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The tuned mass-damper-inerter for harmonic vibrations suppression, attached mass reduction, and energy harvesting

  • Received : 2016.10.30
  • Accepted : 2017.05.12
  • Published : 2017.06.25
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Abstract

In this paper the tuned mass-damper-inerter (TMDI) is considered for passive vibration control and energy harvesting in harmonically excited structures. The TMDI couples the classical tuned mass-damper (TMD) with a grounded inerter: a two-terminal linear device resisting the relative acceleration of its terminals by a constant of proportionality termed inertance. In this manner, the TMD is endowed with additional inertia, beyond the one offered by the attached mass, without any substantial increase to the overall weight. Closed-form analytical expressions for optimal TMDI parameters, stiffness and damping, given attached mass and inertance are derived by application of Den Hartog's tuning approach to suppress the response amplitude of force and base-acceleration excited single-degree-of-freedom structures. It is analytically shown that the TMDI is more effective from a same mass/weight TMD to suppress vibrations close to the natural frequency of the uncontrolled structure, while it is more robust to detuning effects. Moreover, it is shown that the mass amplification effect of the inerter achieves significant weight reduction for a target/predefined level of vibration suppression in a performance-based oriented design approach compared to the classical TMD. Lastly, the potential of using the TMDI for energy harvesting is explored by substituting the dissipative damper with an electromagnetic motor and assuming that the inertance can vary through the use of a flywheel-based inerter device. It is analytically shown that by reducing the inertance, treated as a mass/inertia-related design parameter not considered in conventional TMD-based energy harvesters, the available power for electric generation increases for fixed attached mass/weight, electromechanical damping, and stiffness properties.

Keywords

Acknowledgement

Supported by : EPSRC

References

  1. Adhikari, S. and Ali, F. (2013), "Energy harvesting dynamic vibration absorbers", J. Appl. Mech., 80(4), 1-9.
  2. Asami, T., Nishihara, O. and Baz, A.M. (2002), "Analytical solutions to $H_{\infty}$ and $H_2$ optimization of dynamic vibration absorber attached to damped linear systems", J. Vib. Acoust., 124(2), 284-295. https://doi.org/10.1115/1.1456458
  3. Bakre, S.V. and Jangid, R.S. (2007), "Optimum parameters of tuned mass damper for damped main system", Struct. Control Health Monit., 14(3), 448-470. https://doi.org/10.1002/stc.166
  4. Bandivadekar, T.B. and Jangid, R.S. (2012), "Mass distribution of multiple tuned mass dampers for vibration control of structures", Int. J. Civil Struct. Eng. 3, 70-84.
  5. Bortoluzzi, D., Casciati, S., Elia, L. and Faravelli, L. (2015), "Design of a TMD solution to mitigate wind-induced local vibrations in an existing timber footbridge", Smart Struct. Syst., 16(3), 459-478. https://doi.org/10.12989/sss.2015.16.3.459
  6. Brock, J.E. (1946), "A note on the damped vibration absorber", J. Appl. Mech., 13, A-284.
  7. Casciati, F. and Giuliano, F. (2009), "Performance of multi-TMD in the towers of suspension bridges", J. Vib. Control, 15(6), 821-847. https://doi.org/10.1177/1077546308091455
  8. Cassidy, I.L., Scruggs, J.T., Behrens, S. and Gavin, H.P. (2011), "Design and experimental characterization of an electromagnetic transducer for large-scale vibratory energy harvesting applications", J. Intel. Mat. Syst. Str., 22(17), 2009-2024. https://doi.org/10.1177/1045389X11421824
  9. Chuan, L., Liang, M., Wang, Y. and Dong, Y. (2012), "Vibration suppression using two terminal flywheel. Part I: Modeling and Characterization", J. Vib. Control, 18(8), 1096-1105. https://doi.org/10.1177/1077546311419546
  10. De Angelis, M., Perno, S., Reggio, A. (2012), "Dynamic response and optimal design of structures with large mass ratio TMD", Earthq. Eng. Struct. D., 41(1), 41-60. https://doi.org/10.1002/eqe.1117
  11. Den Hartog, J.P. (1956), Mechanical Vibrations, McGraw-Hill (4th Ed.), New York, NY, USA.
  12. Dhand, A. and Pullen, K.R. (2015), "Analysis of continuously variable transmission for flywheel energy storage systems in vehicular application", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229(2), 273-290. https://doi.org/10.1177/0954406214533096
  13. Domizio, M., Ambrosini, D. and Curadelli, O. (2015), "Performance of TMDs on nonlinear structures subjected to near-fault earthquakes", Smart Struct. Syst., 16(4), 725-742. https://doi.org/10.12989/sss.2015.16.4.725
  14. Frahm, H. (1911), Device for Damping Vibrations of Bodies, U.S. Patent 989958, USPTO.
  15. Krenk, S. (2005), "Frequency analysis of the tuned mass damper", J. Appl.Mech.-ASME, 72, 936-942. https://doi.org/10.1115/1.2062867
  16. Leung, A.Y.T. and Zhang, H. (2009), "Particle swarm optimization of tuned mass dampers", Eng. Struct., 31(3), 715-728. https://doi.org/10.1016/j.engstruct.2008.11.017
  17. Lin, C.C., Wang, J.F. and Chen, B.L. (2005). "Train-induced vibration control of high-speed railway bridges equipped with multiple tuned mass dampers", J. Bridge Eng. - ASCE, 10(4), 398-414. https://doi.org/10.1061/(ASCE)1084-0702(2005)10:4(398)
  18. Ghosh, A. and Basu, B. (2007), "A closed-form optimal tuning criterion for TMD in damped structures", Structural Control and Health Monitoring, 14(4), 681-692. https://doi.org/10.1002/stc.176
  19. Giaralis, A. and Petrini, F. (2017), "Wind-induced vibration mitigation in tall buildings using the tuned mass-damper-inerter (TMDI)", J. Struct. Eng. - ASCE, accepted for publication.
  20. Gonzalez-Buelga, A., Clare, L.R., Cammarano, A., Neild, S.A., Burrow, S.G. and Inman, D.J. (2014), "An optimised tuned mass damper/harvester device", Structural Control and Health Monitoring, 21(8), 1154-1169. https://doi.org/10.1002/stc.1639
  21. Gonzalez-Buelga, A., Lazar, I., Jiang, J.Z., Neild, S.A. and Inman, D.J. (2016), "Assessing the effect of nonlinearities on the performance of a Tuned Inerter Damper", Struct. Control Health Monit., DOI: 10.1002/stc.1879.
  22. Hendijanizadeh, M., Sharkh, S.M., Elliott, S.J. and Moshrefi-Torbati, M. (2013), "Output power and efficiency of electromagnetic energy harvesting systems with constrained range of motion", Smart Mater. Struct., 22(12), 125009. https://doi.org/10.1088/0964-1726/22/12/125009
  23. Hoang, N., Fujino, Y. and Warnitchai, P. (2008), "Optimal tuned mass damper for seismic applications and practical design formulas", Eng. Struct., 30, 707-715. https://doi.org/10.1016/j.engstruct.2007.05.007
  24. Hu, Y. and Chen, M.Z.Q. (2015), "Performance evaluation for inerter-based dynamic vibration absorbers", Int. J. Mech. Sci., 99, 297-307. https://doi.org/10.1016/j.ijmecsci.2015.06.003
  25. Hu, Y., Chen, M.Z.Q., Shu, Z. and Huang L. (2015), "Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution", J. Sound Vib., 346, 17-36, DOI:10.1016/j.jsv.2015.02.041.
  26. Hu, Y., Chen, M.Z.Q., Xu, S. and Liu Y. (2016), "Semiactive inerter and its application in adaptive tuned vibration absorbers", IEEE T. Control Syst. Technol., DOI: 10.1109/TCST.2016.2552460.
  27. Jokic, M., Stegic, M. and Butkovic, M. (2011), "Reduced-order multiple tuned mass damper optimization: A bounded real lemma for descriptor systems approach", J. Sound Vib., 330, 5259-5268. https://doi.org/10.1016/j.jsv.2011.06.005
  28. Makihara, K., Hirai, H., Yamamoto, Y. and Fukunaga, H. (2015), "Self-reliant wireless health monitoring based on tuned-massdamper mechanism", Smart Struct. Syst., 15(6), 1625-1642. https://doi.org/10.12989/sss.2015.15.6.1625
  29. Marian, L. and Giaralis, A. (2014), "Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems", Probab. Eng. Mech., 38, 156-164. https://doi.org/10.1016/j.probengmech.2014.03.007
  30. Marian, L. and Giaralis, A. (2013), "Optimal design of inerter devices combined with TMDs for vibration control of buildings exposed to stochastic seismic excitations", Proceedings of the 11th ICOSSAR International Conference on Structural Safety and Reliability for Integrating Structural Analysis, Risk and Reliability, New York, June.
  31. Masri, S.F. and Caffrey, J.P. (2017), "Transient response of a SDOF system with an inerter to nonstationary stochastic excitation", J. Appl. Mech. - ASCE, 84(4), 041005. https://doi.org/10.1115/1.4035930
  32. Ormondroyd, J. and Den Hartog, J.P. (1928), "The theory of the dynamic vibration absorber", J. Appl. Mech. - ASCE, 50, 9-22.
  33. Papageorgiou, C. and Smith, M.C. (2005), "Laboratory experimental testing of inerters", Proceedings of the IEEE Conference on Decision and Control, Seville, Spain, December.
  34. 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. D., DOI:10.1002/eqe.2861.
  35. Rana, R. and Soong, T.T. (1998), "Parametric study and simplified design of tuned mass dampers", Eng. Struct., 20(3), 193-204. https://doi.org/10.1016/S0141-0296(97)00078-3
  36. Ricciardelli, F. and Vickery, B.J. (1999), "Tuned vibration absorbers with dry friction damping", Earthq. Eng. Struct. D., 28(7), 707-724. https://doi.org/10.1002/(SICI)1096-9845(199907)28:7<707::AID-EQE836>3.0.CO;2-C
  37. Rome, L.C., Flynn, L., Goldman, E.M. and Yoo, T.D. (2005), "Generating electricity while walking with loads", Science, 309(5741), 1725-1728. https://doi.org/10.1126/science.1111063
  38. Salvi, J. and Rizzi, E. (2016), "Closed-form optimum tuning formulas for passive tuned mass dampers under benchmark excitations", Smart Struct. Syst., 17(2), 231-256. https://doi.org/10.12989/sss.2016.17.2.231
  39. Shen, W., Zhu, S. and Xu, Y.l. (2012), "An experimental study on self-powered vibration control and monitoring system using electromagnetic TMD and wireless sensors", Sensor. Actuat. - A, 180, 166-176. https://doi.org/10.1016/j.sna.2012.04.011
  40. Shen, Z., Zhu, S., Zhu, H. and Xu, Y.L. (2016), "Electromagnetic energy harvesting from structural vibrations during earthquakes", Smart Struct. Syst., 18(3), 449-470. https://doi.org/10.12989/sss.2016.18.3.449
  41. Smith, M.C. (2002), "Synthesis of mechanical networks: the inerter", IEEE T. Autom. Control, 47(10), 1648-1662. https://doi.org/10.1109/TAC.2002.803532
  42. Swift, S.J., Smith, M.C., Glover, A.R., Papageorgiou, C., Gartner, B. and Houghton, N.E. (2013), "Design and modelling of a fluid inerter", Int. J. Control, 86(11), 2035-2051. https://doi.org/10.1080/00207179.2013.842263
  43. Tang, X. and Zuo, L. (2012), "Simultaneous energy harvesting and vibration control of structures with tuned mass dampers", J. Intel. Mat. Syst. Str., 23(18), 2117-2127. https://doi.org/10.1177/1045389X12462644
  44. Tributsch, A. and Adam, C. (2012), "Evaluation and analytical approximation of Tuned Mass Dampers performance in an earthquake environment", Smart Struct. Syst., 10(2), 155-179. https://doi.org/10.12989/sss.2012.10.2.155
  45. Wang, F.C., Hong, M.F. and 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. https://doi.org/10.1243/09544062JMES2199
  46. Wang, J.F. and Lin, C.C. (2015), "Extracting parameters of TMD and primary structure from the combined system responses", Smart Struct. Syst., 16(5), 937-960. https://doi.org/10.12989/sss.2015.16.5.937
  47. Warburton, G.B. (1982), "Optimum absorber parameters for various combinations of response and excitation parameters", Earthq. Eng. Struct. D., 10(3), 381-401. https://doi.org/10.1002/eqe.4290100304
  48. Xu, K. and Igusa, T. (1992), "Dynamic characteristics of multiple substructures with closely spaced frequencies", Earthq. Eng. Struct. D., 21, 1059-1070. https://doi.org/10.1002/eqe.4290211203
  49. Yamaguchi, H. and Harnpornchai, N. (1993), "Fundamental characteristics of multiple tuned mass dampers for suppressing harmonically forced oscillations", Earthq. Eng. Struct. D., 22(1), 51-62. https://doi.org/10.1002/eqe.4290220105
  50. Yang, F., Sedaghati, R. and Esmailzadeh, E. (2015), "Optimal design of distributed tuned mass dampers for passive vibration control of structures", Struct. Control Health Monit., 22, 221-236. https://doi.org/10.1002/stc.1670
  51. Zhu, S., Shen, W.A. and Zu, Y.L. (2012), "Linear electromagnetic devices for vibration damping and energy harvesting: Modeling and testing", Eng. Struct., 34(1), 198-212. https://doi.org/10.1016/j.engstruct.2011.09.024
  52. Zuo, L. (2009), "Effective and robust vibration control using series multiple tuned-mass dampers", J. Vib. Acoust., 131(3), 031003. https://doi.org/10.1115/1.3085879
  53. Zuo, L. and Tang, X. (2013), "Large-scale vibration energy harvesting", J. Intel. Mat. Syst. Str., 24(11), 1405-1430. https://doi.org/10.1177/1045389X13486707

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