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Inerter-Based Isolation System

  • Michael Z. Q. ChenEmail author
  • Yinlong Hu
Chapter

Abstract

This chapter is concerned with the problem of analysis and optimization of the inerter-based isolators based on a “uni-axial” single-degree-of-freedom isolation system. In the first part, in order to gain an in-depth understanding of inerter from the prospective of vibration, the frequency responses of both parallel-connected and series-connected inerters are analyzed. In the second part, three other inerter-based isolators are introduced and the tuning procedures in both the \(H_\infty \) optimization and the \(H_2\) optimization are proposed in an analytical manner. The achieved \(H_2\) and \(H_\infty \) performance of the inerter-based isolators is superior to that achieved by the traditional dynamic vibration absorber (DVA) when the same inertance-to-mass (or mass) ratio is considered. Moreover, the inerter-based isolators have two unique properties, which are more attractive than the traditional DVA: first, the inertance-to-mass ratio of the inerter-based isolators can easily be larger than the mass ratio of the traditional DVA without increasing the physical mass of the whole system; second, there is no need to mount an additional mass on the object to be isolated.

Keywords

Vibration isolation \(H_\infty \) optimization \(H_2\) optimization Transmissibility Analytical analysis. 

References

  1. Asami, T., Wakasono, T., Kameoka, K., Hasegawa, M., & Sekiguchi, H. (1991). Optimum design of dynamic absorbers for a system subjected to random excitation. JSME International Journal Series III, 34(2), 218–226.Google Scholar
  2. Carrella, A., Brennan, M. J., Waters, T. P., & Lopes, V, Jr. (2012). Force and displacment transimissibility of a nonlinear isolator with high-static-low-dynamic-stiffness. International Journal of Mechanical Sciences, 55(1), 22–29.CrossRefGoogle Scholar
  3. Chen, M. Z. Q., Papageorgiou, C., Scheibe, F., Wang, F. C., & Smith, M. C. (2009). The missing mechanical circuit element. IEEE Circuits and Systems Magazine, 9(1), 10–26.CrossRefGoogle Scholar
  4. Chen, M. Z. Q., Hu, Y., Li, C., & Chen, G. (2015). Performance benefits of using inerter in semiactive suspensions. IEEE Transactions on Control System Technology, 23(4), 1571–1577.CrossRefGoogle Scholar
  5. Chen, M. Z. Q., Hu, Y., Huang, L., & Chen, G. (2014). Influence of inerter on natural frequencies of vibration systems. Journal of Sound and Vibration, 333(7), 1874–1887.CrossRefGoogle Scholar
  6. Cheung, Y. L., & Wong, W. O. (2011a). H-infinity optimization of a variant design of the dynamic vibration absorber-Revisited and new results. Journal of Sound and Vibration, 330(16), 3901–3912.CrossRefGoogle Scholar
  7. Cheung, Y. L., & Wong, W. O. (2011b). \({H_{2}}\) optimization of a non-traditional dynamic vibration abosorber for vibration control of structures under random force excitation. Journal of Sound and Vibration, 330(6), 1039–1044.CrossRefGoogle Scholar
  8. Den Hartog, J. P. (1985). Mechanical Vibrations. New York: Dover Publications, INC.zbMATHGoogle Scholar
  9. Doyle, J. C., Francis, B. A., & Tannenbaum, A. R., et al. (1992). Feedback Control Theory. Oxford: Maxwell Macmillan Int.Google Scholar
  10. Dylejko, P. G., & MacGillivray, I. R. (2014). On the concept of a transmission absorber to suppress internal resonance. Journal of Sound and Vibration, 333, 2719–2734.CrossRefGoogle Scholar
  11. Hu, Y., Chen, M. Z. Q., & Shu, Z. (2014). Passive vehicle suspensions employing inerters with multiple performance requirements. Journal of Sound and Vibration, 333(8), 2212–2225.CrossRefGoogle Scholar
  12. Hu, Y., Chen, M. Z. Q., Shu, Z., & Huang, L. (2014). Vibration analysis for isolation system with inerter. In Proceedings of the 33rd Chinese Control Conference (pp. 6687–6692). China: Nanjing.Google Scholar
  13. Inman, D. J. (2008). Engineering Vibration (3rd ed.). Upper Saddle River: Prentice-Hall Inc.Google Scholar
  14. Lazar, I. F., Neild, S. A., & Wagg, D. J. (2014). Using an inerter-based device for structural vibration suppression. Earthquake Engineering and Structure Dynamics, 43(8), 1129–1147.CrossRefGoogle Scholar
  15. Marian, L., & Giaralis, A. (2014). Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems. Probabilistic Engineering Mechanics, 38, 156–164.CrossRefGoogle Scholar
  16. Nishihara, O., & Asami, T. (2002). Closed-form solutions to the exact optimizations of dynamic vibration absorbers (minimizations of the maximum amplitude magnification factors). Journal of Vibration and Acoustics, 124(4), 576–582.CrossRefGoogle Scholar
  17. Ren, M. Z. (2001). A variant design of the dynamic vibration absorber. Journal of Sound and Vibration, 245(4), 762–770.CrossRefGoogle Scholar
  18. Rivin, E. I. (2003). Passive Vibration Isolation. New York: ASME Press.CrossRefGoogle Scholar
  19. Piersol, A. G., & Paez, T. L. (2010). Harris’ Shock and Vibration Handbook (6th ed.). New York: McGraw-Hill.Google Scholar
  20. Scheibe, F., & Smith, M. C. (2009). Analytical solutions for optimal ride comfort and tyre grip for passive vehicle suspensions. Vehile System Dynamics, 47(10), 1229–1252.CrossRefGoogle Scholar
  21. Smith, M. C. (2002). Synthesis of mechanical networks: The inerter. IEEE Transaction on Automatic Control, 47(1), 1648–1662.MathSciNetCrossRefGoogle Scholar
  22. Smith, M. C., & Wang, F. C. (2004). Performance benefits in passive vehicle suspensions employing inerters. Vehicle System Dynamics, 42(4), 235–257.CrossRefGoogle Scholar
  23. Wang, F.-C., & Chan, H. A. (2011). Vehicle suspensions with a mechatronic network strut. Vehicle System Dynamics, 49(5), 811–830.CrossRefGoogle Scholar
  24. Wang, F.-C., Hsieh, M.-R., & Chen, H.-J. (2012). Stability and performance analysis of a full-train system with inerters. Vehicle System Dynamics, 50(4), 545–571.CrossRefGoogle Scholar
  25. Wang, K., Chen, M. Z. Q., & Hu, Y. (2014). Synthesis of biquadratic impedances with at most four passive elements. Journal of the Franklin Institute, 351(3), 1251–1267.CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. and Science Press, Beijing 2019

Authors and Affiliations

  1. 1.School of AutomationNanjing University of Science and TechnologyNanjingChina
  2. 2.College of Energy and Electrical EngineeringHohai UniversityNanjingChina

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