Technical Briefs

Mode Coupling-Type Instability of a Beam Subjected to Coulomb Friction

[+] Author and Article Information
Yasuhiro Seo

Graduate Student
School of Integrated Design Engineering,
Keio University,
Yokohama, Kanagawa 223-8522, Japan
e-mail: only1-xp@a2.keio.jp

Hiroshi Yabuno

Department of Mechanical Engineering,
Faculty of Science and Technology,
Keio University,
Yokohama, Kanagawa 223-8522, Japan
e-mail: yabuno@mech.keio.ac.jp

Go Kono

Graduate Student
School of Integrated Design Engineering,
Keio University,
Yokohama, Kanagawa 223-8522, Japan
e-mail: gogogoh20@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received October 29, 2012; final manuscript received April 12, 2013; published online June 19, 2013. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 135(6), 064502 (Jun 19, 2013) (7 pages) Paper No: VIB-12-1305; doi: 10.1115/1.4024219 History: Received October 29, 2012; Revised April 12, 2013

To analyze the excitation mechanism of self-excited oscillation in a beam that is in contact with a moving floor surface such as a cleaning blade, which is a beam mounted in a laser printer to clean the photoreceptor, we study a beam subjected to Coulomb friction and theoretically predict the occurrence of self-excited oscillation through mode-coupling instability. We present an extensible beam model, and derive its governing nonlinear equations by means of special Cosserat theory, which allows for the extensibility of the beam to be considered. The boundary conditions on the end of the beam are unique because the end of the beam makes contact with the moving floor surface. We used a discretized linearized governing equation and performed linear stability analysis. The results indicate that self-excited oscillation in the beam is produced due to both Coulomb friction and mode coupling of the bending and extension of the beam based on the extensibility in the axial direction.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Inagaki, Y., Nohara, T., Kono, G., Kasama, M., and Yoshizawa, M., 2009, “Dynamics of a Cleaning Blade Based on a 2DOF Link Model,” ASME Conference Proceedings, San Diego, August 30–September 2, Vol. 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B, ASME, New York, pp. 329–338.
Ruan, J., and Bhushan, B., 1994, “Atomic-Scale Friction Measurements Using Friction Force Microscopy,” ASME J. Tribol., 116(2), pp. 378–388. [CrossRef]
Den Hartog, J. P., 1984, Mechanical Vibrations, Dover, New York, pp. 289–290.
Nayfeh, A. H., and Mook, D. T., 1995, Nonlinear Oscillations, Wiley-Interscience, New York, pp. 106–107.
Wickens, A. H., 1965, “The Dynamics Stability of a Simplified Four-Wheel Railway Vehicle Having Profiled Wheels,” Academic Press, New York, pp. 385–406.
Seyranian, A. P., and Mailybaev, A. A., 2003, Multiparameter Stability Theory With Mechanical Applications, World Scientific, Hackensack, NJ, pp. 9–14.
Shin, K., Oh, J., and Brennan, M., 2002, “Nonlinear Analysis of Friction-Induced Vibrations of a Two-Degree-of Freedom Model for Disc Brake Squeal Noise,” JSME Int. J., 45(2), pp. 426–432. [CrossRef]
Ziegler, H., 1968, Principles of Structural Stability, 2nd ed., Birkhäuser, Basel, Switzerland, pp. 26–33.
Païdoussis, M. P., 1998, Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 1, Academic Press, New York.
Kasama, M., Yoshizawa, M., Yu, Y., and Itoh, T., 2008, “Coupled-Mode Flutter of a Cleaning Blade System in a Laser Printer,” J. Syst. Des. Dyn., 2(3), pp. 849–860.
Kono, G., Inagaki, Y., Yabuno, H., Nohara, T., and Kasama, M., 2012, “Analysis of the Frictional Vibration of a Cleaning Blade in Laser Printers Based on a Two-Degree-of-Freedom Model,” J. Comput. Nonlinear Dyn., 7(1), p. 011006. [CrossRef]
Grenouillat, R., and Leblanc, C., 2002, “Simulation of Chatter Vibrations for Wiper Systems,” SAE Technical Paper No. 2002-01-1239.
Antman, S., 1995, Nonlinear Problems of Elasticity, 2nd ed., Springer-Verlag, Berlin, pp. 269–344.
Lacarbonara, W., Paolone, A., and Yabuno, H., 2004, “Modeling of Planar Nonshallow Prestressed Beams Towards Asymptotic Solutions,” Mech. Res. Commun., 31(3), pp. 301–310. [CrossRef]
Crespo da Cilva, M. R. M., and Glynn, C. C., 1978, “Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion,” J. Struct. Mech., 6(4), pp. 437–448. [CrossRef]
Pedersen, P., 1984, “Sensitivity Analysis for Non-Selfadjoint Problems,” Lect. Notes Math., 1086, pp. 119–130. [CrossRef]
Sugiyama, Y., Tanaka, Y., Kishi, T., and Kawagoe, H., 1985, “Effect of a Spring Support on the Stability of Pipes Conveying Fluid,” J. Sound Vib., 100(2), pp. 257–270. [CrossRef]
The Imaging Society of Japan, 1996, “Denshi Shashin no Gijyutu no Ouyou,” Corona, pp. 302–308 (in Japanese).
Marsden, J., and Ratiu, T., 1999, Introduction to Mechanics and Symmetry, Springer, New York, pp. 45–46.
Païdoussis, M. P., 1998, Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 1, Academic Press, New York, pp. 67–69.


Grahic Jump Location
Fig. 1

Analytical model of beam subjected to frictional force

Grahic Jump Location
Fig. 4

Forces and moments acting on beam element at x = l

Grahic Jump Location
Fig. 3

Strains acting on beam element

Grahic Jump Location
Fig. 2

Kinematic description of analytical model

Grahic Jump Location
Fig. 5

Root locus obtained through discretization of system as functions of δ (α = 30,000, μ = 0.15)

Grahic Jump Location
Fig. 6

Real parts and imaginary parts of λ as functions of δ (α = 30,000, μ = 0.15)




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