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Technical Brief

A Closed-Form Optimal Tuning of Mass Dampers for One Degree-of-Freedom Systems Under Rotating Unbalance Forcing

[+] Author and Article Information
T. Argentini

Department of Mechanical Engineering,
Politecnico di Milano,
via La Masa 1,
Milano 20156, Italy
e-mail: tommaso.argentini@polimi.it

M. Belloli

Department of Mechanical Engineering,
Politecnico di Milano,
via La Masa 1,
Milano 20156, Italy
e-mail: marco.belloli@polimi.it

P. Borghesani

School of Chemistry,
Physics and Mechanical Engineering,
Queensland University of Technology,
#2 George Street,
Brisbane, Queensland 4000, Australia
e-mail: p.borghesani@qut.edu.au

Given a quadratic equation ax2 + bx + c = 0 with solutions x1 and x2, then (1/x1)+(1/x2)=-(b/c).

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 27, 2014; final manuscript received January 5, 2015; published online February 18, 2015. Assoc. Editor: Yukio Ishida.

J. Vib. Acoust 137(3), 034501 (Jun 01, 2015) (6 pages) Paper No: VIB-14-1101; doi: 10.1115/1.4029576 History: Received March 27, 2014; Revised January 05, 2015; Online February 18, 2015

This paper is focused on the study of a vibrating system forced by a rotating unbalance and coupled to a tuned mass damper (TMD). The analysis of the dynamic response of the entire system is used to define the parameters of such device in order to achieve optimal damping properties. The inertial forcing due to the rotating unbalance depends quadratically on the forcing frequency and it leads to optimal tuning parameters that differ from classical values obtained for pure harmonic forcing. Analytical results demonstrate that frequency and damping ratios, as a function of the mass parameter, should be higher than classical optimal parameters. The analytical study is carried out for the undamped primary system, and numerically investigated for the damped primary system. We show that, for practical applications, proper TMD tuning allows to achieve a reduction in the steady-state response of about 20% with respect to the response achieved with a classically tuned damper.

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References

Den Hartog, J., 1956, Mechanical Vibrations, 4th ed., McGraw-Hill, New York.
Brock, J. E., 1946, “A Note on the Damped Vibration Absorber,” ASME J. Appl. Mech., 13(4), p. A284.
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]
Asami, T., Nishihara, O., and Baz, A., 2002, “Analytical Solutions to H and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems,” ASME J. Vib. Acoust., 124(2), pp. 284–295. [CrossRef]
Bisegna, P., and Caruso, G., 2012, “Closed-Form Formulas for the Optimal Pole-Based Design of Tuned Mass Dampers,” J. Sound Vib., 331(10), pp. 2291–2314. [CrossRef]
Krenk, S., 2005, “Frequency Analysis of the Tuned Mass Damper,” ASME J. Appl. Mech., 72(6), pp. 936–942. [CrossRef]
Tsai, H.-C., and Lin, G.-C., 1994, “Explicit Formulae for Optimum Absorber Parameters for Force-Excited and Viscously Damped Systems,” J. Sound Vib., 176(5), pp. 585–596. [CrossRef]
Ghosh, A., and Basu, B., 2007, “A Closed-Form Optimal Tuning Criterion for TMD in Damped Structures,” Struct. Control Health Monit., 14(4), pp. 681–692. [CrossRef]
Randall, S., Halsted, D., III, and Taylor, D., 1981, “Optimum Vibration Absorbers for Linear Damped Systems,” ASME J. Mech. Des., 103(4), pp. 908–913. [CrossRef]
Liu, K., and Coppola, G., 2010, “Optimal Design of Damped Dynamic Vibration Absorber for Damped Primary Systems,” Trans. Can. Soc. Mech. Eng., 34(1), pp. 119–135.
Thompson, A., 1980, “Optimizing the Untuned Viscous Dynamic Vibration Absorber With Primary System Damping: A Frequency Locus Method,” J. Sound Vib., 73(3), pp. 469–472. [CrossRef]
Pennestr, E., 1998, “An Application of Chebyshev's Min–Max Criterion to the Optimal Design of a Damped Dynamic Vibration Absorber,” J. Sound Vib., 217(4), pp. 757–765. [CrossRef]
Brown, B., and Singh, T., 2011, “Minimax Design of Vibration Absorbers for Linear Damped Systems,” J. Sound Vib., 330(11), pp. 2437–2448. [CrossRef]
Jang, S.-J., Brennan, M., Rustighi, E., and Jung, H.-J., 2012, “A Simple Method for Choosing the Parameters of a Two Degree-of-Freedom Tuned Vibration Absorber,” J. Sound Vib., 331(21), pp. 4658–4667. [CrossRef]
Liu, K., and Liu, J., 2005, “The Damped Dynamic Vibration Absorbers: Revisited and New Result,” J. Sound Vib., 284(35), pp. 1181–1189. [CrossRef]
Krenk, S., and Hogsberg, J., 2014, “Tuned Mass Absorber on a Flexible Structure,” J. Sound Vib., 333(6), pp. 1577–1595. [CrossRef]
Ali, S., and Adhikari, S., 2013, “Energy Harvesting Dynamic Vibration Absorbers,” ASME J. Appl. Mech., 80(4), p. 041004. [CrossRef]
Puksand, H., 1975, “Optimum Conditions for Dynamic Vibration Absorbers for Variable Speed Systems With Rotating or Reciprocating Unbalance,” Int. J. Mech. Eng. Educ., 3(2), pp. 145–152.
Thompson, A. G., 1980, “Optimizing the Untuned Viscous Dynamic Vibration Absorber With Primary System Damping: A Frequency Locus Method,” J. Sound Vib., 73(3), pp. 469–472. [CrossRef]
Argentini, T., Belloli, M., Robustelli, F., Martegani, L., and Fraternale, G., 2013, “Innovative Designs for the Suspension System of Horizontal-Axis Washing Machines: Secondary Suspensions and Tuned Mass Dampers,” ASME Paper No. IMECE2013-64425. [CrossRef]

Figures

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Fig. 1

Damped TMD connected to a primary system forced by a rotating unbalance

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Fig. 2

Magnitude of X˜ versus g with nonoptimal TMD parameters (f = 1 and μ = 0.05)

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Fig. 3

Optimal TMD parameters as a function of mass parameter μ

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Fig. 8

Ratio of maxima ||X˜num||∞ as a function of ζ for μ = 0.05: solution 1 and solution 2

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Fig. 4

Magnitude of X˜ versus g with optimal TMD parameters, using μ = 0.05

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Fig. 5

Magnitude of Y˜ versus g with optimal TMD parameters, using μ = 0.05

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Fig. 6

Ratio between the maxima of the frequency response functions (infinity norm) obtained with classical and optimal parameters as a function of the mass ratio

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Fig. 7

Numerically optimized values of ζd and f as a function of ζ for μ = 0.05: solution 1 and solution 2

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Fig. 9

Optimized frequency response functions |X˜num| for solutions 1 and 2, for increasing values on ζ. For this example, with μ = 0.05, the threshold is ζ = 0.012. Solutions 1 and 2—before threshold, solution 1—after threshold, and solution 2—after threshold.

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Fig. 10

ζlim as a function of the mass ratio μ

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