Skip to main content
SpringerLink
Log in

Dynamic characteristics analysis for a quasi-zero-stiffness system coupled with mechanical disturbance

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this paper, an analysis is given about dynamic characteristics for a quasi-zero-stiffness isolator coupled with mechanical disturbance from a view of engineering application. In addition to traditional Columbo friction and linear damping in the vertical direction, the influence of other disturbing parameters such as geometrically nonlinear damping, friction and inertia of rods is also taken into consideration. The dynamic equation is formulated with parameters above to give an investigation of static characteristics, respectively, based on Newton’s second law and D’Alembert’s principle. Moreover, the frequency–amplitude response and transmissibility characteristics are obtained for this model subjected to the vibrating base by using average method with the introduction of piecewise function and then analyze the effect on the vibration response and isolation caused by disturbance. Furthermore, the passive vibration isolation simulation is conducted to verify the theorem. Therefore, it is recommended that the geometrically nonlinear damping can be introduced to the quasi-zero-stiffness system appropriately which can decrease the peak value of transmissibility in the low-frequency range, and nearly has no effect on the high-frequency region. And the mass of the rod should not be bigger than \(10^{-3}\) times of the isolator. The conclusions can provide engineering guidance for design and application about quasi-zero-stiffness system.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Molyneux, W.G.: The support of an aircraft for ground resonance tests: a survey of available methods. Aircr. Eng. Aerosp. Technol. 30, 160–166 (1958). https://doi.org/10.1108/eb032976

    Article  Google Scholar 

  2. Carrella, A., Brennan, M.J., Waters, T.P., et al.: Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 55, 22–29 (2012). https://doi.org/10.1016/j.ijmecsci.2011.11.012

    Article  Google Scholar 

  3. Carrella, A., Brennan, M.J., Waters, T.P., et al.: Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 322, 70–717 (2009). https://doi.org/10.1016/j.jsv.2008.11.034

    Article  Google Scholar 

  4. Carrella, A., Brennan, M.J.: Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 301, 678–689 (2007). https://doi.org/10.1016/j.jsv.2006.10.011

    Article  Google Scholar 

  5. Thanh, D.L., Kyoung, K.A.: Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat. J. Sound Vib. 333, 1245–1268 (2014). https://doi.org/10.1016/j.jsv.2013.10.027

    Article  Google Scholar 

  6. Thanh, D.L., Kyoung, K.A.: Experimental investigation of a vibration isolation system using negative stiffness structure. J. Sound Vib. 330, 6311–6335 (2011). https://doi.org/10.1016/j.ijmecsci.2013.02.009

    Article  Google Scholar 

  7. Wang, X., Zhou, J., Xu, D., et al.: Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness. Nonlinear Dyn. 87, 633–646 (2017). https://doi.org/10.1007/s11071-016-3065-x

    Article  Google Scholar 

  8. Li, Y., Xu, D.: Vibration attenuation of high dimensional quasi-zero stiffness floating raft system. Int. J. Mech. Sci. 126, 186–195 (2017). https://doi.org/10.1016/j.ijmecsci.2017.03.029

    Article  Google Scholar 

  9. Li, Y., Xu, D.: Force transmissibility of floating raft systems with quasi-zero-stiffness isolators. J. Vib. Control 24, 3608–3616 (2018). https://doi.org/10.1177/1077546317708460

    Article  MathSciNet  Google Scholar 

  10. Wang, K., Zhou, J., Xu, D.: Sensitivity analysis of parametric errors on the performance of a torsion quasi-zero-stiffness vibration isolator. Int. J. Mech. Sci. 134, 336–346 (2017). https://doi.org/10.1016/j.ijmecsci.2017.10.026

    Article  Google Scholar 

  11. Zhou, J., Xiao, Q., Xu, D., et al.: A novel quasi-zero-stiffness strut and its applications in six-degree-of-freedom vibration isolation platform. J. Sound Vib. 394, 47–59 (2017). https://doi.org/10.1016/j.jsv.2017.01.021

    Article  Google Scholar 

  12. Tuo, J., Deng, Z., Zhang, H., et al.: A 3-axis torsion quasi-zero-stiffness-based sensor system for angular vibration measurement. J. Vib. Control 24, 4325–4336 (2017). https://doi.org/10.1177/1077546317724016

    Article  MathSciNet  Google Scholar 

  13. Tuo, J., Deng, Z., Huang, W., et al.: A six degree of freedom passive vibration isolator with quasi-zero-stiffness-based supporting. J. Low Freq. Noise Vib. Active Control 37, 279–294 (2017). https://doi.org/10.1177/1461348418756020

    Article  Google Scholar 

  14. Cheng, C., Li, S., Wang, Y., et al.: Resonance response of a quasi-zero stiffness vibration isolator considering a constant force. J. Vib. Eng. Technol. 6, 471–481 (2018). https://doi.org/10.1007/s42417-018-0064-x

    Article  Google Scholar 

  15. Su, P., Wu, J., Liu, S., et al.: A study of a nonlinear magnetic vibration isolator with quasi-zero-stiffness. J. VibroEng. 20, 310–320 (2018). https://doi.org/10.21595/jve.2017.18602

    Article  Google Scholar 

  16. Valeev, A.: Dynamics of a group of quasi-zero stiffness vibration isolators with slightly different parameters. J. Low Freq. Noise Vib. Active Control 37, 640–653 (2018). https://doi.org/10.1177/1461348418756022

    Article  Google Scholar 

  17. Zhou, Y., Chen, P., Mosqueda, G.: Analytical and numerical investigation of quasi-zero stiffness vertical isolation system. J. Eng. Mech. 145, 1–13 (2019). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001611

    Article  Google Scholar 

  18. Liu, X., Zhao, Q., Zhang, Z., et al.: An experiment investigation on the effect of Coulomb friction on the displacement transmissibility of a quasi-zero stiffness isolator. J. Mech. Sci. Technol. 33, 121–127 (2019). https://doi.org/10.1007/s12206-018-1212-7

    Article  Google Scholar 

  19. Margielewicz, J., Gaska, D., Litak, G.: Evolution of the geometric structure of strange attractors of a quasi-zero stiffness vibration isolator. Chaos Solitons Fractals 118, 47–57 (2019). https://doi.org/10.1016/j.chaos.2018.11.012

    Article  MathSciNet  Google Scholar 

  20. Ding, H., Ji, J., Chen, L.: Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mech. Syst. Signal Process. 121, 675–688 (2019). https://doi.org/10.1016/j.ymssp.2018.11.057

    Article  Google Scholar 

  21. Ding, H., Chen, L.: Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators. Nonlinear Dyn. 95(3), 2367–2382 (2019). https://doi.org/10.1007/s11071-018-4697-9

    Article  MATH  Google Scholar 

  22. Cao, Q., Wiercigroch, M., Pavlovskaia, E.E., et al.: Archetypal oscillator for smooth and discontinuous dynamics. Phys. Rev. 74, 1–5 (2006). https://doi.org/10.1103/PhysRevE.74.046218

    Article  MathSciNet  Google Scholar 

  23. Cao, Q., Xiong, Y., Wiercigroch, M.: A novel model of dipteran flight mechanism. Int. J. Dyn. Control 1, 1–11 (2019). https://doi.org/10.1007/s40435-013-0001-5

    Article  Google Scholar 

  24. Cao, Q., Wiercigroch, M., Pavlovskaia, E., et al.: Bifurcations and the penetrating rate analysis of a model for percussive drilling. Acta. Mech. Sin. 26, 467–475 (2010). https://doi.org/10.1007/s10409-010-0346-3

    Article  MathSciNet  MATH  Google Scholar 

  25. Tian, R., Cao, Q., Li, Z.: Hopf bifurcations for the recently proposed smooth-and-discontinuous oscillator. Chin. Phys. Lett. 27, 1–4 (2010). https://doi.org/10.1088/0256-307X/27/7/074701

    Article  Google Scholar 

  26. Tian, R., Cao, Q., Yang, S.: The codimension-two bifurcation for the recent proposed SD oscillator. Nonlinear Dyn. 59, 19–27 (2010). https://doi.org/10.1007/s11071-009-9517-9

    Article  MathSciNet  MATH  Google Scholar 

  27. Han, Y., Cao, Q., Chen, Y., et al.: A novel smooth and discontinuous oscillator with strong irrational nonlinearities. Sci. China Phys. Mech. Astron. 55, 1832–1843 (2012). https://doi.org/10.1007/s11433-012-4880-9

    Article  Google Scholar 

  28. Li, Z., Cao, Q., Wiercigroch, M., et al.: Analysis of the periodic solutions of a smooth and discontinuous oscillator. Acta. Mech. Sin. 29, 575–582 (2013). https://doi.org/10.1007/s10409-013-0061-y

    Article  MathSciNet  MATH  Google Scholar 

  29. Hao, Z., Cao, Q.: The isolation characteristics of an archetypal dynamical model with stable-quasi-zero-stiffness. J. Sound Vib. 340, 61–79 (2015). https://doi.org/10.1016/j.jsv.2014.11.038

    Article  Google Scholar 

  30. Hao, Z., Cao, Q., Wiercigroch, M.: Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses. Nonlinear Dyn. 87, 987–1014 (2017). https://doi.org/10.1007/s11071-016-3093-6

    Article  Google Scholar 

  31. Hao, Z., Cao, Q.: A novel dynamical model for GVT nonlinear supporting system with stable-quasi-zero-stiffness. J. Sound Vib. 52, 199–213 (2014). https://doi.org/10.2140/jomms.2014.9.105

    Article  Google Scholar 

  32. Mostaghel, N., Davis, T.: Representations of Coulomb friction for dynamic analysis. Earthq. Eng. Struct. Dyn. 26, 541–548 (1997). https://doi.org/10.1002/(SICI)1096-9845(199705)26:5<541::AID-EQE660>3.0.CO;2-W

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support from the major project of Natural Science Foundation of China under Grant No. 11732006.

Author information

Authors and Affiliations

  1. Centre for Nonlinear Dynamics Research, School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China

    Xiaohan Zhang, Qingjie Cao & Wenhu Huang

Authors
  1. Xiaohan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingjie Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenhu Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qingjie Cao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

This work was supported by the Natural Science Foundation of China (major program) under 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, X., Cao, Q. & Huang, W. Dynamic characteristics analysis for a quasi-zero-stiffness system coupled with mechanical disturbance. Arch Appl Mech 91, 1449–1467 (2021). https://doi.org/10.1007/s00419-020-01832-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-020-01832-x

Keywords

Search

Navigation