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Journal of Vibration and Acoustics | Volume 135 | Issue 6 | Technical Brief
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

Professor
Mem. ASME
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
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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.
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Figures

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Fig. 1

Analytical model of beam subjected to frictional force

+Analytical model of beam subjected to frictional force
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Analytical model of beam subjected to frictional force
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Fig. 2

Kinematic description of analytical model

+Kinematic description of analytical model
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Kinematic description of analytical model
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Fig. 3

Strains acting on beam element

+Strains acting on beam element
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Strains acting on beam element
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Fig. 4

Forces and moments acting on beam element at x = l

+Forces and moments acting on beam element at x = l
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Forces and moments acting on beam element at x = l
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Fig. 5

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

+Root locus obtained through discretization of system as functions of δ (α = 30,000, μ = 0.15)
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Root locus obtained through discretization of system as functions of δ (α = 30,000, μ = 0.15)
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Fig. 6

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

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

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