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Research Papers

In- and Out-of-Plane Vibrations of a Rotating Plate With Frictional Contact: Investigations on Squeal Phenomena

[+] Author and Article Information
Gottfried Spelsberg-Korspeter

Department of Mechanical Engineering, Dynamics and Vibrations Group, Technische Universität Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germanyspeko@dyn.tu-darmstadt.de

Daniel Hochlenert

Department of Mechanical Engineering, Dynamics and Vibrations Group, Technische Universität Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germanyhochlenert@dyn.tu-darmstadt.de

Oleg N. Kirillov1

Department of Mechanical Engineering, Dynamics and Vibrations Group, Technische Universität Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germanykirillov@dyn.tu-darmstadt.de

Peter Hagedorn

Department of Mechanical Engineering, Dynamics and Vibrations Group, Technische Universität Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germanypeter.hagedorn@dyn.tu-darmstadt.de

1

Visiting from the Institute of Mechanics, Moscow State Lomonosov University, Michurinskii Prospect 1, 119192 Moscow, Russia.

J. Appl. Mech 76(4), 041006 (Apr 22, 2009) (15 pages) doi:10.1115/1.3112734 History: Received June 15, 2007; Revised February 03, 2009; Published April 22, 2009

Rotating plates are used as a main component in various applications. Their vibrations are mainly unwanted and interfere with the functioning of the complete system. The present paper investigates the coupling of disk (in-plane) and plate (out-of-plane) vibrations of a rotating annular Kirchhoff plate in the presence of a distributed frictional loading on its surface. The boundary value problem is derived from the basics of the theory of elasticity using Kirchhoff’s assumptions. This results in precise information about the coupling between the disk and the plate vibrations under the action of frictional forces. At the same time we obtain a new model, which is efficient for analytical treatment. Approximations to the stability boundaries of the system are calculated using a perturbation approach. In the last part of the paper nonlinearities are introduced leading to limit cycles due to self-excited vibrations.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Kirchhoff plate in distributed frictional contact

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Figure 12

Prestress due to rotation of the disk (Ω=0.28)

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Figure 13

Spectrum of the out-of-plane vibrations of the unperturbed problem (prestressed plate) for ri=0.154 (spectral mesh)

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Figure 14

Spectrum of the perturbed plate problem for γ=δ=3. Dashed lines: unperturbed problem; lower plot: zoom for small Ω.

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Figure 2

Kirchhoff plate in pointwise frictional contact

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Figure 8

λ1ε for the perturbed disk problem for ri=0.153

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Figure 9

Three-dimensional stability boundaries

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Figure 10

Stability boundaries in the sub- and supercritical ranges

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Figure 11

Comparison of analytical and numerical results for Ω=10−3 (dot: stable; cross: unstable)

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Figure 15

Stiffness characteristic

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Figure 16

Bifurcation diagram

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Figure 3

Contact kinematics

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Figure 5

Spectrum of the out-of-plane vibrations of the unperturbed problem (plate) for ri=0.154 (spectral mesh)

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Figure 6

Spectrum of the in-plane vibrations of the unperturbed problem (disk) for ri=0.153

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Figure 7

Spectrum of the perturbed plate problem for γ=δ=3. Dashed lines: unperturbed problem; lower plot: zoom for small Ω.

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