Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Input energy spectra and energy characteristics of the hysteretic nonlinear structure with an inerter system

  • Wang, Yanchao (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Chen, Qingjun (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Zhao, Zhipeng (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Hu, Xiuyan (Shanghai Institute of Technology, College of Urban Construction and Safety Engineering)
  • Received : 2020.05.01
  • Accepted : 2020.08.13
  • Published : 2020.12.25
⟨ Previous Next ⟩

Abstract

The typical inerter system, the tuned viscous mass damper (TVMD), has been proven to be efficient. It is characterized by an energy-dissipation-enhancement effect, whereby the dashpot deformation of TVMD can be amplified for enhanced energy dissipation efficiency. However, existing studies related to TVMD have mainly been performed on elastic structures, so the working mechanism remains unclear for nonlinear structures. To deal with this, an energy-spectrum analysis framework is developed systematically for classic bilinear hysteretic structures with TVMD. Considering the soil effect, typical bedrock records are propagated through the soil deposit, for which the designed input energy spectra are proposed by considering the TVMD parameters and structural nonlinear properties. Furthermore, the energy-dissipation-enhancement effect of TVMD is quantitatively evaluated for bilinear hysteretic structures. The results show that the established designed input energy spectra can be employed to evaluate the total energy-dissipation burden for a nonlinear TVMD structure. Particularly, the stiffness of TVMD is the dominant factor in adjusting the total input energy. Compared with the case of elastic structures, the energy-dissipation-enhancement effect of TVMD for nonlinear structures is weakened so that the expected energy-dissipation effect of TVMD is replaced by the accumulated energy dissipation of the primary structure.

Keywords

Acknowledgement

The research described in this paper was financially supported by the National Natural Science Foundation of China (grant no. 51778489), the National Science and Technology Pillar Program of China (grant no. 2015BAK17B04), and the Basic Research Project of State Key Laboratory of Ministry of Science and Technology (grant no. SLDRCE19A-02). All support is gratefully acknowledged.

References

  1. Akiyama, H. (1985), Earthquake-Resistant Limit-State Design for Buildings, University of Tokyo Press.
  2. Alici, F.S. and Sucuoglu, H. (2018), "Elastic and inelastic nearfault input energy spectra", Earthq. Spectra, 34(2), 611-637 https://doi.org/10.1193/090817eqs175m.
  3. Alici, F.S. and Sucuoglu, H. (2016), "Prediction of input energy spectrum: attenuation models and velocity spectrum scaling", Earthq. Eng. Struct. Dynam., 45(13), 2137-2161 https://doi.org/10.1002/eqe.2749.
  4. Benavent-Climent, A., Lopez-Almansa, F. and Bravo-Gonzalez, D.A. (2010), "Design energy input spectra for moderate-to-high seismicity regions based on Colombian earthquakes", Soil Dynam. Earthq. Eng., 30(11), 1129-1148 https://doi.org/10.1016/j.soildyn.2010.04.022.
  5. Benavent-Climent, A. and Mota-Paez, S. (2017), "Earthquake retrofitting of R/C frames with soft first story using hysteretic dampers: Energy-based design method and evaluation", Eng. Struct., 137, 19-32 https://doi.org/10.1016/j.engstruct.2017.01.053.
  6. Chapman, M.C. (1999), "On the use of elastic input energy for seismic hazard analysis", Earthq. Spectra, 15(4), 607-635 https://doi.org/10.1193/1.1586064.
  7. Chen, H.T., Jia, S.M. and He, X.F. (2019), "Dynamic characteristics of multiple inerter-based dampers for suppressing harmonically forced oscillations", Struct. Eng. Mech., 72(6), 747-762 https://doi.org/10.12989/sem.2019.72.6.747.
  8. 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.
  9. 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.
  10. Cheng, Y., Lucchini, A. and Mollaioli, F. (2020), "Ground-motion prediction equations for constant-strength and constant-ductility input energy spectra", Bullet. Earthq. Eng., 18(1), 37-55 https://doi.org/10.1007/s10518-019-00725-x.
  11. Chong, S.H. (2017), "Soil dynamic constitutive model for characterizing the nonlinear-hysteretic response", Appl. Sci.-Basel, 7(11), 1110 https://doi.org/10.3390/app7111110.
  12. Chou, C.C. and Uang, C.M. (2003), "A procedure for evaluating seismic energy demand of framed structures", Earthq. Eng. Struct. Dynam., 32(2), 229-244 https://doi.org/10.1002/eqe.221.
  13. Conde-Conde, J. and Benavent-Climent, A. (2019), "Construction of elastic spectra for high damping", Eng. Struct., 191, 343-357 https://doi.org/10.1016/j.engstruct.2019.04.047.
  14. 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 Institute, 356(14), 7626-7649 https://doi.org/10.1016/j.jfranklin.2018.11.012.
  15. De Domenico, D. and Ricciardi, G. (2018), "Earthquake-resilient design of base isolated buildings with TMD at basement: Application to a case study", Soil Dynam. Earthq. Eng., 113, 503-521 https://doi.org/10.1016/j.soildyn.2018.06.022.
  16. De Domenico, D. and Ricciardi, G. (2018), "An enhanced base isolation system equipped with optimal tuned mass damper inerter (TMDI)", Earthq. Eng. Struct. Dynam., 47(5), 1169-1192 https://doi.org/10.1002/eqe.3011.
  17. De Domenico, D. and Ricciardi, G. (2018), "Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems", Earthq. Eng. Struct. Dynam., 47(12), 2539-2560 https://doi.org/10.1002/eqe.3098.
  18. 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.
  19. De Domenico, D., Ricciardi, G. and Zhang, R.F. (2020), "Optimal design and seismic performance of tuned fluid inerter applied to structures with friction pendulum isolators", Soil Dynam. Earthq. Eng., 132, 106099 https://doi.org/10.1016/j.soildyn.2020.106099.
  20. Decanini, L.D. and Mollaioli, F. (1998), "Formulation of elastic earthquake input energy spectra", Earthq. Eng. Struct. Dynam., 27(12), 1503-1522 https://doi.org/10.1002/(sici)1096-9845(199812)27:12<1503::Aid-eqe797>3.3.Co;2-1.
  21. Dindar, A.A., Yalcin, C., Yuksel, E., Ozkaynak, H. and Buyukozturk, O. (2015), "Development of earthquake energy demand spectra", Earthq. Spectra, 31(3), 1667-1689 https://doi.org/10.1193/011212EQS010M.
  22. Fajfar, P. and Vidic, T. (1994), "Consistent inelastic design spectra: hysteretic and input energy", Earthq. Eng. Struct. Dynam., 23(5), 523-537 https://doi.org/10.1002/eqe.4290230505.
  23. Garrido, H., Curadelli, O. and Ambrosini, D. (2013), "Improvement of tuned mass damper by using rotational inertia through tuned viscous mass damper", Eng. Struct., 56, 2149-2153 https://doi.org/10.1016/j.engstruct.2013.08.044.
  24. Gates, N.C. (1977), "The earthquake response of deteriorating systems", Earthquake Engineering Research Laboratory; Pasadena, California,
  25. Ge, Q., Xiong, F., Xie, L., Chen, J. and Yu, M. (2019), "Dynamic interaction of soil - Structure cluster", Soil Dynam. Earthq. Eng., 123, 16-30 https://doi.org/10.1016/j.soildyn.2019.04.020.
  26. Greco, R. and Marano, G.C. (2013), "Optimum design of tuned mass dampers by displacement and energy perspectives", Soil Dynam. Earthq. Eng., 49, 243-253 https://doi.org/10.1016/j.soildyn.2013.02.013.
  27. Gullu, A., Yuksel, E., Yalcin, C., Dindar, A.A., Ozkaynak, H. and Buyukozturk, O. (2019), "An improved input energy spectrum verified by the shake table tests", Earthq. Eng. Struct. Dynam., 48(1), 27-45 https://doi.org/10.1002/eqe.3121.
  28. Hashash, Y.M.A. and Park, D. (2001), "Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment", Eng. Geology, 62(1-3), 185-206 https://doi.org/10.1016/s0013-7952(01)00061-8.
  29. Huang, Y., Ye, W. and Chen, Z. (2009), "Seismic response analysis of the deep saturated soil deposits in Shanghai", Environ. Geology, 56(6), 1163-1169 https://doi.org/10.1007/s00254-008-1216-1.
  30. Ikago, K., Saito, K. and Inoue, N. (2012), "Seismic control of single-degree-of-freedom structure using tuned viscous mass damper", Earthq. Eng. Struct. Dynam., 41(3), 453-474 https://doi.org/10.1002/eqe.1138.
  31. Javidialesaadi, A. and Wierschem, N.E. (2019), "Energy transfer and passive control of single-degree-of-freedom structures using a one-directional rotational inertia viscous damper", Eng. Struct., 196, 109339 https://doi.org/10.1016/j.engstruct.2019.109339.
  32. 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 Dynam. Earthq. Eng., 129, 105924 https://doi.org/10.1016/j.soildyn.2019.105924.
  33. Kawamata, S. (1973), "Development of a vibration control system of structures by means of mass pumps", Institute of Industrial Science, University of Tokyo; Tokyo, Japan,
  34. Li, C.X. and Cao, L.Y. (2019), "High performance active tuned mass damper inerter for structures under the ground acceleration", Earthq. Struct., 16(2), 149-163 https://doi.org/10.12989/eas.2019.16.2.149.
  35. Lin, J.L., Bui, M.T. and Tsai, K.C. (2014), "An energy-based approach to the generalized optimal locations of viscous dampers in two-way asymmetrical buildings", Earthq. Spectra, 30(2), 867-889 https://doi.org/10.1193/052312eqs196m.
  36. Lopez-Almansa, F., Yazgan, A.U. and Benavent-Climent, A. (2013), "Design energy input spectra for high seismicity regions based on Turkish registers", Bullet. Earthq. Eng., 11(4), 885-912 https://doi.org/10.1007/s10518-012-9415-2.
  37. Martin, P.P. and Seed, H.B. (1982), "One-dimensional dynamic ground response analyses", J. Geotechnical Eng. Division-ASCE, 108(7), 935-952 https://doi.org/10.1061/AJGEB6.0001316
  38. 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.
  39. Montgomery, D.C., Runger, G.C. and Hubele, N.F. (2009), Engineering Statistics, John Wiley and Sons, NJ, USA.
  40. Ordaz, M., Huerta, B. and Reinoso, E. (2003), "Exact computation of input-energy spectra from Fourier amplitude spectra", Earthq. Eng. Struct. Dynam., 32(4), 597-605 https://doi.org/10.1002/eqe.240.
  41. Pan, C., Zhang, R.F., Luo, H., Li, C. and Shen, H. (2018), "Demand-based optimal design of oscillator with parallel-layout viscous inerter damper", Struct. Control Health Monitor., 25(1), e2051 https://doi.org/10.1002/Stc.2051.
  42. 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. Dynam., 46(8), 1367-1388 https://doi.org/10.1002/eqe.2861.
  43. Reggio, A. and De Angelis, M. (2015), "Optimal energy-based seismic design of non-conventional Tuned Mass Damper (TMD) implemented via inter-story isolation", Earthq. Eng. Struct. Dynam., 44(10), 1623-1642 https://doi.org/10.1002/eqe.2548.
  44. Rinaldin, G., Amadio, C. and Fragiacomo, M. (2017), "Effects of seismic sequences on structures with hysteretic or damped dissipative behaviour", Soil Dynam. Earthq. Eng., 97, 205-215 https://doi.org/10.1016/j.soildyn.2017.03.023.
  45. Takewaki, I. (2004), "Bound of earthquake input energy", J. Struct. Eng., 130(9), 1289-1297 https://doi.org/10.1061/(ASCE)0733-9445(2004)130:9(1289).
  46. Takewaki, I. (2004), "Frequency domain modal analysis of earthquake input energy to highly damped passive control structures", Earthq. Eng. Struct. Dynam., 33(5), 575-590 https://doi.org/10.1002/eqe.361.
  47. 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 Monitor., 19(6), 590-608 https://doi.org/10.1002/stc.457.
  48. Trifunac, M.D. and Brady, A.G. (1975), "Study on duration of strong earthquake ground motion", Bullet. Seismolgical Soc. America, 65(3), 581-626
  49. Uang, C.M. and Bertero, V.V. (1990), "Evaluation of seismic energy in structures", Earthq. Eng. Struct. Dynam., 19(1), 77-90 https://doi.org/10.1002/eqe.4290190108.
  50. 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.
  51. Zhang, R.F., Zhao, Z.P., Pan, C., Ikago, K. and Xue, S.T. (2020), "Damping enhancement principle of inerter system", Struct. Control Health Monitor., e2523 https://doi.org/10.1002/stc.2523.
  52. Zhao, Z.P., Chen, Q.J., Zhang, R.F., Jiang, Y.Y. and Xia, Y.Y. (2020), "Interaction of two adjacent structures coupled by inerter-based system considering soil conditions", J. Earthq. Eng., https://doi.org/10.1080/13632469.2020.1778585.
  53. Zhao, Z.P., Chen, Q.J., Zhang, R.F., Pan, C. and Jiang, Y.Y. (2019), "Optimal design of an inerter isolation system considering the soil condition", Eng. Struct., 196, 109324 https://doi.org/10.1016/j.engstruct.2019.109324.
  54. Zhao, Z.P., Chen, Q.J., Zhang, R.F., Pan, C. and Jiang, Y.Y. (2020), "Energy dissipation mechanism of inerter systems", J. Mech. Sci., 184, 105845 https://doi.org/10.1016/j.ijmecsci.2020.105845.
  55. Zhao, Z.P., Zhang, R.F., Jiang, Y.Y. and Pan, C. (2019), "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.
  56. Zhao, Z.P., Zhang, R.F., Jiang, Y.Y. and Pan, C. (2019), "A tuned liquid inerter system for vibration control", J. Mech. Sci., 164, 105171 https://doi.org/10.1016/j.ijmecsci.2019.105171.
  57. Zhou, Y., Song, G., Huang, S. and Wu, H. (2019), "Input energy spectra for self-centering SDOF systems", Soil Dynam. Earthq. Eng., 121, 293-305 https://doi.org/10.1016/j.soildyn.2019.03.017.