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Research Papers

Experimental and Numerical Study of the Vibration of Stationary and Rotating Annular Disks

[+] Author and Article Information
Salem Bashmal

Assistant Professor
Department of Mechanical Engineering,
King Fahd University of
Petroleum and Minerals,
P.O. Box 399,
Dhahran 31261, Saudi Arabia
e-mail: bashmal@kfupm.edu.sa

Rama Bhat

Professor
Department of Mechanical and
Industrial Engineering,
Concordia University,
1455 De Maisonneuve Boulevard West,
Montreal, QC H3G 1M8, Canada
e-mail: rama.bhat@concordia.ca

Subhash Rakheja

Department of Mechanical and
Industrial Engineering,
Concordia University,
1455 De Maisonneuve Boulevard West,
Montreal, QC H3G 1M8, Canada
e-mail: subhash.rakheja@concordia.ca

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 29, 2015; final manuscript received April 6, 2016; published online May 26, 2016. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 138(5), 051003 (May 26, 2016) (11 pages) Paper No: VIB-15-1499; doi: 10.1115/1.4033359 History: Received November 29, 2015; Revised April 06, 2016

Numerical and experimental investigations are carried out to study the combined effect of rotation and support nonuniformity on the modal characteristics of circular thick disks. The laboratory experiments on stationary and rotating circular disks are conducted to investigate the effects of partial support conditions on the in-plane and out-of-plane vibration responses of annular disks with different radius ratios. Numerical results suggested that the nonuniformity of the support along the circumferential directions of the boundaries affects the modal characteristics of the disk along the in-plane and out-of-plane directions, while introducing additional coupling between the modes. Specifically, some of the frequency peaks in the frequency spectrum obtained under uniform boundary conditions split into two distinct peaks in the presence of a point support. The results show that the in-plane modes of vibration are comparable with those associated with out-of-plane modes and are contributing to the total noise radiation. The coupling between in-plane and out-of-plane modes is found to be quite significant due to the nonuniformity of the boundary conditions. The experimental study confirms the split in natural frequencies of the disk that is observed in the numerical results due to both rotation and support nonuniformity. The applicability and accuracy of the formulations is further examined through analysis of modal characteristics of a railway wheel in contact with the rail.

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References

Thompson, D. J. , 1993, “ Wheel-Rail Noise Generation, Part II: Wheel Vibration,” J. Sound Vib., 161(3), pp. 401–419. [CrossRef]
Tzou, K. I. , Wickert, J. A. , and Akay, A. , 1998, “ In-Plane Vibration Modes of Arbitrarily Thick Disks,” ASME J. Vib. Acoust., 120(2), pp. 384–391. [CrossRef]
Hashemi, S. H. , Farhadi, S. , and Carra, S. , 2009, “ Free Vibration Analysis of Rotating Thick Plates,” J. Sound Vib., 323(1–2), pp. 366–384. [CrossRef]
Spelsberg-Korspeter, G. , Hochlenert, D. , Kirillov, O. N. , and Hagedorn, P. , 2009, “ In-and Out-of-Plane Vibrations of a Rotating Plate With Frictional Contact: Investigations on Squeal Phenomena,” ASME J. Appl. Mech., 76(4), p. 041006. [CrossRef]
Thompson, D. J. , and Jones, C. J. C. , 2000, “ A Review of the Modelling of Wheel/Rail Noise Generation,” J. Sound Vib., 231(3), pp. 519–536. [CrossRef]
Lee, H. , and Singh, R. , 2005, “ Self and Mutual Radiation From Flexural and Radial Modes of a Thick Annular Disk,” J. Sound Vib., 286(4), pp. 1032–1040. [CrossRef]
Lee, H. , 2004, “ Influence of In-Plane Modes of a Rotor to Brake Noise,” ASME Paper No. IMECE2004-62324.
Lee, H. , and Singh, R. , 2004, “ Determination of Sound Radiation From a Simplified Disk-Brake Rotor by a Semi-Analytical Method,” Noise Control Eng. J., 52(5), pp. 225–239. [CrossRef]
Hirano, Y. , and Okazaki, K. , 1976, “ Vibrations of a Circular Plate Having Partly Clamped or Partly Simply Supported Boundary,” Bull. JSME, 19(132), pp. 610–618. [CrossRef]
Keer, L. M. , and Stahl, B. , 1972, “ Eigenvalue Problems of Rectangular Plates With Mixed Edge Conditions,” ASME J. Appl. Mech., 39(2), pp. 513–520. [CrossRef]
Irie, T. , and Yamada, G. , 1978, “ Free Vibration of Circular Plate Elastically Supported at Some Points,” Bull. JSME, 21(161), pp. 1602–1609. [CrossRef]
Leissa, A. W. , Laura, P. A. A. , and Gutierrez, R. H. , 1979, “ Transverse Vibrations of Circular Plates Having Nonuniform Edge Constraints,” J. Acoust. Soc. Am., 66(1), pp. 180–184. [CrossRef]
Laura, P. A. A. , and Ficcadenti, G. M. , 1980, “ Transverse Vibrations of Circular Plates of Varying Thickness With Non-Uniform Edge Constraints,” Appl. Acoust., 13(3), pp. 227–236. [CrossRef]
Narita, Y. , and Leissa, A. W. , 1980, “ Transverse Vibration of Simply Supported Circular Plates Having Partial Elastic Constraints,” J. Sound Vib., 70(1), pp. 103–116. [CrossRef]
Amabili, M. , Pierandrei, R. , and Frosali, G. , 1997, “ Analysis of Vibrating Circular Plates Having Non-Uniform Constraints Using the Modal Properties of Free-Edge Plates: Application to Bolted Plates,” J. Sound Vib., 206(1), pp. 23–38. [CrossRef]
Hasheminejad, S. M. , Ghaheri, A. , and Rezaei, S. , 2012, “ Semi-Analytic Solutions for the Free In-Plane Vibrations of Confocal Annular Elliptic Plates With Elastically Restrained Edges,” J. Sound Vib., 331(2), pp. 434–456. [CrossRef]
Kim, C.-B. , Cho, H. S. , and Beom, H. G. , 2012, “ Exact Solutions of In-Plane Natural Vibration of a Circular Plate With Outer Edge Restrained Elastically,” J. Sound Vib., 331(9), pp. 2173–2189. [CrossRef]
Shi, X. , Shi, D. , Qin, Z. , Wang, Q. , Shi, X. , Shi, D. , Qin, Z. , and Wang, Q. , 2014, “ In-Plane Vibration Analysis of Annular Plates With Arbitrary Boundary Conditions, In-Plane Vibration Analysis of Annular Plates With Arbitrary Boundary Conditions,” Sci. World J., 2014, p. e653836.
Khare, S. , and Mittal, N. D. , 2015, “ Free Vibration Analysis of Thin Circular and Annular Plate With General Boundary Conditions,” Eng. Solid Mech., 3(4), pp. 245–252. [CrossRef]
Eastep, F. E. , and Hemmig, F. G. , 1982, “ Natural Frequencies of Circular Plates With Partially Free, Partially Clamped Edges,” J. Sound Vib., 84(3), pp. 359–370. [CrossRef]
Febbo, M. , Vera, S. A. , and Laura, P. A. A. , 2005, “ Free, Transverse Vibrations of Thin Plates With Discontinuous Boundary Conditions,” J. Sound Vib., 281(1), pp. 341–356. [CrossRef]
Narita, Y. , and Leissa, A. W. , 1981, “ Flexural Vibrations of Free Circular Plates Elastically Constrained Along Parts of the Edge,” Int. J. Solids Struct., 17(1), pp. 83–92. [CrossRef]
Boennen, D. , and Walsh, S. J. , 2012, “ A Cyclosymmetric Beam Model and a Spring-Supported Annular Plate Model for Automotive Disc Brake Vibration,” ISRN Mech. Eng., 2012, p. 739384. [CrossRef]
Jin, G. , Ye, T. , Shi, S. , Jin, G. , Ye, T. , and Shi, S. , 2015, “ Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates With Arbitrary Boundary Conditions, Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates With Arbitrary Boundary Conditions,” Shock Vib., 2015, p. e896204.
Burdess, J. S. , Wren, T. , and Fawcett, J. N. , 1987, “ Plane Stress Vibrations in Rotating Discs,” Proc. Inst. Mech. Eng., Part C, 201(1), pp. 37–44. [CrossRef]
Chen, J.-S. , and Jhu, J.-L. , 1996, “ In-Plane Response of a Rotating Annular Disk Under Fixed Concentrated Edge Loads,” Int. J. Mech. Sci., 38(12), pp. 1285–1293. [CrossRef]
Chen, J.-S. , and Jhu, J.-L. , 1996, “ On the In-Plane Vibration and Stability of a Spinning Annular Disk,” J. Sound Vib., 195(4), pp. 585–593. [CrossRef]
Hamidzadeh, H. R. , 2002, “ In-Plane Free Vibration and Stability of Rotating Annular Discs,” Proc. Inst. Mech. Eng., Part K, 216(4), pp. 371–380.
Hamidzadeh, H. R. , and Sarfaraz, E. , 2012, “ Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks,” ASME Paper No. IMECE2012-86479.
Deshpande, M. , and Mote, C. D., Jr ., 2003, “ In-Plane Vibrations of a Thin Rotating Disk,” ASME J. Vib. Acoust., 125(1), pp. 68–72. [CrossRef]
Dousti, S. , and Abbas Jalali, M. , 2012, “ In-Plane and Transverse Eigenmodes of High-Speed Rotating Composite Disks,” ASME J. Appl. Mech., 80(1), p. 011019. [CrossRef]
Norouzi, H. , and Younesian, D. , 2014, “ Forced Vibration Analysis of Spinning Disks Subjected to Transverse Loads,” Int. J. Struct. Stab. Dyn., 15(03), p. 1450049. [CrossRef]
Sato, S. , and Matsuhisa, H. , 1978, “ Study on the Mechanism of Train Noise and Its Countermeasure—1. Characteristics of Wheel Vibration,” JSME Bull., 21(160), pp. 1475–1481.
Ambati, G. , Bell, J. F. W. , and Sharp, J. C. K. , 1976, “ In-Plane Vibrations of Annular Rings,” J. Sound Vib., 47(3), pp. 415–432. [CrossRef]
Lee, H. , 2003, “ Modal Acoustic Radiation Characteristics of a Thick Annular Disk,” Ph.D. thesis, The Ohio State University, Columbus, OH.
Bashmal, S. , Bhat, R. , and Rakheja, S. , 2011, “ In-Plane Free Vibration Analysis of an Annular Disk With Point Elastic Support,” Shock Vib., 18(4), pp. 627–640. [CrossRef]
Bashmal, S. M. , Bhat, R. B. , and Rakheja, S. , 2009, “ In-Plane Free Vibration of Circular Annular Rotating Disks,” 38th International Congress and Exposition on Noise Control Engineering (INTER-NOISE), Ottawa, Canada, Aug. 23–26, pp. 4404–4412.
So, J. , and Leissa, A. W. , 1998, “ Three-Dimensional Vibrations of Thick Circular and Annular Plates,” J. Sound Vib., 209(1), pp. 15–41. [CrossRef]
Bhat, R. B. , 1985, “ Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method,” J. Sound Vib., 102(4), pp. 493–499. [CrossRef]
Bashmal, S. , Bhat, R. , and Rakheja, S. , 2010, “ Analysis of In-Plane Modal Characteristics of an Annular Disk With Multiple Point Supports,” ASME Paper No. IMECE2009-10033.
Holland, R. , 1966, “ Numerical Studies of Elastic-Disk Contour Modes Lacking Axial Symmetry,” J. Acoust. Soc. Am., 40(5), pp. 1051–1057. [CrossRef]
Raman, A. , and Mote, C. D., Jr. , 2001, “ Experimental Studies on the Non-Linear Oscillations of Imperfect Circular Disks Spinning Near Critical Speed,” Int. J. Non-Linear Mech., 36(2), pp. 291–305. [CrossRef]

Figures

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Fig. 1

Geometry and coordinate system used for in-plane vibration analysis of a rotating disk

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Fig. 2

Schematic of experimental setup

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Fig. 3

Schematic of experimental setup for the rotating disk

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Fig. 4

In-plane frequency spectrum of the annular disk with free edges (DISK I)

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Fig. 5

Out-of-plane frequency spectrum of the annular disk with free edges (DISK I)

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Fig. 6

In-plane frequency spectrum of the annular disk with free edges (DISK II)

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Fig. 7

Out-of-plane frequency spectrum of the annular disk with point support (DISK I): angular position of the accelerometer relative to the support: (a) π/2 and (b) π

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Fig. 8

Out-of-plane frequency spectrum of the annular disk with point support (DISK I) due to in-plane excitation

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Fig. 9

In-plane frequency spectrum of the annular disk with point support (DISK I) due to in-plane excitation

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Fig. 10

In-plane frequency spectrum of the annular disk with two-point support (DISK II) due to in-plane excitation

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Fig. 11

Autospectrum of the microphone signal at the out-of-plane position for the annular disk with free edges (DISK I)

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Fig. 12

Autospectrum of the microphone signal at the in-plane position for the annular disk with free edges (DISK I)

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Fig. 13

Frequency spectrum of the sound pressure measured near the stationary aluminum disk (DISK III) subject to an impulse hammer excitation (flexible inner edge and free outer edge)

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Fig. 14

Frequency spectrum of the sound pressure measured near the rotating aluminum disk (DISK III) subject to an impulse hammer excitation (flexible inner edge and free outer edge) at 1920 rpm

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Fig. 15

Frequency spectrum of the sound pressure measured near the stationary aluminum disk (DISK III) subject to an impulse hammer excitation (flexible inner edge and subject to an elastic point support with low support force at the outer edge)

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Fig. 16

Frequency spectrum of the sound pressure measured near the rotating aluminum disk (DISK III) subject to an impulse hammer excitation (flexible inner edge and subject to an elastic point support at the outer edge) at 500 rpm

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