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Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping

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Abstract

A geometric nonlinear damping is proposed and applied to a quasi-zero stiffness (QZS) vibration isolator with the purpose of improving the performance of low-frequency vibration isolation. The force, stiffness and damping characteristics of the system are presented first. The steady-state solutions of the QZS system are obtained based on the averaging method for both force and base excitations and further verified by numerical simulation. The force and displacement transmissibility of the QZS vibration isolator are then analysed. The results indicate that increasing the nonlinear damping can effectively suppress the force transmissibility in resonant region with the isolation performance in higher frequencies unaffected. In addition, the application of the nonlinear damping in the QZS vibration isolator can essentially eliminate the unbounded response for the base excitation. Finally, the equivalent damping ratio is defined and discussed from the viewpoint of vibration control.

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References

  1. Naude, A.F., Snyman, J.A.: Optimisation of road vehicle passive suspension systems. Part 1. Optimisation algorithm and vehicle model. Appl. Math. Model. 27(4), 249–261 (2003)

    Article  MATH  Google Scholar 

  2. Kamesh, D., Pandiyan, R., Ghosal, A.: Passive vibration isolation of reaction wheel disturbances using a low frequency flexible space platform. J. Sound Vib. 331(6), 1310–1330 (2012)

    Article  Google Scholar 

  3. Yao, G.C., Huang, W.C.: Performance of a guideway seismic isolator with magnetic springs for precision machinery. Earthq. Eng. Struct. Dyn. 38(2), 181–203 (2009)

    Article  Google Scholar 

  4. Den Hartog, J.P.: Mechanical Vibrations. McGraw-Hill, New York (1956)

    MATH  Google Scholar 

  5. Alabuzhev, P., Gritchin, A., Kim, L., Migirenko, G., Chon, V., Stepanov, P.: Vibration Protecting and Measuring System with Quasi-Zero Stiffness. Taylor & Francis Group, New York (1989)

    Google Scholar 

  6. Platus, D.L.: Negative-stiffness-mechanism vibration isolation systems. In: Proceedings of SPIE’s International Symposium on Vibration Control in Microelectronics, pp. 44–54 (1991)

  7. Carrella, A., Brennan, M.J., Waters, T.P.: Static analysis of a passive vibration isolation with quasi-zero-stiffness characteristic. J. Sound Vib. 301(3–5), 678–689 (2007)

    Article  Google Scholar 

  8. Carrella, A., Brennan, M.J., Waters, T.P., Lopes, JrV: Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. Int. J. Mech. Sci. 55(1), 22–29 (2012)

    Article  Google Scholar 

  9. 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(26), 6311–6335 (2011)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. Liu, X., Huang, X., Hua, H.: On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vib. 332(14), 3359–3376 (2013)

    Article  Google Scholar 

  12. Huang, X., Liu, X., Sun, J., Zhang, Z., Hua, H.: Effect of the system imperfections on the dynamic response of a high-static-low-dynamic stiffness vibration isolator. Nonlinear Dyn. 76(2), 1157–1167 (2014)

    Article  MathSciNet  Google Scholar 

  13. Xu, D., Yu, Q., Zhou, J., Bishop, S.R.: Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 332(14), 3377–3389 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Meng, L., Sun, J., Wu, W.: Theoretical design and characteristics analysis of a quasi-zero stiffness isolator using a disk spring as negative stiffness element. Shock Vib. 2015, 1–19 (2015)

    Google Scholar 

  16. Ibrahim, R.A.: Recent advances in nonlinear passive vibration isolators. J. Sound Vib. 314(3–5), 371–452 (2008)

    Article  Google Scholar 

  17. Lang, Z.Q., Jing, X.J., Billings, S.A., Tomlinson, G.R., Peng, Z.K.: Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems. J. Sound Vib. 323(1), 352–365 (2009)

    Article  Google Scholar 

  18. Milovanovic, Z., Kovacic, I., Brennan, M.J.: On the displacement transmissibility of a base excited viscously damped nonlinear vibration isolator. J. Vib. Acoust. 131(5), 054502 (2009)

    Article  Google Scholar 

  19. Guo, P.F., Lang, Z.Q., Peng, Z.K.: Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Nonlinear Dyn. 67(4), 2671–2687 (2012)

  20. Peng, Z.K., Lang, Z.Q., Jing, X.J., Billings, S.A., Tomlinson, G.R., Guo, L.Z.: The transmissibility of vibration isolators with a nonlinear antisymmetric damping characteristic. J. Vib. Acoust. 132(1), 014501 (2010)

    Article  Google Scholar 

  21. Lee, D., Taylor, D.P.: Viscous damper development and future trends. Struct. Design Tall Build. 10(5), 311–320 (2001)

    Article  Google Scholar 

  22. Lv, Q., Yao, Z.: Analysis of the effects of nonlinear viscous damping on vibration isolator. Nonlinear Dyn. 79(4), 2325–2332 (2015)

    Article  MathSciNet  Google Scholar 

  23. Tang, B., Brennan, M.J.: A comparison of two nonlinear damping mechanisms in a vibration isolator. J. Sound Vib. 332(3), 510–520 (2013)

    Article  Google Scholar 

  24. Sun, J., Huang, X., Liu, X., Xiao, F., Hua, H.: Study on the force transmissibility of vibration isolators with geometric nonlinear damping. Nonlinear Dyn. 74(4), 1103–1112 (2013)

    Article  Google Scholar 

  25. Cheng, C., Li, S., Wang, Y., Jiang, X.: On the analysis of a piecewise nonlinear-linear vibration isolator with high-static-low-dynamic-stiffness under base excitation. J. Vibroeng. 17(7), 3453–3470 (2015)

    Google Scholar 

  26. Nayfeh, A.H., Mook, D.T.: Nonlinear oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

  27. Savadkoohi, A.T., Lamarque, C.H., Dimitrijevic, Z.: Vibratory energy exchange between a linear and a nonsmooth system in the presence of the gravity. Nonlinear Dyn. 70(2), 1473–1483 (2012)

    Article  MathSciNet  Google Scholar 

  28. Starosvetsky, Y., Gendelman, O.V.: Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry. Phys. D 237(13), 1719–1733 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  29. Jazar, G.N., Houim, R., Narimani, A., Golnaraghi, M.F.: Frequency response and jump avoidance in a nonlinear passive engine mount. J. Vib. Control 12(11), 1205–1237 (2006)

    Article  MATH  Google Scholar 

  30. Hu, H., Dowell, E.H., Virgin, L.N.: Resonances of a harmonically forced Duffing oscillator with time delay state feedback. Nonlinear Dyn. 15(4), 311–327 (1998)

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Funding of Jiangsu Innovation Program for Graduate Education (KYLX15_0256), the National Natural Science Foundation of China (51675262), the Open Project of State Key Laboratory for Strength and Vibration of Mechanical Structures (SV2015-KF-01) and the Fundamental Research Funds for the Central Universities (XZA15003).

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Authors and Affiliations

  1. College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Chun Cheng, Shunming Li, Yong Wang & Xingxing Jiang

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  1. Chun Cheng
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  2. Shunming Li
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  3. Yong Wang
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  4. Xingxing Jiang
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Correspondence to Chun Cheng.

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Cheng, C., Li, S., Wang, Y. et al. Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping. Nonlinear Dyn 87, 2267–2279 (2017). https://doi.org/10.1007/s11071-016-3188-0

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  • DOI: https://doi.org/10.1007/s11071-016-3188-0

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