Smart Structures and Systems

  • 제26권4호
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  • Pages.481-493
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  • 2020
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

A negative stiffness inerter system (NSIS) for earthquake protection purposes

  • Zhao, Zhipeng (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Chen, Qingjun (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Zhang, Ruifu (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Jiang, Yiyao (Department of Disaster Mitigation for Structures, Tongji University) ;
  • Pan, Chao (College of Civil Engineering, Yantai University)
  • 투고 : 2019.12.19
  • 심사 : 2020.07.02
  • 발행 : 2020.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

The negative stiffness spring and inerter are both characterized by the negative stiffness effect in the force-displacement relationship, potentially yielding an amplifying mechanism for dashpot deformation by being incorporated with a series tuning spring. However, resisting forces of the two mechanical elements are dominant in different frequency domains, thus leading to necessary complementarity in terms of vibration control and the amplifying benefit. Inspired by this, this study proposes a Negative Stiffness Inerter System (NSIS) as an earthquake protection system and developed analytical design formulae by fully utilizing its advantageous features. The NSIS is composed of a sub-configuration of a negative stiffness spring and an inerter in parallel, connected to a tuning spring in series. First, closed-form displacement responses are derived for the NSIS structure, and a stability analysis is conducted to limit the feasible domains of NSIS parameters. Then, the dual advantageous features of displacement reduction and the dashpot deformation amplification effect are revealed and clarified in a parametric analysis, stimulating the establishment of a displacement-based optimal design framework, correspondingly yielding the design formulae in analytical form. Finally, a series of examples are illustrated to validate the derived formulae. In this study, it is confirmed that the synergistic incorporation of the negative stiffness spring and the inerter has significant energy dissipation efficiency in a wide frequency band and an enhanced control effect in terms of the displacement and shear force responses. The developed displacement-based design strategy is suitable to utilize the dual benefits of the NSIS, which can be accurately implemented by the analytical design formulae to satisfy the target vibration control with increased energy dissipation efficiency.

키워드

참고문헌

  1. Antoniadis, I., Chronopoulos, D., Spitas, V. and Koulocheris, D. (2015), "Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element", J. Sound Vib., 346, 37-52. https://doi.org/10.1016/j.jsv.2015.02.028.
  2. Arakaki, T., Kuroda, H., Arima, F., Inoue, Y. and Baba, K. (1999a), "Development of seismic devices applied to ball screw: Part 1 basic performance test of RD-series", AIJ J. Tech. Des., 5(8), 239-244. https://doi.org/10.3130/aijt.5.239_1
  3. Arakaki, T., Kuroda, H., Arima, F., Inoue, Y. and Baba, K. (1999b), "Development of seismic devices applied to ball screw: Part 2 performance test and evaluation of RD-series", AIJ J. Tech. Des., 5(8), 365-370.
  4. Asai, T., Araki, Y. and Ikago, K. (2018), "Structural control with tuned inertial mass electromagnetic transducers", Struct. Control Health Monit., 25(2), e2059. https://doi.org/10.1002/stc.2059.
  5. Chen, M.Z.Q., Hu, Y., Li, C. and Chen, G. (2015), "Performance benefits of using inerter in semiactive suspensions", IEEE Trans. Control Syst. Technol., 23(4), 1571-1577. http://dx.doi.org/10.1109/TCST.2014.2364954.
  6. Chen, Q.J., Zhao, Z.P., Zhang, R.F. and Pan, C. (2018), "Impact of soil-structure interaction on structures with inerter system", J. Sound Vib., 433, 1-15. https://doi.org/10.1016/j.jsv.2018.07.008.
  7. Chen, Q.J., Zhao, Z.P., Xia, Y.Y., Pan, C., Luo, H. and Zhang, R.F. (2019), "Comfort based floor design employing tuned inerter mass system", J. Sound Vib., 458, 143-157. https://doi.org/10.1016/j.jsv.2019.06.019.
  8. Christopoulos, C. and Filiatrault, A. (2006), Principles of Passive Supplemental Damping and Seismic Isolation, Iuss press, Pavia, Italy.
  9. Clark, R.N. (1992), "The Routh-Hurwitz stability criterion, revisited", IEEE Control Syst. Mag., 12(3), 119-120. https://doi.org/10.1109/37.165530.
  10. Crandall, S.H. and Mark, W.D. (2014), Random Vibration in Mechanical System, Academic Press, New York, USA.
  11. Dai, J., Xu, Z.D. and Gai, P.P. (2019), "Tuned mass-damper-inerter control of wind-induced vibration of flexible structures based on inerter location", Eng. Struct., 199, 109585. https://doi.org/10.1016/j.engstruct.2019.109585.
  12. De Domenico, D. and Ricciardi, G. (2018a), "Earthquake-resilient design of base isolated buildings with TMD at basement: Application to a case study", Soil Dyn. Earthq. Eng., 113, 503-521. https://doi.org/10.1016/j.soildyn.2018.06.022.
  13. De Domenico, D. and Ricciardi, G. (2018b), "Improving the dynamic performance of base-isolated structures via tuned mass damper and inerter devices: A comparative study", Struct. Control Health Monit., 25(10), e2234. https://doi.org/10.1002/stc.2234.
  14. De Domenico, D. and Ricciardi, G. (2018c), "Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems", Earthq. Eng. Struct. Dyn., 47(12), 2539-2560. https://dx.doi.org/10.1002/eqe.3098.
  15. De Domenico, D. and Ricciardi, G. (2019), "Earthquake protection of structures with nonlinear viscous dampers optimized through an energy-based stochastic approach", Eng. Struct., 179, 523-539. https://doi.org/10.1016/j.engstruct.2018.09.076.
  16. De Domenico, D., Deastra, P., Ricciardi, G., Sims, N.D. and Wagg, D.J. (2019), "Novel fluid inerter based tuned mass dampers for optimised structural control of base-isolated buildings", J. Franklin Inst., 356(14), 7626-7649. https://doi.org/10.1016/j.jfranklin.2018.11.012.
  17. Di Matteo, A., Masnata, C. and Pirrotta, A. (2019), "Simplified analytical solution for the optimal design of tuned mass damperiInerter for base isolated structures", Mech. Syst. Signal Process., 134, 106337. https://doi.org/10.1016/j.ymssp.2019.106337.
  18. Greco, R. and Marano, G.C. (2013), "Optimum design of tuned mass dampers by displacement and energy perspectives", Soil Dyn. Earthq. Eng., 49, 243-253. https://doi.org/10.1016/j.soildyn.2013.02.013.
  19. Hanson, R.D. and Soong, T.T. (2001), Seismic Design with Supplemental Energy Dissipation Devices, Earthquake Engineering Research Institute, Oakland, CA, USA.
  20. Hwang, J.S., Huang, Y.N. and Hung, Y.H. (2005), "Analytical and experimental study of toggle-brace-damper systems", J. Struct. Eng., 131(7), 1035-1043. https://doi.org/10.1061/(asce)0733-9445(2005)131:7(1035).
  21. Iemura, H. and Pradono, M.H. (2009), "Advances in the development of pseudo-negative-stiffness dampers for seismic response control", Struct. Control Health Monit., 16(7-8), 784-799. https://doi.org/10.1002/stc.345.
  22. Ikago, K., Saito, K. and Inoue, N. (2012), "Seismic control of single-degree-of-freedom structure using tuned viscous mass damper", Earthq. Eng. Struct. Dyn., 41(3), 453-474. https://dx.doi.org/10.1002/eqe.1138.
  23. Jiang, Y.Y., Zhao, Z.P., Zhang, R.F., De Domenico, D. and Pan, C. (2020), "Optimal design based on analytical solution for storage tank with inerter isolation system", Soil Dyn. Earthq. Eng., 129, 105924. https://doi.org/10.1016/j.soildyn.2019.105924.
  24. Kawamata, S. (1973), "Development of a vibration control system of structures by means of mass pumps", Institute of Industrial Science, Tokyo, Japan.
  25. Li, H., Liu, J. and Ou, J. (2011), "Seismic response control of a cable-stayed bridge using negative stiffness dampers", Struct. Control Health Monit., 18(3), 265-288. https://doi.org/10.1002/stc.368.
  26. Ma, R., Bi, K. and Hao, H. (2018), "Mitigation of heave response of semi-submersible platform (SSP) using tuned heave plate inerter (THPI)", Eng. Struct., 177, 357-373. https://doi.org/10.1016/j.engstruct.2018.09.085.
  27. Marian, L. and Giaralis, A. (2017), "The tuned mass-damperinerter for harmonic vibrations suppression, attached mass reduction, and energy harvesting", Smart Struct. Syst., Int. J., 19(6), 665-678. https://doi.org/10.12989/sss.2017.19.6.665.
  28. Masri, S.F. and Caffrey, J.P. (2017), "Transient response of a SDOF system with an inerter to nonstationary stochastic excitation", J. Appl. Mech., 84(4), 041005. https://doi.org/10.1115/1.4035930.
  29. Murakami, Y., Noshi, K., Fujita, K., Tsuji, M. and Takewaki, I. (2013), "Simultaneous optimal damper placement using oil, hysteretic and inertial mass dampers", Earthq. Struct., Int. J., 5(3), 261-276. https://doi.org/10.12989/eas.2013.5.3.261.
  30. Palomares, E., Nieto, A.J., Morales, A.L., Chicharro, J.M. and Pintado, P. (2018), "Numerical and experimental analysis of a vibration isolator equipped with a negative stiffness system", J. Sound Vib., 414, 31-42. https://doi.org/10.1016/j.jsv.2017.11.006.
  31. Pasala, D.T.R., Sarlis, A.A., Nagarajaiah, S., Reinhorn, A.M., Constantinou, M.C. and Taylor, D. (2013), "Adaptive negative stiffness: New structural modification approach for seismic protection", J. Struct. Eng., 139(7), 1112-1123. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000615.
  32. Pietrosanti, D., De Angelis, M. and Basili, M. (2017), "Optimal design and performance evaluation of systems with Tuned Mass Damper Inerter (TMDI)", Earthq. Eng. Struct. Dyn., 46(8), 1367-1388. http://dx.doi.org/10.1002/eqe.2861.
  33. Radu, A., Lazar, I.F. and Neild, S.A. (2019), "Performance-based seismic design of tuned inerter dampers", Struct. Control Health Monit., 26(5), e2346. https://doi.org/10.1002/stc.2346.
  34. Ribakov, Y. and Reinhorn, A.M. (2003), "Design of amplified structural damping using optimal considerations", J. Struct. Eng., 129(10), 1422-1427. https://doi.org/10.1061/(asce)0733-9445(2003)129:10(1422).
  35. Saha, A. and Mishra, S.K. (2019), "Adaptive negative stiffness device based nonconventional tuned mass damper for seismic vibration control of tall buildings", Soil Dyn. Earthq. Eng., 126, 105767. https://doi.org/10.1016/j.soildyn.2019.105767.
  36. Shi, X. and Zhu, S. (2019), "A comparative study of vibration isolation performance using negative stiffness and inerter dampers", J. Franklin Inst., 356(14), 7922-7946. https://doi.org/10.1016/j.jfranklin.2019.02.040.
  37. Smith, M.C. (2002), "Synthesis of mechanical networks: The inerter", IEEE Trans. Automat. Contr., 47(10), 1648-1662. https://doi.org/10.1109/TAC.2002.803532.
  38. Soong, T.T. and Dargush, G.F. (1997), Passive Energy Dissipation Systems in Structural Engineering, Wiley, London, UK.
  39. Spencer, B.F. and Nagarajaiah, S. (2003), "State of the art of structural control", J. Struct. Eng., 129(7), 845-856. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:7(845).
  40. Takewaki, I. (2011), Building Control with Passive Dampers: Optimal Performance-based Design for Earthquakes, John Wiley & Sons, London, UK.
  41. Takewaki, I., Murakami, S., Yoshitomi, S. and Tsuji, M. (2012), "Fundamental mechanism of earthquake response reduction in building structures with inertial dampers", Struct. Control Health Monit., 19(6), 590-608. http://dx.doi.org/10.1002/stc.457.
  42. Tapia, N., Almazan, J. and Baquero, J. (2016), "Development of a novel combined system of deformation amplification and added stiffness and damping: Analytical result and full scale pseudodynamic tests", Eng. Struct., 119, 61-80. https://doi.org/10.1016/j.engstruct.2016.04.004.
  43. Walsh, K.K., Cronin, K.J., Rambo-Roddenberry, M.D. and Grupenhof, K. (2012), "Dynamic analysis of seismically excited flexible truss tower with scissor-jack dampers", Struct. Control Health Monit., 19(8), 723-745. https://doi.org/10.1002/stc.465.
  44. Wang, M., Sun, F.F., Yang, J.Q. and Nagarajaiah, S. (2019a), "Seismic protection of SDOF systems with a negative stiffness amplifying damper", Eng. Struct., 190, 128-141. https://doi.org/10.1016/j.engstruct.2019.03.110.
  45. Wang, X., He, T., Shen, Y., Shan, Y. and Liu, X. (2019b), "Parameters optimization and performance evaluation for the novel inerter-based dynamic vibration absorbers with negative stiffness", J. Sound Vib., 463, 114941. https://doi.org/10.1016/j.jsv.2019.114941.
  46. Wu, B., Shi, P. and Ou, J. (2013), "Seismic performance of structures incorporating magnetorheological dampers with pseudo-negative stiffness", Struct. Control Health Monit., 20(3), 405-421. https://doi.org/10.1002/stc.504.
  47. Zhang, R.F., Zhao, Z.P. and Dai, K. (2019), "Seismic response mitigation of a wind turbine tower using a tuned parallel inerter mass system", Eng. Struct., 180, 29-39. https://doi.org/10.1016/j.engstruct.2018.11.020.
  48. Zhang, R.F., Zhao, Z.P., Pan, C., Ikago, K. and Xue, S.T. (2020), "Damping enhancement principle of inerter system", Struct. Control Health Monit., 27(5), e2523. https://doi.org/10.1002/stc.2523.
  49. Zhao, Z.P., Chen, Q.J., Zhang, R.F., Pan, C. and Jiang, Y.Y. (2019a), "Optimal design of an inerter isolation system considering the soil condition", Eng. Struct., 196, 109324. https://doi.org/10.1016/j.engstruct.2019.109324.
  50. Zhao, Z.P., Zhang, R.F., Jiang, Y.Y. and Pan, C. (2019b), "Seismic response mitigation of structures with a friction pendulum inerter system", Eng. Struct., 193, 110-120. https://doi.org/10.1016/j.engstruct.2019.05.024.
  51. Zhao, Z.P., Zhang, R.F., Jiang, Y.Y. and Pan, C. (2019c), "A tuned liquid inerter system for vibration control", Int. J. Mech. Sci., 164, 105171. https://doi.org/10.1016/j.ijmecsci.2019.105171.
  52. Zhao, Z.P., Zhang, R.F. and Lu, Z. (2019d), "A particle inerter system for structural seismic response mitigation", J. Franklin Inst., 356(14), 7669-7688. https://doi.org/10.1016/j.jfranklin.2019.02.001.
  53. Zhao, Z.P., Chen, Q.J., Zhang, R.F., Pan, C. and Jiang, Y.Y. (2020), "Energy dissipation mechanism of inerter systems", Int. J. Mech. Sci., 184, 105845. https://doi.org/10.1016/j.ijmecsci.2020.105845.

피인용 문헌

  1. An inerter-system chain and energy-based optimal control of adjacent single-degree-of-freedom structures vol.28, pp.2, 2021, https://doi.org/10.12989/sss.2021.28.2.245
  2. Closed‐form design formulae for seismically isolated structure with a damping enhanced inerter system vol.28, pp.12, 2020, https://doi.org/10.1002/stc.2840