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TECHNICAL PAPERS

Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures

[+] Author and Article Information
M. Kim, J. Moon, J. A. Wickert

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890

J. Vib. Acoust 122(1), 62-68 (Jul 01, 1997) (7 pages) doi:10.1115/1.568443 History: Received August 01, 1996; Revised July 01, 1997
Copyright © 2000 by ASME
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References

Figures

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Schematic of the test apparatus. Aluminum disks were preloaded by a hydraulic press against spacers to obtain rotationally periodic contact, or against a solid axisymmetric flange.
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Measured collocated transfer functions of the disk with nominally clamped-free boundary conditions (upper), and with six equally-spaced displacement and slope constraints around the inner edge (lower). Values of ND, and the sine or cosine orientation of the split modes, are indicated.
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Measured sine and cosine members of the split three nodal diameter doublet, having distinct frequencies 196 and 219 Hz; N=6 stiffness features with locations indicated at top. The shapes are sectioned along r=c to highlight variation in θ.
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Measured mode shape of the disk which illustrates spatial modulation; N=6 stiffness features. This mode has repeated natural frequency, and is asymptotic to (0,4). As indicated by the Fourier decomposition, significant contamination occurs at k=2.
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Doublet modes companion to Fig. 4, as predicted by a finite element model; N=6 stiffness features. The S (——) and C (– – –) members have repeated frequency, but each is spatially modulated, an is any linear combination of them. Contamination occurs for each mode at k=2, and to lesser degrees at k=8 and 10.
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Isometric and section views of a measured mode shape of the disk; N=6 stiffness features. This mode has repeated natural frequency, and is asymptotic to (0,5).
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Predicted antisymmetric mode shape which is asymptotic to (0,5) S;N=6 stiffness features. The symmetric companion has repeated frequency, but it is not shown here for clarity. Contamination occurs at k=1, and to a lesser degree at k=7.
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Checkerboard diagram depicting the contamination wavenumbers for each base mode in the presence of six features
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Measured mode shape of the disk which illustrates spatial modulation; N=5 inertia features. This mode has repeated natural frequency, and is asymptotic to (0,4). As indicated by the Fourier decomposition, significant contamination occurs at k=1.
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Checkerboard diagram depicting the contamination wavenumbers for each base mode in the presence of five features
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Measured mode shape of the disk which illustrates spatial modulation; N=5 inertia features. This mode has repeated natural frequency, and is asymptotic to (0,6). As indicated by the Fourier decomposition, significant contamination occurs at k=1 and 4.
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Photograph of a typical automotive disk brake rotor
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Predicted circumferential sections of the rotor’s ND=3 base mode taken around the (a) outer and (b) inner edges of the rotor’s cheeks. N=4 stiffness features model the constraint of the mounting studs. A radial gradient of modulation at k=1 exists, being most acute around the inner periphery.

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