Research Papers

Dynamic Analysis of a Series Iwan Model Derived From a Continuous Frictional Interface

[+] Author and Article Information
Dinar Deshmukh

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: dinarvd@gmail.com

Edward Berger

School of Engineering Education and School
of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: bergere@purdue.edu

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 26, 2014; final manuscript received October 31, 2014; published online December 11, 2014. Assoc. Editor: Guilhem Michon.

J. Vib. Acoust 137(2), 021007 (Apr 01, 2015) (10 pages) Paper No: VIB-14-1100; doi: 10.1115/1.4029003 History: Received March 26, 2014; Revised October 31, 2014; Online December 11, 2014

Reduced-order models for characterizing friction interfaces have been investigated for the last 75 years. Recent work has been focused on microslip formulations of the interface behavior, where a continuous interface is approximated with a multipoint contact model. A novel multipoint friction model is presented in this work, which is entirely derived from a shear-lag approach to resolve the kinematic state of the friction interface under the presence of tangential loading. Both static and dynamic loading conditions are analyzed and comparisons are drawn between the continuous and discrete models. The series Iwan model presented in this work differentiates between the elastic and friction components of the interface displacement, both parameters being calibrated using material properties and model geometry. The response characteristics of the series Iwan model under dynamic loading conditions are also investigated. The series Iwan model is in good agreement with the shear-lag approach for results such as propagation of the slip zone with increasing pullout force. The transient response of the structural mass and the kinematic states of the Iwan elements are convergent with increasing model order. A direct physical correlation between the response of the series Iwan model and kinematics of the continuous interface is developed, which greatly enhances the appeal of this particular model for simulating interface phenomena.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Johnson, K., 1961, “Energy Dissipation at Spherical Surfaces in Contact Transmitting Oscillating Forces,” J. Mech. Eng. Sci., 3(4), pp. 362–368. [CrossRef]
Cattaneo, C., 1938, “Sul contatto di due corpi elastici: Distribuzione locale degli sforzi,” Reconditi dell Academia Nazionale dei Lincei, 27, pp. 342–348, 434–436, 474–478.
Mindlin, R. D., 1949, “Compliance of Elastic Bodies in Contact,” ASME J. Appl. Mech., 16, pp. 259–268.
Hertz, H., 1881, “On the Contact of Elastic Bodies,” J. Rein. Angew. Math., 92, pp. 56–57.
Cox, H., 1952, “The Elasticity and Strength of Paper and Other Fibrous Materials,” Br. J. Appl. Phys., 3(3), pp. 72–79. [CrossRef]
Clyne, T., 1989, “A Simple Development of the Shear Lag Theory Appropriate for Composites With a Relatively Small Modulus Mismatch,” Mater. Sci. Eng., A, 122(2), pp. 183–192. [CrossRef]
Hartog, J. D., 1931, “Forced Vibrations With Combined Coulomb and Viscous Friction,” ASME J. Appl. Mech., APM-53-9, pp. 107–115.
Menq, C.-H., Griffin, J., 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(2), pp. 300–305. [CrossRef]
Wang, J., and Shieh, W., 1991, “The Influence of Variable Friction Coefficient on the Dynamic Behavior of a Blade With Friction Damper,” J. Sound Vib., 149(1), pp. 137–145. [CrossRef]
Iwan, W., 1966, “A Distributed–Element Model for Hysteresis and Its Steady–State Dynamic Response,” ASME J. Appl. Mech., 33(4), pp. 893–900. [CrossRef]
Sanliturk, K., Imregun, M., and Ewins, D. J., 1997, “Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers,” ASME J. Vib. Acoust., 119(1), pp. 96–103. [CrossRef]
Sextro, W., 1999, “Forced Vibration of Elastic Structures With Frictional Contacts,” ASME 1999 Design Engineering Technical Conferences, Las Vegas, NV, Sept. 12–15, ASME Paper No. DETC99/VIB-8180.
Berger, E., and Krousgrill, C., 2002, “On Friction Damping Modeling Using Bilinear Hysteresis Elements,” ASME J. Vib. Acoust., 124(3), pp. 367–375. [CrossRef]
Rajaei, M., and Ahmedian, H., 2014, “Development of Generalized Iwan Model to Simulate Frictional Contact With Variable Normal Loads,” Appl. Math. Model., 38(15–16), pp. 4006–4018. [CrossRef]
Ahmedian, H., and Rajaei, M., 2014, “Identification of Iwan Distribution Density Function in Frictional Contacts,” J. Sound Vib., 333(15), pp. 3382–3393. [CrossRef]
Xiao, H., Shao, Y., and Xu, J., 2014, “Investigation Into the Energy Dissipation of a Lap Joint Using the One-Dimensional Microslip Friction Model,” Eur. J. Mech. A, 43, pp. 1–8. [CrossRef]
Argatov, I., and Butcher, E., 2012, “On the Iwan Models for Lap-Type Bolted Joints,” Int. J. Non-Linear Mech., 46(2), pp. 347–356. [CrossRef]
Quinn, D., 2001, “Distributed Friction and Microslip in Mechanical Joints With Varying Degrees-of-Freedom,” ASME Design Engineering Technical Conferences, Pittsburgh, PA, Sept. 9–12, ASME Paper No. DETC2001/VIB-21514.
Quinn, D., and Segalman, D., 2002, “Using Series–Series Iwan–Type Models for Understanding Joint Dynamics,” Sandia National Laboratories, Albuquerque, NM, Technical Report No. SAND2002–4120J.
Deshmukh, D., Berger, E., Mackin, T., and Inglis, H., 2005, “Convergence Behaviors of Reduced–Order Models for Frictional Contacts,” ASME J. Vib. Acoust., 127(4), pp. 370–381. [CrossRef]
Ferri, A. A., and Heck, B. S., 1995, “Vibration Analysis of Dry Friction Damped Turbine Blades Using Singular Perturbation Theory,” ASME J. Vib. Acoust., 120(2), pp. 588–595. [CrossRef]
Eriten, M., Polycarpou, A., and Bergman, L., 2012, “A Physics-Based Friction Model and Integration to a Simple Dynamical System,” ASME J. Vib. Acoust., 134(5), p. 051012. [CrossRef]
Kiang, J.-W., and Feeny, B., 2011, “Balancing Energy to Estimate Damping in a Forced Oscillator With Compliant Contact,” J. Sound Vib., 330(9), pp. 2049–2061. [CrossRef]
Ferri, A., 1995, “Friction Damping and Isolation Systems,” ASME J. Vib. Acoust., 117(B), pp. 196–206. [CrossRef]
Berger, E., 2002, “Friction Modeling for Dynamic System Simulation,” ASME Appl. Mech. Rev., 55(6), pp. 535–577. [CrossRef]
Deshmukh, D., Berger, E., Begley, M. R., and Komaragiri, U., 2007, “Correlation of a Discrete Friction (Iwan) Element and Continuum Approaches to Predict Interface Sliding Behavior,” Eur. J. Mech. A, 26(2), pp. 212–224. [CrossRef]
Hutchinson, J., and Jensen, H., 1990, “Models of Fiber Debonding and Pullout in Brittle Composites With Friction,” Mech. Mater., 9(2), pp. 139–163. [CrossRef]
Rogers, P., and Boothroyd, G., 1975, “Damping at Metallic Interfaces Subjected to Oscillating Tangential Loads,” ASME J. Manuf. Sci. Eng., 97(3), 1087–1093. [CrossRef]
Smallwood, D., Gregory, D., and Coleman, R., 2000, “Damping Investigations of a Simplified Frictional Shear Joint,” Sandia National Laboratories, Albuquerque, NM, Technical Report No. SAND2000-1929C.
Vingsbo, O., and Söderberg, S., 1988, “On Fretting Maps,” Wear, 126(2), pp. 131–147. [CrossRef]
Goodman, L., and Brown, C., 1962, “Energy Dissipation in Contact Friction: Constant Normal and Cyclic Tangential Loading,” ASME J. Appl. Mech., 29(1), pp. 17–22. [CrossRef]
Lobitz, D., Gregory, D. L., and Smallwood, D. O., 2000, “Comparison of Finite Element Predictions to Measurements From the Sandia Microslip Experiment,” Sandia National Laboratories, Albuquerque, NM, Technical Report No. SAND2000-2799C.
Segalman, D., 2001, “An Initial Overview of Iwan Modeling for Mechanical Joints,” Sandia National Laboratories, Albuquerque, NM, Technical Report No. SAND2001-0811.


Grahic Jump Location
Fig. 1

Single fiber pullout model

Grahic Jump Location
Fig. 2

New Iwan element and its kinematic states. (a) New Iwan element, (b) sticking state, and (c) slipping state.

Grahic Jump Location
Fig. 3

Calibration scheme to determine k2's with n = 8

Grahic Jump Location
Fig. 4

Series Iwan model with nonzero mass

Grahic Jump Location
Fig. 5

Normalized first natural frequencies of linearized Iwan model and quasi-static structural displacement of the contact edge (d, normalized by the interface length L) for varying stick zone sizes

Grahic Jump Location
Fig. 6

Variation of slip zone with applied stress for E1/E2 = 1.0 and f = 0.25

Grahic Jump Location
Fig. 7

Convergence of (a) structural amplitude and (b) kinematic states for constant forcing (γ = 1.0; percentage averaged over one forcing cycle)

Grahic Jump Location
Fig. 8

Convergence of frictional energy dissipated for constant forcing (γ = 1.0; Ω = 1.0)

Grahic Jump Location
Fig. 9

Hysteresis loops for (a) constant forcing frequency (Ω = 0.8) and (b) constant forcing amplitude (γ = 0.5)

Grahic Jump Location
Fig. 10

Variation of (a) structural amplitude and (b) frictional energy dissipated with applied forcing frequency. (The dashed backbone curve is a trend line connecting the frequency response peaks.)

Grahic Jump Location
Fig. 11

Variation of (a) power law exponent and (b) slip length with applied forcing frequency




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