Skip to main content
Log in

Accurate modeling and analysis of a typical nonlinear vibration isolator with quasi-zero stiffness

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

A typical quasi-zero stiffness (QZS) vibration isolator composed of two lateral springs and a vertical spring has been widely studied previously, aiming to widen the frequency range of isolation without increasing the static displacement. However, there is still a gap between the previous dynamic model and the practical application, due to the neglection of some factors that may exist in practical situations. In this paper, a more accurate dynamic model is established with consideration of these practical factors. The dynamic behavior and dynamic characteristics of this typical QZS isolator are analyzed based upon the accurate dynamic model. The biggest difference between the newly proposed dynamic model and the previous one lies in the damping characteristics. Therefore, we specially investigate the damping effects, from which it is found that the vibration isolation performance can be further enhanced by proper design of the damping parameters.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Carrella, A.: Passive vibration isolators with high-static–low-dynamic stiffness. Ph.D. thesis, University of Southampton, ISVR (2008)

  2. Ibrahim, R.A.: Recent advances in nonlinear passive vibration isolators. J. Sound Vib. 314, 371–452 (2008)

    Google Scholar 

  3. Liu, C.R., Yu, K.P.: A high-static–low-dynamic-stiffness vibration isolator with the auxiliary system. Nonlinear Dyn. 94, 1549–1567 (2018)

    Google Scholar 

  4. Liu, C.R., Yu, K.P.: Superharmonic resonance of the quasi-zero-stiffness vibration isolator and its effect on the isolation performance. Nonlinear Dyn. (2020). https://doi.org/10.1007/s11071-020-05509-6

    Article  Google Scholar 

  5. Carrella, A., Brennan, M.J., Waters, T.P.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301, 678–689 (2007)

    Google Scholar 

  6. Carrella, A., Brennan, M.J., Waters, T.P.: Optimization of a quasi-zero-stiffness isolator. J. Mech. Sci. Technol. 21, 946–949 (2007)

    Google Scholar 

  7. Carrella, A., Brennan, M.J., Kovacic, I., Waters, T.P.: On the force transmissibility of a vibration isolator with quasi-zero stiffness. J. Sound Vib. 322, 707–717 (2009)

    Google Scholar 

  8. Carrella, A., Brennan, M.J., Waters, T.P., Lopes Jr., V.: Force and displacement transmissibility of a nonlinear isolator with high-static–low-dynamic-stiffness. Int. J. Mech. Sci. 55, 22–29 (2012)

    Google Scholar 

  9. Carrella, A., Friswell, M.I., Zotov, A., Ewins, D.J., Tichonov, A.: Using nonlinear springs to reduce the whirling of a rotating shaft. Mech. Syst. Signal Process. 23, 2228–2235 (2009)

    Google Scholar 

  10. Kovacic, I., Brennan, M.J., Waters, T.P.: A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. J. Sound Vib. 315, 700–711 (2008)

    Google Scholar 

  11. Hao, Z.F., Cao, Q.J.: The isolation characteristics of an archetypal dynamical model with stable-quasi-zero-stiffness. J. Sound Vib. 340, 61–79 (2015)

    Google Scholar 

  12. Hao, Z.F., Cao, Q.J.: Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses. Nonlinear Dyn. 87, 987–1014 (2017)

    Google Scholar 

  13. Lan, C.C., Yang, S.A., Wu, Y.S.: Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads. J. Sound Vib. 333, 4843–4858 (2014)

    Google Scholar 

  14. Ramirez, D.F.L., Ferguson, N.S., Brennan, M.J., Tang, B.: An experimental nonlinear low dynamic stiffness device for shock isolation. J. Sound Vib. 347, 1–13 (2015)

    Google Scholar 

  15. Zhou, J.X., Wang, X.L., Xu, D.L., Bishop, S.: Nonlinear dynamic characteristics of a quasi-zero stiffness vibration isolator with cam–roller–spring mechanisms. J. Sound Vib. 346, 53–69 (2015)

    Google Scholar 

  16. Le, T.D., Ahn, K.K.: Experimental investigation of a vibration isolation system using negative stiffness structure. Int. J. Mech. Sci. 70, 99–112 (2013)

    Google Scholar 

  17. Le, T.D., Ahn, K.K.: A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat. J. Sound Vib. 330, 6311–6335 (2011)

    Google Scholar 

  18. Sun, X.T., Jing, X.J.: Analysis and design of a nonlinear stiffness and damping system with a scissor-like structure. Mech. Syst. Signal Process. 66–67, 723–742 (2016)

    Google Scholar 

  19. Sun, X.T., Jing, X.J., Xu, J., Cheng, L.: Vibration isolation via a scissor-like structured platform. J. Sound Vib. 333, 2404–2420 (2014)

    Google Scholar 

  20. Sun, X.T., Jing, X.J.: A nonlinear vibration isolator achieving high-static–low-dynamic stiffness and tunable anti-resonance frequency band. Mech. Syst. Signal Process. 80, 166–188 (2016)

    Google Scholar 

  21. Wu, Z.J., Jing, X.J., Bian, J., Li, F.M., Allen, R.: Vibration isolation by exploring bio-inspired structural nonlinearity. Bioinspir. Biomin. 10, 056015 (2015)

    Google Scholar 

  22. Zhang, W., Zhao, J.B.: Analysis on nonlinear stiffness and vibration isolation performance of scissor-like structure with full types. Nonlinear Dyn. 86, 17–36 (2016)

    Google Scholar 

  23. Liu, C.C., Jing, X.J., Li, F.M.: Vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure. Int. J. Mech. Sci. 98, 169–177 (2015)

    Google Scholar 

  24. Liu, C.C., Jing, X.J., Chen, Z.B.: Band stop vibration suppression using a passive X-shape structured lever-type isolation system. Mech. Syst. Signal Process. 68–69, 342–353 (2016)

    Google Scholar 

  25. Liu, X.T., Huang, X.C., Hua, H.X.: On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vib. 332, 3359–3376 (2013)

    Google Scholar 

  26. Huang, X.C., Liu, X.T., Sun, J.Y., Zhang, Z.Y., Hua, H.X.: Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: a theoretical and experimental study. J. Sound Vib. 333, 1132–1148 (2014)

    Google Scholar 

  27. Huang, X.C., Liu, X.T., Sun, J.Y., Zhang, Z.Y., Hua, H.X.: Effect of the system imperfections on the dynamic response of a high-static–low-dynamic stiffness vibration isolator. Nonlinear Dyn. 76, 1157–1167 (2014)

    MathSciNet  Google Scholar 

  28. Fulcher, B.A., Shahan, D.W., Haberman, M.R., Seepersad, C.C., Wilson, P.S.: Analytical and experimental investigation of buckled beams as negative stiffness elements for passive vibration and shock isolation systems. J. Vib. Acoust. 136, 031009 (2014)

    Google Scholar 

  29. Huang, X.C., Liu, X.T., Hua, H.X.: On the characteristics of an ultra-low frequency nonlinear isolator using sliding beam as negative stiffness. J. Mech. Sci. Technol. 28, 813–822 (2014)

    Google Scholar 

  30. Ding, H., Chen, L.Q.: Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dyn. 95, 2367–2382 (2019)

    MATH  Google Scholar 

  31. Robertson, W.S., Kidner, M.R.F., Cazzolato, B.S., Zander, A.C.: Theoretical design parameters for a quasi-zero stiffness magnetic spring for vibration isolation. J. Sound Vib. 326, 88–103 (2009)

    Google Scholar 

  32. Li, Q., Zhu, Y., Xu, D.F., Hu, J.C., Min, W., Pang, L.C.: A negative stiffness vibration isolator using magnetic spring combined with rubber membrane. J. Mech. Sci. Technol. 27, 813–824 (2013)

    Google Scholar 

  33. Zheng, Y.S., Zhang, X.N., Luo, Y.J., Zhang, Y.H., Xie, S.L.: Analytical study of a quasi-zero stiffness coupling using a torsion magnetic spring with negative stiffness. Mech. Syst. Signal Process. 100, 135–151 (2018)

    Google Scholar 

  34. Li, H., Zhang, J.: Design and analysis of a magnetic QZS vibration isolator. Appl. Mech. Mater. 470, 484–488 (2013)

    Google Scholar 

  35. Zhou, N., Liu, K.: A tunable high-static–low-dynamic stiffness vibration isolator. J. Sound Vib. 329, 1254–1273 (2010)

    Google Scholar 

  36. Wu, W.J., Chen, X.D., Shan, Y.H.: Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness. J. Sound Vib. 333, 2958–2970 (2014)

    Google Scholar 

  37. Zheng, Y.S., Zhang, X.N., Luo, Y.J., Yan, B., Ma, C.C.: Design and experiment of a high-static–low-dynamic stiffness isolator using a negative stiffness magnetic spring. J. Sound Vib. 360, 31–52 (2016)

    Google Scholar 

  38. Carrella, A., Brennan, M.J., Waters, T.P., Shin, K.: On the design of a high-static–low-dynamic stiffness isolator using linear mechanical springs and magnets. J. Sound Vib. 315, 712–720 (2008)

    Google Scholar 

  39. Dong, G.X., Zhang, X.N., Xie, S.L., Yan, B., Luo, Y.J.: Simulated and experimental studies on a high-static–low-dynamic stiffness isolator using magnetic negative stiffness spring. Mech. Syst. Signal Process. 86, 188–203 (2017)

    Google Scholar 

  40. Robertson, W., Cazzolato, B., Zander, A.: Theoretical analysis of a non-contact spring with inclined permanent magnets for load-independent resonance frequency. J. Sound Vib. 331, 1331–1341 (2012)

    Google Scholar 

  41. Xu, D.L., Yu, Q.P., Zhou, J.X., Bishop, S.R.: Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 332, 3377–3389 (2013)

    Google Scholar 

  42. Shin, K.: On the performance of a single degree-of-freedom high-static–low-dynamic stiffness magnetic vibration isolator. Int. J. Precis. Eng. Manuf. 15, 439–445 (2014)

    Google Scholar 

  43. Zhu, T., Cazzolato, B., Robertson, W.S.P., Zander, A.: Vibration isolation using six degree-of-freedom quasi-zero stiffness magnetic levitation. J. Sound Vib. 358, 48–73 (2015)

    Google Scholar 

  44. Wang, X.L., Zhou, J.X., Xu, D.L., Ouyang, H.J., Duan, Y.: Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dyn. 87, 633–646 (2017)

    Google Scholar 

  45. Wang, Y., Li, S.M., Neild, S.A., Jiang, J.Z.: Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness. Nonlinear Dyn. 88, 635–654 (2017)

    Google Scholar 

  46. Lu, Z.Q., Brennan, M.J., Yang, T.J., Li, X.H., Liu, Z.G.: An investigation of a two-stage nonlinear vibration isolation system. J. Sound Vib. 332, 1456–1464 (2013)

    Google Scholar 

  47. Lu, Z.Q., Yang, T.J., Brennan, M.J., Liu, Z.G., Chen, L.Q.: Experimental investigation of a two-stage nonlinear vibration isolation system with high-static–low-dynamic stiffness. J. Appl. Mech. 84, 021001 (2017)

    Google Scholar 

  48. Zhou, J.X., Xiao, Q.Y., Xu, D.L., Ouyang, H.J., Li, Y.L.: A novel quasi-zero-stiffness strut and its applications in six-degree-of-freedom vibration isolation platform. J. Sound Vib. 394, 59–74 (2017)

    Google Scholar 

  49. Wu, Z.J., Jing, X.J., Sun, B., Li, F.M.: A 6DOF passive vibration isolator using X-shape supporting structures. J. Sound Vib. 380, 90–111 (2016)

    Google Scholar 

  50. Hu, F.Z., Jing, X.J.: A 6-DOF passive vibration isolator based on Stewart structure with X-shaped legs. Nonlinear Dyn. 91, 157–185 (2018)

    Google Scholar 

  51. Zhou, J.X., Wang, K., Xu, D.L., Ouyang, H.J., Li, Y.L.: A six degrees-of-freedom vibration isolation platform supported by a hexapod of quasi-zero-stiffness struts. J. Vib. Acoust. 139, 034502 (2017)

    Google Scholar 

  52. Zheng, Y.S., Li, Q.P., Yan, B., Luo, Y.J., Zhang, X.N.: A Stewart isolator with high-static–low-dynamic stiffness struts based on negative stiffness magnetic springs. J. Sound Vib. 422, 390–408 (2018)

    Google Scholar 

  53. Liu, C.R., Yu, K.P., Pang, S.W.: A novel eight-legged vibration isolation platform with dual-pyramid-shape struts. Meccanica 54, 873–899 (2019)

    MathSciNet  Google Scholar 

  54. Dong, G.X., Zhang, Y.H., Luo, Y.J., Xie, S.L., Zhang, X.N.: Enhanced isolation performance of a high-static–low-dynamic stiffness isolator with geometric nonlinear damping. Nonlinear Dyn. 93, 2339–2356 (2018)

    Google Scholar 

  55. Cheng, C., Li, S.M., Wang, Y., Jiang, X.X.: Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping. Nonlinear Dyn. 87, 2267–2279 (2017)

    Google Scholar 

  56. Meng, Q.G., Yang, X.F., Li, W., Lu, E., Sheng, L.C.: Research and analysis of quasi-zero-stiffness isolator with geometric nonlinear damping. Shock Vib. 2017, 6719054 (2017)

    Google Scholar 

  57. Milovanovic, Z., Kovacic, I., Brennan, M.J.: On the displacement transmissibility of a base excited viscously damped nonlinear vibration isolator. J. Vib. Acoust. 131, 054502 (2019)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank Prof. Zhao for the helpful suggestions on the results presented in this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kaiping Yu.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, C., Yu, K. Accurate modeling and analysis of a typical nonlinear vibration isolator with quasi-zero stiffness. Nonlinear Dyn 100, 2141–2165 (2020). https://doi.org/10.1007/s11071-020-05642-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05642-2

Keywords

Navigation