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Research Papers

Optimal Vibration Absorber With a Friction Damper

[+] Author and Article Information
Alok Sinha

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: axs22@psu.edu

Krishna T. Trikutam

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: trikutamkrishnateja@gmail.com

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 8, 2017; final manuscript received October 12, 2017; published online November 10, 2017. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 140(2), 021015 (Nov 10, 2017) (7 pages) Paper No: VIB-17-1247; doi: 10.1115/1.4038272 History: Received June 08, 2017; Revised October 12, 2017

The response of a single degree-of-freedom spring mass system connected to a vibration absorber with a friction damper and subjected to a sinusoidal excitation is considered in this paper. Two possible configurations of the friction damper, rigid and flexible, are explored in details. Optimization of the parameters of absorbers with both these damper configurations to minimize the peak value of the frequency response of the primary system is presented. Results from this minimax optimization approach are compared to the classical solutions for a vibration absorber with linear viscous damper.

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References

Den Hartog, J. P. , 1985, Mechanical Vibrations, Dover Publications, New York.
Sinha, A. , 2010, Vibration of Mechanical Systems, Cambridge University Press, New York. [CrossRef]
Sinha, A. , 2009, “ Optimal Damped Vibration Absorber for Narrow Band Random Excitations: A Mixed H2/H Optimization,” Probab. Eng. Mech., 24(2), pp. 251–254. [CrossRef]
Sinha, A. , 2015, “ Optimal Damped Vibration Absorber: Including Multiple Modes and Excitation Due to Rotating Unbalance,” ASME J. Vib. Acoust., 137(6), p. 064501. [CrossRef]
Asami, T. , and Nishihara, O. , 2003, “ Closed-Form Exact Solution to H Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems),” ASME J. Vib. Acoust., 125(3), pp. 398–405. [CrossRef]
Ricciardelli, F. , and Vickery, B. J. , 1999, “ Tuned Vibration Absorbers With Dry Friction Damping,” J. Earthquake Eng. Struct. Dyn., 28(7), pp. 707–723. [CrossRef]
Gewei, Z. , and Basu, B. , 2010, “ A Study on Friction-Tuned Mass Damper: Harmonic Solution and Statistical Linearization,” J. Vib. Control, 17(5), pp. 721–731. [CrossRef]
Pisal, A. Y. , and Jangid, R. S. , 2016, “ Dynamic Response of Structure With Tuned Mass Friction Damper,” Int. J. Adv. Struct. Eng., 8(4), pp. 363–377. [CrossRef]
Hartung, A. , Schmieg, H. , and Vielsack, P. , 2001, “ Passive Vibration Absorber With Dry Friction,” Arch. Appl. Mech., 71(6–7), pp. 463–472. [CrossRef]
Abe, M. , 1996, “ Tuned Mass Dampers for Structures With Bilinear Hysteresis,” ASCE J. Eng. Mech., 122(8), pp. 797–800. [CrossRef]
Sinha, A. , and Griffin, J. H. , 1985, “ Stability of Limit Cycles in Frictionally Damped and Aerodynamically Unstable Rotor Stages,” J. Sound Vib., 103(3), pp. 341–356. [CrossRef]
Fang, J. , Wang, Q. , and Wang, S. , 2012, “ Min-Max Criterion to the Optimal Design of Vibration Absorber in a System With Coulomb Friction and Viscous Damping,” Nonlinear Dyn., 70(1), pp. 393–400.
Vidmar, B. J. , Feeny, B. F. , Shaw, S. , Haddow, A. G. , Geist, B. K. , and Verhanovitz, N. J. , 2012, “ The Effects of Coulomb Friction on the Performance of Centrifugal Pendulum Vibration Absorbers,” Nonlinear Dyn., 69(1–2), pp. 589–600. [CrossRef]
Sinha, A. , 2016, “ Vibration Absorbers for a Mistuned Bladed Disk,” ASME Paper No. GT2016-56076.
Cha, D. , and Sinha, A. , 2010, “ Computation of the Optimal Normal Load for a Mistuned and Frictionally Damped Bladed Disk Assembly Under Different Types of Excitation,” ASME J. Comput. Nonlinear Dyn., 6(2), p. 021012. [CrossRef]
Yang, B. D. , and Menq, C. H. , 1998, “ Characterization of 3D Contact Kinematics and Prediction of Resonant Response of Structures Having 3D Frictional Constraint,” J. Sound Vib., 217(5), pp. 909–925. [CrossRef]
Sanliturk, K. Y. , Ewins, D. J. , Elliott, R. , and Green, J. , 2001, “ Friction Damper Optimization: Simulation of Rainbow Tests,” ASME J. Eng. Gas Turbines Power, 123(4), pp. 930–939. [CrossRef]
Melanie, M. , 1996, An Introduction to Genetic Algorithms, MIT Press, Cambridge, MA.
MATLAB, 2016, “ Matlab,” The MathWorks, Inc., Natick, MA.
Bathe, K.-J. , 1996, Finite Element Procedures, 1st ed., Prentice Hall, Upper Saddle River, NJ.

Figures

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Fig. 1

Vibration absorber with a RFD

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Fig. 2

Vibration absorber with a FFD

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Fig. 3

Nondimensional friction force versus relative displacement

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Fig. 4

Response from numerical integration of differential equations (RFD, μ = 0.25, λ = 1, κ=0.5, g=0.8)

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Fig. 5

Response from numerical integration of differential equations (FFD, μ = 0.25, λ = 1, κ=0.75, g=0.8, k¯=0.5)

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Fig. 6

Frequency responses of main mass for vibration absorber with RFD for different values of nondimensional slip load κ (μ = 0.25, λ = 1)

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Fig. 7

Frequency responses of main mass for vibration absorbers with RFD and highly stiff (k¯=1000) FFDs (μ = 0.25, λ = 1)

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Fig. 8

Frequency responses of main mass for vibration absorber with optimal and nonoptimal parameters (RFD, μ=0.1)

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Fig. 9

Optimal natural frequency ratio of vibration absorber as function of mass ratio μ

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Fig. 10

Optimal slip load of vibration absorber as a function of mass ratio μ

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Fig. 11

Minimum value of the maximum amplitude of main mass as a function of mass ratio μ

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Fig. 12

Equivalent viscous damping ratio for optimal vibration absorber as a function of mass ratio μ

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Fig. 13

Frequency responses of main mass for vibration absorber with FFD for different values of nondimensional slip load κ(μ = 0.25, λ = 1, k¯=0.5)

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Fig. 14

Frequency responses of main mass for vibration absorber with optimal and nonoptimal parameters (FFD, μ=0.1)

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