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Research Papers

Roughness-Induced Vibration Caused by a Tangential Oscillating Mass on a Plate

[+] Author and Article Information
Joachim Feldmann

 Technische Universität Berlin, Einsteinufer 25, D-10587 Berlin, Germanyjoachim.feldmann@tu-berlin.de

J. Vib. Acoust 134(4), 041002 (May 31, 2012) (9 pages) doi:10.1115/1.4005828 History: Received November 05, 2010; Revised December 06, 2011; Published May 29, 2012; Online May 31, 2012

This work examines the dynamic behavior of a system consisting of a mass-block on the rough surface of a simply supported plate, harmonically excited in the tangential direction. The vertical excitation emerges from roughness, tracked by the mass-block. Low-frequency sliding results in high-frequency vertical excitation up to the ultrasonic range. The conditions of the elastic contact between the two bodies are modeled in the form of vertical contact stiffness. A specific friction law with a behavior similar to an elastically coupled coulomb damper represents the tangential direction. The model allows for the study of the interaction between the tangential friction behavior and the vertical roughness-induced vibrations. Parameters of interest are friction velocity, mass-block weight, surface roughness, and contact material. Because of nonlinearities, the theoretical model must be solved within the time domain. The theoretical results are verified through experimental results of a corresponding setup. The subject combines material science, contact mechanics, and structural dynamics.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 9

(a) Friction force versus tangential displacement. (b) Derivation of the curve in (a), result is equivalent to the global tangential stiffness of the contact. Example of a sliding velocity of 10 mm/s rms over 2.5 periods, compare Fig.6.

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Figure 10

Calculated vertical acceleration amplitudes versus time. (a) Result for mass-block, and (b) result for plate. Friction velocity is 10 mm/s rms.

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Figure 11

Calculated vertical acceleration amplitudes versus time. (a) Result for mass-block, and (b) result for plate. Friction velocity is 100 mm/s rms.

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Figure 12

Measured vertical acceleration amplitudes versus time. (a) Result for mass-block, and (b) result for plate. Friction velocity is 10 mm/s rms.

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Figure 13

Measured vertical acceleration amplitudes versus time. (a) Result for mass-block, and (b) result for plate. Friction velocity is 100 mm/s rms.

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Figure 14

Calculated vertical acceleration spectrums of mass (thin line) and plate (thick line). (a) Results for a friction velocity of 10 mm/s rms, and (b) results for a friction velocity of 100 mm/s rms. At high frequencies, the responses of the mass are limited by a simulated electrical noise of the corresponding measurement device, compare Fig. 1.

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Figure 15

Measured vertical acceleration spectrums of mass (thin line) and plate (thick line). (a) Results for a friction velocity of 10 mm/s rms, and (b) results for a friction velocity of 100 mm/s rms

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Figure 8

Calculated relation friction force versus friction velocity, exemplary of 10 mm/s rms

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Figure 7

Tangential velocity (100 mm/s rms) of mass-block versus time: (a) calculated, (b) measured

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Figure 6

Tangential velocity (10 mm/s rms) of mass-block versus time: (a) calculated, (b) measured

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Figure 5

Wavenumber spectrums of mean original roughness input (thin line), and actual roughness input (thick line). (a) Oscillation stroke ± 0.227 mm rms, (b) oscillation stroke ± 2.27 mm rms. Values result from friction velocity 10 mm/s and 100 mm/s, respectively, divided by the excitation angular frequency 6.28 × 7 Hz. Results based on measured and processed 3D roughness.

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Figure 4

Test setup: mass-block on a rough steel plate, external shaker excitation

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Figure 3

Friction versus friction velocity, exemplary for 10 mm/s rms, one complete cycle

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Figure 2

Time dependence (a), and corresponding spectrum (b) of the plate’s applied impulse response with boundary conditions “simply supported”

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Figure 1

Scheme of the investigated theoretical model: i  =  actual contact point

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