0
Research Papers

Application of Viscous and Iwan Modal Damping Models to Experimental Measurements From Bolted Structures

[+] Author and Article Information
Brandon J. Deaner

Mercury Marine,
W6250 Pioneer Road,
P.O. Box 1939,
Fond du Lac, WI 54936-1939
e-mail: brandon.deaner@mercmarine.com

Matthew S. Allen

Associate Professor
Department of Engineering Physics,
University of Wisconsin-Madison,
535 Engineering Research Building,
1500 Engineering Drive,
Madison, WI 53706
e-mail: msallen@engr.wisc.edu

Michael J. Starr

Sandia National Laboratories,
P.O. Box 5800,
Albuquerque, NM 87185
e-mail: mjstarr@sandia.gov

Daniel J. Segalman

Department of Engineering Physics,
University of Wisconsin-Madison,
538 Engineering Research Building,
1500 Engineering Drive,
Madison, WI 53706
e-mail: segalman@wisc.edu

Hartono Sumali

Science, Technology and
Engineering Integration,
Sandia National Laboratories,
P.O. Box 5800,
Albuquerque, NM 87185
e-mail: hsumali@sandia.gov

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 1, 2013; final manuscript received November 8, 2014; published online January 20, 2015. Assoc. Editor: Weidong Zhu.

J. Vib. Acoust 137(2), 021012 (Apr 01, 2015) (12 pages) Paper No: VIB-13-1188; doi: 10.1115/1.4029074 History: Received June 01, 2013; Revised November 08, 2014; Online January 20, 2015

Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the structure and comparisons suggest that the model captures the stiffness and damping accurately over a range of forcing levels.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Segalman, D. J., 2001, “An Initial Overview of Iwan Modelling for Mechanical Joints,” Sandia National Laboritories, Albuquerque, NM, Report No. SAND2001-0811.
Segalman, D. J., 2005, “A Four-Parameter Iwan Model for Lap-Type Joints,” ASME J. Appl. Mech., 72(5), pp. 752–760. [CrossRef]
Segalman, D. J., and Starr, M. J., 2012, “Iwan Models and Their Provenance,” ASME Paper No. DETC2012-71534. [CrossRef]
Allen, M. S., and Mayes, R. L., 2010, “Estimating the Degree of Nonlinearity in Transient Responses With Zeroed Early-Time Fast Fourier Transforms,” Mech. Syst. Sig. Process., 24(7), pp. 2049–2064. [CrossRef]
Segalman, D. J., and Holzmann, W., 2005, “Nonlinear Response of a Lap-Type Joint Using a Whole-Interface Model,” 23rd International Modal Analysis Conference (IMAC-XXIII), Orlando, FL, Jan. 31–Feb. 3.
Segalman, D. J., 2010, “A Modal Approach to Modeling Spatially Distributed Vibration Energy Dissipation,” Sandia National Laboratories, Albuquerque, NM, Livermore, CA, Report No. SAND2010-4763.
Deaner, B. J., Allen, M. S., Starr, M. J., and Segalman, D. J., 2014, “Investigation of Modal Iwan Models for Structures With Bolted Joints,” Topics in Experimental Dynamic Substructuring (Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 2), Springer, New York, pp. 9–25. [CrossRef]
Eriten, M., Kurt, M., Luo, G., Michael, D., McFarland, Bergman, L. A., and Vakakis, A. F., 2013, “Nonlinear System Identification of Frictional Effects in a Beam With a Bolted Joint Connection,” Mech. Syst. Sig. Process., 39(1–2), pp. 245–264. [CrossRef]
Reuss, P., Kruse, S., Peter, S., Morlock, F., and Gaul, L., 2013, “Identification of Nonlinear Joint Characteristic in Dynamic Substructuring,” Topics in Experimental Dynamic Substructuring (Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 2), Springer, New York, pp. 27–36. [CrossRef]
Reuss, P., Zeumer, B., Herrmann, J., and Gaul, L., 2012, “Consideration of Interface Damping in Dynamic Substructuring,” Topics in Experimental Dynamics Substructuring and Wind Turbine Dynamics (Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 2), Springer, New York, pp. 81–88. [CrossRef]
Bograd, S., Reuss, P., Schmidt, A., Gaul, L., and Mayer, M., 2011, “Modeling the Dynamics of Mechanical Joints,” Mech. Syst. Sig. Process., 25(8), pp. 2801–2826. [CrossRef]
Hammami, C., and Balmes, E., 2014, “Meta-Models of Repeated Dissipative Joints for Damping Design Phase,” 26th International Seminar on Modal Analysis (ISMA), Leuven, Belgium, Sept. 15–17, pp. 2573–2584.
Petrov, E. P., and Ewins, D. J., 2003, “Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks,” ASME J. Turbomach., 125(2), pp. 364–371. [CrossRef]
Segalman, D. J., Gregory, D. L., Starr, M. J., Resor, B. R., Jew, M. D., Lauffer, J. P., and Ames, N. M., 2009, “Handbook on Dynamics of Jointed Structures,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2009-4164.
Gregory, D. L., Resor, B. R., and Coleman, R. G., 2003, “Experimental Investigations of an Inclined Lap-Type Bolted Joint,” Sandia National Laboritories, Albuquerque, NM, Report No. SAND2003-1193.
Sracic, M. W., Allen, M. S., and Sumali, H., 2012, “Identifying the Modal Properties of Nonlinear Structures Using Measured Free Response Time Histories From a Scanning Laser Doppler Vibrometer,” 30th International Modal Analysis Conference, Jacksonville, FL, Jan. 30–Feb. 2.
Zhang, Q., Allemang, R. J., and Brown, D. L., 1990, “Modal Filter: Concept and Application,” 8th International Modal Analysis Conference (IMAC VIII), Kissimmee, FL, Jan. 29–Feb. 1.
Stearns, S. D., 2003, Digital Signal Processing With Examples in matlab, CRC Press, Boca Raton, FL.
Braun, S., and Feldman, M., 2011, “Decomposition of Non-Stationary Signals Into Varying Time Scales: Some Aspects of the EMD and HVD Methods,” Mech. Syst. Sig. Process., 25(7), pp. 2608–2630. [CrossRef]
Sumali, H., and Kellogg, R. A., 2011, “Calculating Damping From Ring-Down Using Hilbert Transform and Curve Fitting,” 4th International Operational Modal Analysis Conference (IOMAC), Istanbul, Turkey, May 9–11.
Feldman, M., 2011, “Hilbert Transform in Vibration Analysis,” Mech. Syst. Sig. Process., 25(3), pp. 735–802. [CrossRef]
Kerschen, G., Vakakis, A. F., Lee, Y. S., McFarland, D. M., and Bergman, L. A., 2008, “Toward a Fundamental Understanding of the Hilbert-Huang Transform in Nonlinear Structural Dynamics,” JVC/J. Vib. Control, 14(1–2), pp. 77–105. [CrossRef]
Jones, D. R., Perttunen, C. D., and Stuckman, B. E., 1993, “Lipschitzian Optimization Without the Lipschitz Constant,” J. Optim. Theory Appl., 79(1), pp. 157–181. [CrossRef]
Coleman, T., Branch, M. A., and Grace, A., 2003, Optimization Toolbox for Use With matlab, The MathWorks, Natick, MA.
Dickinson, S. M., 1978, “On the Use of Simply Supported Plate Functions in Raleigh's Method Applied to the Flexural Vibration of Rectangular Plates,” J. Sound Vib., 59(1), pp. 143–146. [CrossRef]
Carne, T. G., Griffith, D. T., and Casias, M. E., 2007, “Support Conditions for Experimental Modal Analysis,” Sound Vib., 41, pp. 10–16.
Allen, M. S., and Ginsberg, J. H., 2006, “A Global, Single-Input-Multi-Output (SIMO) Implementation of the Algorithm of Mode Isolation and Applications to Analytical and Experimental Data,” Mech. Syst. Sig. Process.20(5), pp. 1090–1111. [CrossRef]
Allen, M. S., and Ginsberg, J. H., 2005, “Global, Hybrid, MIMO Implementation of the Algorithm of Mode Isolation,” 23rd International Modal Analysis Conference (IMAC XXIII), Orlando, FL, Jan. 31–Feb. 3.

Figures

Grahic Jump Location
Fig. 1

Schematic of the model for each modal DOF. Each mode has a unique set of Iwan parameters that characterize its nonlinear damping and a viscous damper that captures the linear component of the damping.

Grahic Jump Location
Fig. 2

Photograph of the two-beam test structure

Grahic Jump Location
Fig. 3

Photograph of the suspension setup for the two-beam test structure

Grahic Jump Location
Fig. 4

Two-beam mass normalized mode shapes at 3.39 N m torque

Grahic Jump Location
Fig. 5

Comparison between measured natural frequency versus force and two models

Grahic Jump Location
Fig. 6

Energy dissipation comparison of two optimized modal models to experimental data over a range of forces

Grahic Jump Location
Fig. 7

Slope of energy dissipation versus modal force for modal Iwan models and a polynomial fit to the experimental measurements

Grahic Jump Location
Fig. 8

ZEFFTs for the midpoint of the structure for both the experimental measurement (solid lines) and the model (dashed lines)

Grahic Jump Location
Fig. 9

Zoomed in view of the first resonant peak with ZEFFTs for the both the experimental measurement (solid lines) and the model (dashed lines)

Grahic Jump Location
Fig. 10

Time response comparison of the filtered experimental measurement (solid lines) and the model (dashed lines)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In