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Research Papers

Optimum Tuning of Passive Tuned Mass Dampers for the Mitigation of Pulse-Like Responses

[+] Author and Article Information
Jonathan Salvi

Department of Engineering and
Applied Sciences,
University of Bergamo,
viale G. Marconi 5,
Dalmine (BG) I-24044, Italy
e-mail: jonathan.salvi@unibg.it

Egidio Rizzi

Department of Engineering and
Applied Sciences,
University of Bergamo,
viale G. Marconi 5,
Dalmine (BG) I-24044, Italy
e-mail: egidio.rizzi@unibg.it

Emiliano Rustighi

Institute of Sound and Vibration Research,
University of Southampton,
Highfield, Southampton SO17 1BJ, UK
e-mail: er@isvr.soton.ac.uk

Neil S. Ferguson

Institute of Sound and Vibration Research,
University of Southampton,
Highfield, Southampton SO17 1BJ, UK
e-mail: nsf@isvr.soton.ac.uk

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 17, 2018; final manuscript received May 25, 2018; published online July 3, 2018. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 140(6), 061014 (Jul 03, 2018) (14 pages) Paper No: VIB-18-1027; doi: 10.1115/1.4040475 History: Received January 17, 2018; Revised May 25, 2018

Tuned mass dampers (TMDs) are typically introduced and calibrated as natural passive control devices for the vibration mitigation of the steady-state response of primary structures subjected to persistent excitations. Otherwise, this work investigates the optimum tuning of TMDs toward minimizing the transient structural response. Specifically, a single-degree-of-freedom (SDOF) system is considered as a primary structure, with added TMD, subjected to pulse-like excitations. First, the system is analytically analyzed, within the time domain, for unit impulse base displacement, through Laplace transform. Then, the tuning process is numerically explored by an optimization procedure focused on an average response index, to extract the optimum condition toward best TMD calibration. The efficiency of the proposed control device is then assessed and demonstrated through further post-tuning numerical tests, by considering as dynamic loadings: first, a time unit impulse base displacement, coherent with the source description above; second, different pulse-like excitations, to detect the effectiveness of the so-conceived TMD for generic ideal shock actions; third, a set of nonstationary earthquake excitations, to enquire the achievable level of seismic isolation. It is shown that this leads to a consistent passive TMD in such a transient excitation context, apt to mitigate the average response. Additionally, the present tuning forms a necessary optimum background for a possible upgrade to a hybrid TMD, with the potential addition of an active controller to the so-optimized TMD, to achieve even further control performance, once turned on, specifically for abating the peak response, too.

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References

Jang, S.-J. , Brennan, M. J. , and Rustighi, E. , 2010, “ Comparing the Performance of Optimally Tuned Dynamic Vibration Absorbers With Very Large or Very Small Moment of Inertia,” ASME J. Vib. Acoust., 132(3), p. 034501.
Zilletti, M. , Elliott, S. J. , and Rustighi, E. , 2012, “ Optimisation of Dynamic Vibration Absorbers to Minimise Kinetic Energy and Maximise Internal Power Dissipation,” J. Sound Vib., 331(18), pp. 4093–4100. [CrossRef]
Salvi, J. , and Rizzi, E. , 2015, “ Optimum Tuning of Tuned Mass Dampers for Frame Structures Under Earthquake Excitation,” Struct. Control Health Monit., 22(4), pp. 707–715. [CrossRef]
Salvi, J. , and Rizzi, E. , 2016, “ Closed-Form Optimum Tuning Formulas for Passive Tuned Mass Dampers Under Benchmark Excitations,” Smart Struct. Syst., 17(2), pp. 231–256. [CrossRef]
Salvi, J. , and Rizzi, E. , 2017, “ Optimum Earthquake-Tuned TMDs: Seismic Performance and New Design Concept of Balance of Split Effective Modal Masses,” Soil Dyn. Earthquake Eng., 101, pp. 67–80. [CrossRef]
Salvi, J. , Rizzi, E. , Rustighi, E. , and Ferguson, N. S. , 2015, “ On the Optimisation of a Hybrid Tuned Mass Damper for Impulse Loading,” Smart Mater. Struct., 24(8), p. 085010. [CrossRef]
Parulekar, Y. M. , and Reddy, G. R. , 2009, “ Passive Response Control Systems for Seismic Response Reduction: A State-of-the-Art Review,” Int. J. Struct. Stab. Dyn., 9(1), pp. 151–177. [CrossRef]
Liu, Y. , Lin, C.-C. , Parker, J. , and Zuo, L. , 2016, “ Exact H2 Optimal Tuning and Experimental Verification of Energy-Harvesting Series Electromagnetic Tuned-Mass Dampers,” ASME J. Vib. Acoust., 138(6), p. 061003. [CrossRef]
Li, S. , and Tang, J. , 2017, “ On Vibration Suppression and Energy Dissipation Using Tuned Mass Particle Damper,” ASME J. Vib. Acoust., 139(1), p. 011008. [CrossRef]
Frahm, H. , 1911, “ Device for Damping Vibrations of Bodies,” U.S. Patent No. 989958.
Ormondroyd, J. , and Den Hartog, J. P. , 1928, “ The Theory of the Dynamic Vibration Absorber,” ASME J. Appl. Mech., 50(7), pp. 9–22.
Brock, J. E. , 1946, “ A Note on the Damped Vibration Absorber,” ASME J. Appl. Mech., 13(4), pp. 1–284.
Den Hartog, J. P. , 1956, Mechanical Vibrations, 4th ed., McGraw-Hill, New York.
Ioi, T. , and Ikeda, K. , 1978, “ On the Dynamic Vibration Damped Absorber of the Vibration System,” Bull. Jpn. Soc. Mech. Eng., 21(151), pp. 64–71. [CrossRef]
Randall, S. E. , Halsted, D. M. , and Taylor, D. L. , 1981, “ Optimum Vibration Absorbers for Linear Damped Systems,” ASME J. Mech. Des., 103(4), pp. 908–913. [CrossRef]
Rana, R. , and Soong, T. T. , 1998, “ Parametric Study and Simplified Design of Tuned Mass Dampers,” Eng. Struct., 20(3), pp. 193–204. [CrossRef]
Bakre, S. V. , and Jangid, R. S. , 2006, “ Optimum Parameters of Tuned Mass Damper for Damped Main System,” Struct. Control Health Monit., 14(3), pp. 448–470. [CrossRef]
Krenk, S. , and Høgsberg, J. , 2008, “ Tuned Mass Absorbers on Damped Structures Under Random Load,” Probab. Eng. Mech., 23(4), pp. 408–415. [CrossRef]
Warburton, G. B. , 1982, “ Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters,” Earthquake Eng. Struct. Dyn., 10(3), pp. 381–401. [CrossRef]
Asami, T. , Nishihara, O. , and Baz, A. M. , 2002, “ Analytical Solutions to H and H2 Optimization of Dynamic Vibration Absorber Attached to Damped Linear Systems,” ASME J. Vib. Acoust., 124(2), pp. 284–295. [CrossRef]
Leung, A. Y. T. , and Zhang, H. , 2009, “ Particle Swarm Optimization of Tuned Mass Dampers,” Eng. Struct., 31(3), pp. 715–728. [CrossRef]
Bandivadekar, T. P. , and Jangid, R. S. , 2013, “ Optimization of Multiple Tuned Mass Dampers for Vibration Control of System Under External Excitation,” J. Vib. Control, 19(12), pp. 1854–1871. [CrossRef]
Marano, G. C. , and Greco, R. , 2011, “ Optimization Criteria for Tuned Mass Dampers for Structural Vibration Control Under Stochastic Excitation,” J. Vib. Control, 17(5), pp. 679–688. [CrossRef]
Setareh, M. , 2001, “ Use of Semi-Active Mass Dampers for Vibration Control of Force-Excited Structures,” Struct. Eng. Mech., 11(4), pp. 341–356. [CrossRef]
Sun, C. , Nagarajaiah, S. , and Dick, A. J. , 2014, “ Family of Smart Tuned Mass Dampers With Variable Frequency Under Harmonic Excitations and Ground Motions: Closed-Form Evaluation,” Smart Struct. Syst., 13(2), pp. 319–341. [CrossRef]
Tigli, O. F. , 2012, “ Optimum Vibration Absorber (Tuned Mass Damper) Design for Linear Damped Systems Subjected to Random Loads,” J. Sound Vib., 331(13), pp. 3035–3049. [CrossRef]
Aly, A. M. , 2014, “ Vibration Control of High-Rise Buildings for Wind: A Robust Passive and Active Tuned Mass Damper,” Smart Struct. Syst., 13(3), pp. 473–500. [CrossRef]
Morga, M. , and Marano, G. C. , 2014, “ Optimization Criteria of TMD to Reduce Vibrations Generated by the Wind in a Slender Structure,” J. Vib. Control, 20(16), pp. 2404–2416. [CrossRef]
Adam, C. , and Furtmüller, T. , 2010, “ Seismic Performance of Tuned Mass Dampers,” Mechanics and Model-Based Control of Smart Materials and Structures, 1st ed., H. Irschik , M. Krommer , K. Watanabe , and T. Furukawa , eds., Springer-Verlag, Wien, Austria, pp. 11–18. [CrossRef]
Desu, N. B. , Dutta, A. , and Deb, S. K. , 2007, “ Optimal Assessment and Location of Tuned Mass Dampers for Seismic Response Control of a Plan-Asymmetrical Building,” Struct. Eng. Mech., 26(4), pp. 459–477. [CrossRef]
Matta, E. , 2011, “ Performance of Tuned Mass Dampers against Near-Field Earthquakes,” Struct. Eng. Mech., 39(5), pp. 621–642. [CrossRef]
Tributsch, A. , and Adam, C. , 2012, “ Evaluation and Analytical Approximation of Tuned Mass Damper Performance in an Earthquake Environment,” Smart Struct. Syst., 10(2), pp. 155–179. [CrossRef]
Matta, E. , 2013, “ Effectiveness of Tuned Mass Dampers against Ground Motion Pulses,” ASCE J. Struct. Eng., 139(2), pp. 188–198. [CrossRef]
Farshidianfar, A. , and Soheili, S. , 2013, “ Ant Colony Optimization of Tuned Mass Dampers for Earthquake Oscillations of High-Rise Structures Including Soil-Structure Interaction,” Soil Dyn. Earthquake Eng., 51, pp. 14–22. [CrossRef]
Miranda, J. C. , 2016, “ Discussion of System Intrinsic Parameters of Tuned Mass Dampers Used for Seismic Response Reduction,” Struct. Control Health Monit., 23(2), pp. 349–368. [CrossRef]
Bekdaş, G. , and Nigdeli, S. M. , 2017, “ Metaheuristic Based Optimization of Tuned Mass Dampers Under Earthquake Excitation by Considering Soil-Structure Interaction,” Soil Dyn. Earthquake Eng., 92, pp. 443–461. [CrossRef]
Abé, M. , and Igusa, T. , 1996, “ Semi-Active Dynamic Vibration Absorbers for Controlling Transient Response,” J. Sound Vib., 198(5), pp. 547–569. [CrossRef]
Quaranta, G. , Mollaioli, F. , and Monti, G. , 2016, “ Effectiveness of Design Procedures for Linear TMD Installed on Inelastic Structures Under Pulse-like Ground Motion,” Earthquakes Struct., 10(1), pp. 239–260. [CrossRef]
Chen, G. , and Wu, J. , 2003, “ Experimental Study on Multiple Tuned Mass Dampers to Reduce Seismic Responses of a Three-Storey Building Structure,” Earthquake Eng. Struct. Dyn., 32(5), pp. 793–810. [CrossRef]
Xiang, P. , and Nishitani, A. , 2015, “ Optimum Design and Application of Non-Traditional Tuned Mass Damper Toward Seismic Response Control With Experimental Test Verification,” Earthquake Eng. Struct. Dyn., 44(13), pp. 2199–2220. [CrossRef]
Wu, Q. , Zhao, X. , and Zheng, R. , 2016, “ Experimental Study on a Tuned-Mass Damper of Offshore for Vibration Reduction,” J. Phys.: Conf. Ser., 744(2016), p. 012045. [CrossRef]
Jabary, R. N. , and Madabhushi, G. S. P. , 2015, “ Tuned Mass Damper Effects on the Response of Multi-Storied Structures Observed in Geotechnical Centrifuge Tests,” Soil Dyn. Earthquake Eng., 77, pp. 373–380. [CrossRef]
Jabary, R. N. , and Madabhushi, G. S. P. , 2017, “ Tuned Mass Damper Positioning Effects on the Seismic Response of a Soil-MDOF-Structure System,” J. Earthquake Eng., 31(2), pp. 1–22.
Jabary, R. N. , and Madabhushi, G. S. P. , 2017, “ Structure-Soil-Structure Interaction Effects on Structures Retrofitted With Tuned Mass Dampers,” Soil Dyn. Earthquake Eng., 100, pp. 301–315. [CrossRef]
Salvi, J. , Pioldi, F. , and Rizzi, E. , 2018, “ Optimum Tuned Mass Dampers Under Seismic Soil-Structure Interaction,” (under review).
Bakre, S. V. , and Jangid, R. S. , 2004, “ Optimum Multiple Tuned Mass Dampers for Base-Excited Damped Main System,” Int. J. Struct. Stability Dyn., 4(4), pp. 527–542. [CrossRef]
Pioldi, F. , Ferrari, R. , and Rizzi, E. , 2015, “ Output-Only Modal Dynamic Identification of Frames by a Refined FDD Algorithm at Seismic Input and High Damping,” Mech. Syst. Signal Process., 68–69, pp. 265–291.
Pioldi, F. , Ferrari, R. , and Rizzi, E. , 2015, “ Earthquake Structural Modal Estimates of Multi-Storey Frames by a Refined Frequency Domain Decomposition Algorithm,” J. Vib. Control, 23(13), pp. 2037–2063. [CrossRef]
Pioldi, F. , Ferrari, R. , and Rizzi, E. , 2017, “ Seismic FDD Modal Identification and Monitoring of Building Properties From Real Strong-Motion Structural Response Signals,” Struct. Control Health Monit., 24(11), e. e1982.
Ghahari, S. F. , Abazarsa, F. , and Taciroglu, E. , 2017, “ Blind Modal Identification of Non-Classically Damped Structures Under Non-Stationary Excitations,” Struct. Control Health Monit., 24(6), e. e1925.
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), pp. 937–960. [CrossRef]
Pioldi, F. , Salvi, J. , and Rizzi, E. , 2016, “ Refined FDD Modal Dynamic Identification From Earthquake Responses With Soil-Structure Interaction,” Int. J. Mech. Sci., 127, pp. 47–61. [CrossRef]
Villaverde, R. , 1993, “ Reduction in Seismic Response With Heavily-Damped Vibration Absorbers,” Earthquake Eng. Struct. Dyn., 13(1), pp. 33–42. [CrossRef]
Villaverde, R. , and Koyama, L. A. , 1993, “ Damped Resonant Appendages to Increase Inherent Damping in Buildings,” Earthquake Eng. Struct. Dyn., 22(6), pp. 491–507. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Structural parameters and absolute dynamic degrees-of-freedom of a SDOF linear primary structure (index 1), subjected to generic base displacement xg(t)

Grahic Jump Location
Fig. 2

Structural parameters and absolute dynamic degrees-of-freedom of a 2DOF linear mechanical system comprised of a SDOF primary structure (index 1) equipped with an added TMD (index 2), subjected to generic base displacement xg(t)

Grahic Jump Location
Fig. 3

H2 norm of the primary structure displacement as a function of tuning variables f, ζ2, for ζ1 = 0.03 and for different values of mass ratio μ: (a) μ = 0.02 and (b) μ = 0.05

Grahic Jump Location
Fig. 4

Optimum TMD parameters at variable mass ratio μ for different values of structural damping ratio ζ1: (a) frequency ratio fopt and (b) TMD damping ratio ζ2opt

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Fig. 5

Optimum TMD parameters at variable mass ratio μ, with structural damping ratio ζ1 = 0.03, for different dynamic excitations: (a) frequency ratio fopt and (b) TMD damping ratio ζ2opt

Grahic Jump Location
Fig. 6

Percentage reduction of the H2 norm of the displacement of the primary structure at variable mass ratio μ for different values of structural damping ratio ζ1: (a) proposed tuning method and (b) Den Hartog tuning method [13]

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Fig. 7

Primary structure displacement time history with ζ1 = 0: (a) proposed tuning method and (b) Den Hartog tuning method[13]

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Fig. 8

Primary structure displacement time history with ζ1 = 0.03: (a) proposed tuning method and (b) Den Hartog tuning method [13]

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Fig. 9

Response displacement time histories x1(t) with μ = 0.02, ζ1 = 0 for different seismic signals, with passive TMD optimized for unit impulse base displacement: (a) Imperial Valley, 1940, (b) Loma Prieta, 1989, (c) Kobe, 1995, and (d) L'Aquila, 2009

Grahic Jump Location
Fig. 10

Response displacement time histories x1(t) with μ = 0.05, ζ1 = 0.03 for different seismic signals, with passive TMD optimized for unit impulse base displacement: (a) Imperial Valley, 1940, (b) Loma Prieta, 1989, (c) Kobe, 1995, and (d) L'Aquila, 2009

Grahic Jump Location
Fig. 11

Scheme of pulse-like excitations adopted in Sec. 5.2

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