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TECHNICAL PAPERS

On the Secondary Resonance of a Spinning Disk Under Space-Fixed Excitations

[+] Author and Article Information
Jen-San Chen, Chin-Yi Hua, Chia-Min Sun

Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617

J. Vib. Acoust 126(3), 422-429 (Jul 30, 2004) (8 pages) doi:10.1115/1.1760562 History: Received June 01, 2001; Revised December 01, 2003; Online July 30, 2004
Copyright © 2004 by ASME
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References

Benson,  R. C., and Bogy,  D. B., 1978, “Deflection of a Very Flexible Spinning Disk Due to a Stationary Transverse Load,” ASME J. Appl. Mech., 45, pp. 636–642.
Cole,  K. A., and Benson,  R. C., 1988, “Fast Eigenfunction Approach for Computing Spinning Disk Deflections,” ASME J. Appl. Mech., 55, pp. 453–457.
Ono,  K., and Maeno,  T., 1987, “Theoretical and Experimental Investigation on Dynamic Characteristics of a 3.5-Inch Flexible Disk Due to a Point Contact Head,” Tribology and Mechanics of Magnetic Storage Systems, 3, SP.21, (STLE), pp. 144–151.
Jiang,  Z. W., Chonan,  S., and Abe,  H., 1990, “Dynamic Response of a Read/Write Head Floppy Disk System Subjected to Axial Excitation,” ASME J. Vibr. Acoust., 112, pp. 53–58.
Chen,  J. S., and Hsu,  C. M., 1997, “On the Transient Response of a Spinning Disk Under a Space-Fixed Step Load,” ASME J. Appl. Mech., 64, pp. 1017–1019.
Chen,  J. S., and Hsu,  C. M., 1997, “Forced Response of a Spinning Disk Under Space-Fixed Couples,” J. Sound Vib., 206, pp. 627–639.
Nowinski,  J. L., 1964, “Nonlinear Transverse Vibrations of a Spinning Disk,” ASME J. Appl. Mech., 31, pp. 72–78.
Tobias,  S. A., and Arnold,  R. N., 1957, “The Influence of Dynamical Imperfection on the Vibration of Rotating Disks,” Proc. Inst. Mech. Eng., 171, pp. 669–690.
Maher, J. F., and Adams, G. G., 1991, “The Point-Load Solution Using Linearized von Karman Plate Theory for a Spinning Flexible Disk Near a Baseplate,” STLE/ASME Tribology Conference, St. Louis, Missouri, pp. 1–9.
Torii,  T., Yasuda,  K., and Toyada,  T., 1998, “Nonlinear Forced Oscillation of a Rotating Disk Excited at a Point Fixed in Space,” JSME Int. J., Ser. C, 41, pp. 592–598.
Raman,  A., and Mote,  C. D., 1999, “Non-linear Oscillations of Circular Plates Near a Critical Speed Resonance,” Int. J. Non-Linear Mech., 34, pp. 139–157.
Chen,  J. S., 1999, “Steady State Deflection of a Circular Plate Rotating Near Its Critical Speed,” ASME J. Appl. Mech., 66, pp. 1015–1017.
Nayfeh,  T. A., and Vakakis,  A. F., 1994, “Subharmonic Travelling Waves in a Geometrically Non-Linear Circular Plate,” Int. J. Non-Linear Mech., 29, pp. 233–245.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley, New York.

Figures

Grahic Jump Location
Natural frequency loci of a freely spinning disk
Grahic Jump Location
Steady state solutions as functions of ς when γ=2ω0303̄+ες, where ω03=11.94,ω03̄=25.74, and ε=0.001. Other parameters are Ω=2.3, α=0.4, q03=10,000, and cf=0.2.
Grahic Jump Location
(a) Time history and (b) the corresponding Poincare map when ς=8 for the combination resonance case in Fig. 2. The initial conditions are c03(0)=9.98 and ċ03(0)=121.57i.
Grahic Jump Location
Steady state solutions as functions of ς when γ=1/2(ω0303̄)+ες, where ω03=11.94,ω03̄=25.74, and ε=0.001. Other parameters are Ω=2.3, α=0.4, q03=3000, and cf=0.2.
Grahic Jump Location
(a) Time history and (b) the corresponding Poincare map when ς1=7 for the simultaneous resonance case in Fig. 5. The initial conditions are c03(0)=0 and ċ03(0)=0.
Grahic Jump Location
Steady state solutions of simultaneous resonance as functions of loading parameter q03 when ς1=4
Grahic Jump Location
Steady state solutions as functions of ς1 when γ=1/3ω03+ες103=14.13,ω03̄=23.55, ε=0.001. Other parameters are Ω=1.57, α=0.4, q03=10,000, and cf=0.2.
Grahic Jump Location
(a) Time history and (b) the corresponding Poincare map when ς1=7 for the simultaneous resonance case in Fig. 5. The initial conditions are c03(0)=−4.96+i2.15 and ċ03(0)=−130.26+i50.83.

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