. 98, 105775 (2021).

    Article  Google Scholar 

  17. X. Shi, J. Xu, T. Chen, Q. Cong, and W. Tian, J. Vib. Control 29, 3357 (2023).

    Article  Google Scholar 

  18. Y. Song, C. Zhang, Z. Li, Y. Li, J. Lian, Q. Shi, and B. Yan, J. Vib. Control 28, 1470 (2022).

    Article  MathSciNet  Google Scholar 

  19. X. Sun, Z. Qi, and J. Xu, Int. J. Non-Linear Mech. 147, 104245 (2022).

    Article  ADS  Google Scholar 

  20. X. Sun, F. Wang, and J. Xu, Int. J. Mech. Sci. 193, 106166 (2021).

    Article  Google Scholar 

  21. X. Sun, Z. Qi, and J. Xu, Acta Mech. Sin. 38, 521543 (2022).

    Article  Google Scholar 

  22. J. Zhou, K. Wang, D. Xu, H. Ouyang, and Y. Li, J. Vib. Acoust. 139, 034502 (2017).

    Article  Google Scholar 

  23. X. Sun, and X. Jing, Mech. Syst. Signal Process. 62–63, 149 (2015).

    Article  ADS  Google Scholar 

  24. X. Sun, J. Xu, X. Jing, and L. Cheng, Int. J. Mech. Sci. 82, 32 (2014).

    Article  Google Scholar 

  25. T. Yang, and Q. Cao, Int. J. Non-Linear Mech. 110, 81 (2019).

    Article  ADS  Google Scholar 

  26. L. Wang, Y. Zhao, T. Sang, H. Zhou, P. Wang, and C. Zhao, Vehicle Syst. Dyn. 60, 1788 (2022).

    Article  ADS  Google Scholar 

  27. G. N. Zhu, J. Y. Liu, Q. J. Cao, Y. F. Cheng, Z. C. Lu, and Z. B. Zhu, Sci. China Tech. Sci. 63, 496 (2020).

    Article  Google Scholar 

  28. J. Zhou, D. Xu, and S. Bishop, J. Sound Vib. 338, 121 (2015).

    Article  ADS  Google Scholar 

  29. G. Gatti, Mech. Syst. Signal Process. 180, 109379 (2022).

    Article  Google Scholar 

  30. G. Gatti, Commun. Nonlinear Sci. Numer. Simul. 83, 105143 (2020).

    Article  MathSciNet  Google Scholar 

  31. G. Gatti, Shock Vib. 2021, 5556088 (2021).

    Article  Google Scholar 

  32. G. Gatti, and C. Svelto, J. Vib. Control 29, 5713 (2023).

    Article  MathSciNet  Google Scholar 

  33. F. Zhao, J. Ji, Q. Luo, S. Cao, L. Chen, and W. Du, Nonlinear Dyn. 104, 349 (2021).

    Article  Google Scholar 

  34. F. Zhao, J. Ji, K. Ye, and Q. Luo, Int. J. Mech. Sci. 192, 106093 (2021).

    Article  Google Scholar 

  35. J. Bian, and X. Jing, Nonlinear Dyn. 101, 2195 (2020).

    Article  Google Scholar 

  36. Y. Chai, X. Jing, and X. Chao, Int. J. Mech. Sci. 218, 107077 (2022).

    Article  Google Scholar 

  37. X. Jing, Y. Chai, X. Chao, and J. Bian, Mech. Syst. Signal Process. 170, 108267 (2022).

    Article  Google Scholar 

  38. Q. Cao, M. Wiercigroch, E. E. Pavlovskaia, C. Grebogi, and J. M. T. Thompson, Phys. Rev. E 74, 046218 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  39. L. Wang, L. Xue, W. Xu, and X. Yue, Int. J. Non-Linear Mech. 96, 56 (2017).

    Article  ADS  Google Scholar 

  40. H. Chen, J. Llibre, and Y. Tang, Nonlinear Dyn. 91, 1755 (2018).

    Article  Google Scholar 

  41. Y. W. Han, Q. J. Cao, Y. S. Chen, and M. Wiercigroch, Sci. China-Phys. Mech. Astron. 55, 1832 (2012).

    Article  ADS  Google Scholar 

  42. B. Zhou, Y. Jin, and H. Xu, Appl. Math. Model. 108, 427 (2022).

    Article  MathSciNet  Google Scholar 

  43. B. Zhou, Y. Jin, and H. Xu, Chaos Soliton. Fract. 162, 112509 (2022).

    Article  Google Scholar 

  44. Y. Han, Q. Cao, and J. Ji, Int. J. Bifurcat. Chaos 25, 1530038 (2015).

    Article  Google Scholar 

  45. X. Huang, and Q. Cao, Int. J. Bifurcat. Chaos 33, 2330031 (2023).

    Article  Google Scholar 

  46. N. Han, and Q. Cao, Int. J. Mech. Sci. 127, 91 (2017).

    Article  Google Scholar 

  47. T. Yang, and Q. Cao, Arch Appl Mech 92, 801 (2022).

    Article  Google Scholar 

  48. G. Zhu, Q. Cao, Z. Wang, Y. Zhang, Y. Chen, and K. C. Woo, Sci. Rep. 12, 21167 (2022).

    Article  ADS  Google Scholar 

  49. A. Carrella, M. J. Brennan, and T. P. Waters, J. Mech. Sci. Technol. 21, 946 (2007).

    Article  Google Scholar 

  50. X. Xu, H. Liu, X. Jiang, and A. V. Atindana, Chin. J. Mech. Eng. 35, 93 (2022).

    Article  Google Scholar 

  51. G. Zhu, X. Du, W. Liu, Q. Cao, K. Lu, Y. Guo, T. Yang, Y. Chen, C. Wei, and J. Pu, Mech. Syst. Signal Process. 208, 110985 (2024).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qingjie Cao.

Ethics declarations

Conflict of interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11732006).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Y., Zhu, G. & Cao, Q. Isolation performances and optimization of triple quasi-zero stiffness isolators. Sci. China Phys. Mech. Astron. 67, 274511 (2024). https://doi.org/10.1007/s11433-023-2371-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-023-2371-0

Navigation