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TECHNICAL PAPERS

On Friction Damping Modeling Using Bilinear Hysteresis Elements

[+] Author and Article Information
E. J. Berger

Computer-Aided Engineering Laboratory, Department of Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072

C. M. Krousgrill

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1288

J. Vib. Acoust 124(3), 367-375 (Jun 12, 2002) (9 pages) doi:10.1115/1.1473831 History: Received July 01, 2001; Revised February 01, 2002; Online June 12, 2002
Copyright © 2002 by ASME
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References

Iwan,  W. D., 1967, “On a Class of Models for the Yielding Behavior of Continuous and Composite Systems,” ASME J. Appl. Mech., 34, pp. 612–617.
Ferri, A. A., and Heck, B. S., 1995, “Vibration Analysis of Dry Friction Damped Turbine Blades Using Singular Perturbation Theory,” Proceedings of the ASME International Mechanical Engineering Congress and Exposition, AMD-Vol. 192, pp. 47–56.
Berger,  E. J., Begley,  M. R., and Mahajani,  M., 2000, “Structural Dynamic Effects on Interface Response-Formulation and Simulation Under Partial Slipping Conditions,” ASME J. Appl. Mech., 67, pp. 785–792.
Den Hartog,  J. P., 1931, “Forced Vibrations with Combined Coulomb and Viscous Damping,” ASME J. Appl. Mech., APM-53-9, pp. 107–115.
Griffin,  J. H., 1980, “Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils,” ASME J. Eng. Power, 102, pp. 329–333.
Menq,  C.-H., Griffin,  J. H., and Bielak,  J., 1986, “The Influence of a Variable Normal Load on the Forced Vibration of a Frictionally Damped Structure,” ASME J. Eng. Gas Turbines Power, 108, pp. 300–305.
Menq,  C.-H., and Griffin,  J. H., 1985, “A Comparison of Transient and Steady State Finite Element Analyses of the Forced Response of a Frictionally Damped Beam,” ASME J. Vibr. Acoust., 107, pp. 19–25.
Cameron, T. M., Griffin, J. H., Kielb, R. E., and Hoosac, T. M., 1987, “An Integrated Approach for Friction Damper Design,” ASME Design Booklet, The Role of Damping in Vibration and Noise Control, ASME DE-Vol. 5, pp. 205–211.
Wang,  J. H., and Chen,  W. K., 1993, “Investigation of the Vibration of a Blade With Friction Damper by HBM,” ASME J. Eng. Gas Turbines Power, 115, pp. 294–299.
Sanliturk,  K. Y., and Ewins,  D. J., 1996, “Modelling Two-Dimensional Friction Contact and Its Application Using Harmonic Balance Method,” J. Sound Vib., 193, pp. 511–523.
Sanliturk,  K. Y., Imregun,  M., and Ewins,  D. J., 1997, “Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers,” ASME J. Vibr. Acoust., 119, pp. 96–103.
Szwedowicz, J., Kissel, M., Ravindra, B., and Kellerer, R., 2001, “Estimation of Contact Stiffness and Its Role in the Design of a Friction Damper,” Proceedings of ASME TURBO EXPO 2001, New Orleans, Louisiana.
Pierre,  C., Ferri,  A. A., and Dowell,  E. H., 1985, “Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method,” ASME J. Appl. Mech., 52, pp. 958–964.

Figures

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Schematic of system mass with collection of damper masses attached in parallel.
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Sensitivity of steady-state response amplitude to changes in damper stiffness ratio k1; sensitivity is highest in region of expected operation near 0.1<k1<1.
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Transition map in damper parameter space (k11) for m1=0.1. The two solid lines indicate the predicted transitions from pure slip to stick-slip (γ1sl), and stick-slip to pure stick (γ1st) steady-state damper response. Simulation results of the full nonlinear equations are shown as discrete points on the graph, with •: pure stick, ×: stick-slip, and ○: pure slip.
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Transition map in damper parameter space (k11) for (a) m1=0.01 and (b) m1=1.0. The two solid lines indicate the predicted transitions from pure slip to stick-slip (γ1sl), and stick-slip to pure stick (γ1st) steady-state damper response. Simulation results of the full nonlinear equations are shown as discrete points on the graph, with •: pure stick, ×: stick-slip, and ○: pure slip.
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Friction-displacement behavior of bilinear hysteresis damping element under (a) monotonic and (b) cyclic loading (not drawn to same scale). Sticking displacement of system is shown for both cases.
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Contours of constant steady-state response amplitude Xo/Xono normalized by the response with no damper, calculated from Eq. (18). The dashed line corresponds to the stick-slip/pure stick boundary.
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Calculations corresponding to Fig. 11 of Ferri and Heck 2 showing the qualitative effect of damper mass, particularly under stick-slip response (k1=0.5).
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Variations in frequency ratio ωn2n1 as a function of damper mass ratio m1 for several values of stiffness ratio k1. Dashed line indicates the frequency ratio corresponding to the optimal vibration absorber for resonance amplitude reduction for the limiting case γ1→0.
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Performance of non-zero mass damper tuned to the system dynamics with k1/m1=Ω=1. Amplitude is normalized by the system mass response amplitude under pure stick conditions, Xost, and in this case k1=m1=1.
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System steady-state response in three-parameter space (k1,m11) showing qualitative effect of each. Responses are normalized by the response with no damper Xono given by Eq. (18).

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