Advertisement

Introduction

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

Abstract

Inerter is a new mechanical element proposed by Professor Malcolm C. Smith from Cambridge University, which is defined as a mechanical two-terminal, one-port device with the property that the equal and opposite force applied at the terminals is proportional to the relative acceleration between the terminals (Smith in IEEE Tran Autom Control 47(1):1648–1662, 2002a).

References

  1. Alujević, N., Čakmak, D., Wolf, H., & Jokić, M. (2018). Passive and active vibration isolation systems using inerter. Journal of Sound and Vibration, 418, 163–183.CrossRefGoogle Scholar
  2. Anderson, B. D. O., & Vongpanitlerd, S. (1973). Network analysis and synthesis. Upper Saddle River, NJ: Prentice-Hall.Google Scholar
  3. Bakis, K. N., Limebeer, D. J. N., Williams, M. S., & Graham, J. M. R. (2016). Passive aeroelastic control of a suspension bridge during erection. Journal of Fluids and Structures, 66, 543–570.CrossRefGoogle Scholar
  4. Bott, R., & Duffin, R. J. (1949). Impedance synthesis without use of transformers. Journal of Applied Physics, 20(8), 816.MathSciNetCrossRefGoogle Scholar
  5. Brzeski, P., Kapitaniak, T., & Perlikowski, P. (2015). Novel type of tuned mass damper with inerter which enables changes of inertance. Journal of Sound and Vibration, 349, 56–66.CrossRefGoogle Scholar
  6. Brzeski, P., Pavlovskaia, E., Kapitaniak, T., & Perlikowski, P. (2015). The application of inerter in tuned mass absorber. International Journal of Non-Linear Mechanics, 70, 20–29.CrossRefGoogle Scholar
  7. Brzeski, P., Lazarek, M., & Perlikowski, P. (2017). Experimental study of the novel tuned mass damper with inerter which enables changes of inertance. Journal of Sound and Vibration, 404, 47–57.CrossRefGoogle Scholar
  8. Chen, M. Z. Q., & Smith, M. C. (2009). Restricted complexity network realizations for passive mechanical control. IEEE Transactions on Automatic Control, 54(10), 2290–2301.MathSciNetCrossRefGoogle Scholar
  9. Chen, M. Z. Q., & Smith, M. C. (2009). A note on tests for positive-real functions. IEEE Transactions on Automatic Control, 54(2), 390–393.MathSciNetCrossRefGoogle Scholar
  10. 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
  11. Chen, M. Z. Q., Hu, Y., & Du, B. (2012). Suspension performance with one damper and one inerter. In Proceedings of the 24th Chinese Control and Decision Conference, Taiyuan, China (pp. 3551–3556).Google Scholar
  12. 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), 1874–87.CrossRefGoogle Scholar
  13. Chen, M. Z. Q., Hu, Y., Li, C., & Chen, G. (2014). Semi-active suspension with semi-active inerter and semi-active damper. IFAC Proceedings Volumes, 47(3), 11225–11230.CrossRefGoogle Scholar
  14. Chen, M. Z. Q., Hu, Y., & Wang, F.-C. (2015). Passive mechanical control with a special class of positive real controllers: Application to passive vehicle suspensions. Journal of Dynamic Systems, Measurement, and Control, 137(12), 121013.CrossRefGoogle Scholar
  15. Chen, M. Z. Q., Hu, Y., Li, C., & Chen, G. (2015). Performance benefits of using inerter in semiactive suspensions. IEEE Transactions on Control Systems Technology, 23(4), 1571–1577.CrossRefGoogle Scholar
  16. Chen, M. Z. Q., Hu, Y., Li, C., & Chen, G. (2016). Application of semi-active inerter in semi-active suspensions via force tracking. Journal of Vibration and Acoustics, 138(4), 041014.CrossRefGoogle Scholar
  17. Chen, M. Z. Q., Wang, K., Zou, Y., & Lam, J. (2013). Realization of a special class of admittances with one damper and one inerter for mechanical control. IEEE Transactions on Automatic Control, 58(7), 1841–1846.MathSciNetCrossRefGoogle Scholar
  18. Chen, M. Z. Q., Wang, K., Zou, Y., & Chen, G. (2015). Realization of three-port spring networks with inerter for effective mechanical control. IEEE Transactions on Automatic Control, 60(10), 2722–2727.MathSciNetCrossRefGoogle Scholar
  19. Dong, X., Liu, Y., & Chen, M. Z. Q. (2015). Application of inerter to aircraft landing gear suspension. In Proceedings of the 34th Chinese Control Conference, July 28–30, Hangzhou, China (pp. 2066–2071).Google Scholar
  20. 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
  21. Evangelou, S., Limebeer, D. J. N., Sharp, R. S., & Smith, M. C. (2006). Control of motorcycle steering instabilities. IEEE Control Systems Magazine, 26(5), 78–88.CrossRefGoogle Scholar
  22. Evangelou, S., Limebeer, D. J. N., Sharp, R. S., & Smith, M. C. (2007). Steering compensation for high-performance motorcycles. Journal of Applied Mechanics, 74(2), 332–346.CrossRefGoogle Scholar
  23. Frahm, H. (1909). Device for damping vibrations of bodies. U.S. Patent, No. 989958. 30.Google Scholar
  24. Gartner, B. J., & Smith, M. C. (2011). Damper and inertial hydraulic device. U.S. Patent 13/577, 234.Google Scholar
  25. Graham, J. M. R., Limebeer, D. J. N., & Zhao, X. (2011). Aeroelastic control of long-span suspension bridges. Journal of Applied Mechanics, 78(4), 041018.CrossRefGoogle Scholar
  26. Hanazawa, Y., Suda, H., & Yamakita, M. (2011). Analysis and experiment of flat-footed passive dynamic walker with ankle inerter. In Proceedings of the 2011 IEEE International Conference on Robotics and Biomimetics, December 7–11, Phuket, Thailand (pp. 86–91).Google Scholar
  27. Hanazawa, Y., & Yamakita, M. (2012). High-efficient biped walking based on flat-footed passive dynamic walking with mechanical impedance at ankles. Journal of Robotics and Mechatronics, 24(3), 498–506.CrossRefGoogle Scholar
  28. Hu, Y., Li, C., & Chen, M. Z. Q. (2012). Optimal control for semi-active suspension with inerter. In Proceedings of the 31st Chinese Control Conference, Hefei, China (pp. 2301–2306).Google Scholar
  29. Hu, Y., & Chen, M. Z. Q. (2015). Performance evaluation for inerter-based dynamic vibration absorbers. International Journal of Mechanical Sciences, 99, 297–307.CrossRefGoogle Scholar
  30. Hu, Y., Wang, K., Chen, Y., & Chen, M. Z. Q. (2018). Inerter-based semi-active suspensions with low-order mechanical admittance via network synthesis. Transactions of the Institute of Measurement and Control. 0142331217744852.Google Scholar
  31. Hu, Y., Chen, M. Z. Q., & Shu, Z. (2014). Passive vehicle suspensions employing inerters with multiple performance requirements. Journal of Sound and Vibration, 333, 2212–2225.CrossRefGoogle Scholar
  32. Hu, Y., Chen, M. Z. Q., Shu, Z., & Huang, L. (2015). Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution. Journal of Sound and Vibration, 346, 17–36.CrossRefGoogle Scholar
  33. Hu, Y., Chen, M. Z. Q., & Smith, M. C. (2018). Natural frequency assignment for mass-chain systems with inerters. Mechanical Systems and Signal Processing, 108, 126–139.CrossRefGoogle Scholar
  34. Hu, Y., Chen, M. Z. Q., & Sun, Y. (2017). Comfort-oriented vehicle suspension design with skyhook inerter configuration. Journal of Sound and Vibration, 405, 34–47.CrossRefGoogle Scholar
  35. Hu, Y., Chen, M. Z. Q., Xu, S., & Liu, Y. (2017). Semiactive inerter and its application in adaptive tuned vibration absorbers. IEEE Transactions on Control Systems Technology, 25(1), 294–300.CrossRefGoogle Scholar
  36. Ikago, K., Saito, K., & Inoue, N. (2012). Seismic control of SDOF structure using tuned viscous mass damper. Earthquake Engineering and Structural Dynamics, 41, 453–474.CrossRefGoogle Scholar
  37. Ikago, K., Sugimura, Y., Saito, K., & Inoue, K. (2012). Modal response characteristics of a multiple-degree-of-freedom structure incorporated with tuned viscous mass damper. Journal of Asian Architecture and Building Engineering, 11, 375–382.CrossRefGoogle Scholar
  38. Jiang, J. Z., Matamoros-Sanchez, A. Z., Zolotas, A., Goodall, R. M., & Smith, M. C. (2013). Passive suspensions for ride quality improvement of two-axle railway vehicles. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 0954409713511592.Google Scholar
  39. Jiang, J. Z., Matamoros-Sanchez, A. Z., Goodall, R. M., & Smith, M. C. (2012). Passive suspensions incorporating inerters for railway vehicles. Vehicle System Dynamics, 50, 263–276.CrossRefGoogle Scholar
  40. Lazarek, M., Brzeski, P., & Perlikowski, P. (2018). Design and identification of parameters of tuned mass damper with inerter which enables changes of inertance. Mechanism and Machine Theory, 119, 161–173.CrossRefGoogle Scholar
  41. 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
  42. Li, P., Lam, J., & Cheung, K. C. (2014). Investigation on semi-active control of vehicle suspension using adaptive inerter. In The 21st International Congress on Sound and Vibration, Beijing, China.Google Scholar
  43. Li, Y., Howcroft, C., Neild, S. A., & Jiang, J. Z. (2017). Using continuation analysis to identify shimmy-suppression devices for an aircraft main landing gear. Journal of Sound and Vibration, 408, 234–251.CrossRefGoogle Scholar
  44. Li, Y., Jiang, J. Z., & Neild, S. (2017). Inerter-based configurations for main-landing-gear shimmy suppression. Journal of Aircraft, 54(2), 684–693.CrossRefGoogle Scholar
  45. Li, Y., Jiang, J. Z., Neild, S. A., & Wang, H. (2017). Optimal inerter-based shock-strut configurations for landing-gear touchdown performance. Journal of Aircraft, 54(5), 1901–1909.CrossRefGoogle Scholar
  46. Li, P., Lam, J., & Cheung, K. C. (2015). Control of vehicle suspension using an adaptive inerter. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 229(14), 1934–1943.Google Scholar
  47. Limebeer, D. J. N., Graham, J. M. R., & Zhao, X. (2011). Buffet suppression in long-span suspension bridges. Annual Reviews in Control, 35(2), 235–246.CrossRefGoogle Scholar
  48. Liu, Y., Chen, M. Z. Q., & Tian, Y. (2015). Nonlinearities in landing gear model incorporating inerter. In Proceeding of the 2015 IEEE International Conference on Information and Automation, Lijiang, China (pp. 696–701)Google Scholar
  49. 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
  50. Molina-Cristobal, A., Papageorgiou, C., Parks, G. T., Smith, M. C., & Clarkson, P. J. (2006). Multi-objective controller design: Evolutionary algorithms and bilinear matrix inequalities for a passive suspension. In Proceedings of the 13th IFAC Workshop on Control Applications of Optimization, Cachan-Paris, France (pp. 386–391).Google Scholar
  51. Ormondroyd, J., & Den Hartog, J. P. (1928). The theory of the dynamic vibration absorber. ASME Journal of Applied Mechanics, 50, 9–22.Google Scholar
  52. Papageorgiou, C., & Smith, M. C. (2005). Laboratory experimental testing of inerters. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, December 12–15 (pp. 3351–3356).Google Scholar
  53. Papageorgiou, C., & Smith, M. C. (2006). Positive real synthesis using matrix inequalities for mechanical networks: Application to vehicle suspension. IEEE Transactions on Control Systems Technology, 14(3), 423–435.CrossRefGoogle Scholar
  54. Piersol, A. G., & Paez, T. L. (2010). Harris’ shock and vibration handbook (6th ed.). New York: McGraw-Hill.Google Scholar
  55. Scheibe, F., & Smith, M. C. (2009). Analytical solutions for optimal ride comfort and tyre grip for passive vehicle suspensions. Vehicle System Dynamics, 47(10), 1229–1252.CrossRefGoogle Scholar
  56. Shen, Y., Chen, L., Yang, X., Shi, D., & Yang, J. (2016). Improved design of dynamic vibration absorber by using the inerter and its application in vehicle suspension. Journal of Sound and Vibration, 361, 148–158.CrossRefGoogle Scholar
  57. Siami, A., Karimi, H. R., Cigada, A., Zappa, E., & Sabbioni, E. (2018). Parameter optimization of an inerter-based isolator for passive vibration control of Michelangelos Rondanini Piet. Mechanical Systems and Signal Processing, 98, 667–683.CrossRefGoogle Scholar
  58. Smith, M. C. (2002a). Synthesis of mechanical networks: The inerter. IEEE Transactions on Automatic Control, 47(1), 1648–1662.MathSciNetCrossRefGoogle Scholar
  59. Smith, M. C. (2002b). Force-controlling mechanical device. U.S. Patent 7,316,303 B2.Google Scholar
  60. Smith, M. C. (2003). The inerter concept and its application. Plenary Lecture, Society of Instrument and Control Engineers (SICE) Annual Conference Fukui, Japan 4 August 2003.Google Scholar
  61. Smith, M. C. (2008). Force-controlling mechanical device. U.S. Patent 7/316 303.Google Scholar
  62. Smith, M. C. (2011). Vehicle dynamics, engineering thought-experiments and Formula One racing. William Mong Distinguished Lecture, The University of Hong Kong, 13 January 2011Google Scholar
  63. Smith, M. C., & Wang, F.-C. (2004). Performance benefits in passive vehicle suspensions employing inerters. Vehicle System Dynamics, 42(4), 235–257.CrossRefGoogle Scholar
  64. Sugimura, Y., Goto, W., Tanizawa, H., Saito, K., & Nimomiya, T. (2012). Response control effect of steel building structure using tuned viscous mass damper. In Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal.Google Scholar
  65. Takewaki, I., Murakami, S., Yoshitomi, S., & Tsuji, M. (2012). Fundamental mechanism of earthquake response resuction in buildind structures with inertial dampers. Journal of Structural Control and Health Monitoring, 19, 590–608.CrossRefGoogle Scholar
  66. Tsai, M. C., & Huang, C. C. (2011). Development of a variable-inertia device with a magnetic planetary gearbox. IEEE/ASME Transactions on mechatronics, 16(6), 1120–1128.CrossRefGoogle Scholar
  67. Tuluie, R. (2010). Fluid Inerter. U.S. Patent 13/575, 017.Google Scholar
  68. Wang, K., Chen, M. Z. Q., Li, C., & Chen, G. (2018). Passive controller realization of a biquadratic impedance with double poles and zeros as a seven-element series-parallel network for effective mechanical control. IEEE Transactions on Automatic Control.  https://doi.org/10.1109/TAC.2018.2794820 (in press).MathSciNetCrossRefGoogle Scholar
  69. Wang, F.-C., Hsu, M.-S., Su, W.-J., & Lin, T. C. (2009). Screw type inerter mechanism. U.S. Patent 2009/0108510 A1.Google Scholar
  70. Wang, R., Meng, X., Shi, D., Zhang, X., Chen, Y., & Chen, L. (2014). Design and test of vehicle suspension system with inerters. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1–6.Google Scholar
  71. Wang, F.-C., & Chan, H.-A. (2011). Vehicle suspensions with a mechatronic network strut. Vehicle System Dynamics, 49(5), 811–830.CrossRefGoogle Scholar
  72. Wang, F.-C., Hong, M. F., & Chen, C. W. (2010). Building suspensions with inerters. Proceedings of the IMechE, Part C: Journal of Mechanical Engineering Science, 224(8), 1605–1616.CrossRefGoogle Scholar
  73. Wang, F.-C., Hong, M. F., & Lin, T. C. (2011). Designing and testing a hydraulic inerter. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(1), 66–72.Google Scholar
  74. 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
  75. Wang, F.-C., & Liao, M.-K. (2010). The lateral stability of train suspension systems employing inerters. Vehicle System Dynamics, 8(5), 619–643.CrossRefGoogle Scholar
  76. Wang, F.-C., Liao, M. K., Liao, B. H., Su, W. J., & Chan, H. A. (2009). The performance improvements of train suspension systems with mechanical networks employing inerters. Vehicle System Dynamics, 47(7), 805–830.CrossRefGoogle Scholar
  77. Wang, F.-C., & Su, W.-J. (2008). Impact of inerter nonlinearities on vehicle suspension control. Vehicle System Dynamics, 46(7), 575–595.CrossRefGoogle Scholar
  78. Yamamoto, K., & Smith, M. C. (2016). Bounded disturbance amplification for mass chains with passive interconnection. IEEE Transactions on Automatic Control, 61(6), 1565–1574.MathSciNetCrossRefGoogle Scholar
  79. Zhang, X. L., Zhang, T., Nie, J., & Chen, L. (2018). A semiactive skyhook-inertance control strategy based on continuously adjustable inerter. Shock and Vibration, 6828621.Google Scholar
  80. Zhang, X. J., Ahmadian, M., & Guo, K. H. (2012). On the benefits of semi-active suspensions with inerters. Shock and Vibration, 19(3), 257–272.CrossRefGoogle Scholar
  81. Zhang, X. L., Liu, J. J., Nie, J. M., & Chen, L. (2014). Design principle and method of a passive hybrid damping suspension system. Applied Mechanics and Materials, 635–637, 1232–1240.CrossRefGoogle Scholar
  82. Zhao, X., Gouder, K., Graham, J. M. R., & Limebeer, D. J. (2016). Buffet loading, dynamic response and aerodynamic control of a suspension bridge in a turbulent wind. Journal of Fluids and Structures, 62, 384–412.CrossRefGoogle Scholar
  83. Zilletti, M. (2016). Feedback control unit with an inerter proof-mass electrodynamic actuator. Journal of Sound and Vibration, 369, 16–28.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

Personalised recommendations