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TECHNICAL PAPERS

Modal Analysis of Ballooning Strings With Small Curvature

[+] Author and Article Information
R. Fan, S. K. Singh, C. D. Rahn

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802

J. Appl. Mech 68(2), 332-338 (Aug 29, 2000) (7 pages) doi:10.1115/1.1355776 History: Received September 07, 1999; Revised August 29, 2000
Copyright © 2001 by ASME
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References

Kong,  X., Rahn,  C., and Goswami,  B., 1999, “Steady State Unwinding of Yarn from Cylindrical Packages,” Textile Res. J., 69, No. 4, pp. 292–306.
Reedman, A., 1998, “Measurement of Lift-Off Position and Rotation Rate During Unwinding,” M. S. thesis, Clemson University, Clemson, SC, Aug.
Batra,  S., Ghosh,  T., and Zeidman,  M., 1992, “An Integrated Approach to Dynamic Analysis of the Ring Spinning Process—III,” Textile Praxis Int., 47, pp. 793–800.
Fraser,  W., 1993, “On the Theory of Ring Spinning,” Philos. Trans. R. Soc. London, Ser. A, A342, pp. 439–468.
Zhu,  F., Hall,  K., and Rahn,  C. D., 1998, “Steady State Response and Stability of Ballooning Strings in Air,” Int. J. Non-Linear Mech., 33, No. 1, pp. 33–46.
Stump,  D., and Fraser,  W., 1996, “Transient Solutions of the Ring-Spinning Balloon Equations,” ASME J. Appl. Mech., 63, pp. 523–528.
Zhu,  F., Sharma,  R., and Rahn,  C. D., 1997, “Vibrations of Ballooning Elastic Strings,” ASME J. Appl. Mech., 64, pp. 676–683.
Zhu,  F., and Rahn,  C. D., 2000, “Limit Cycle Prediction for Ballooning Strings,” Int. J. Non-Linear Mech., 35, No. 3, May, pp. 373–383.
Clark,  J. D., Fraser,  W. B., Sharma,  R., and Rahn,  C. D., 1998, “The Dynamic Response of a Ballooning Yarn: Theory and Experiment,” Proc. R. Soc. London, Ser. A, A454, No. 1978, pp. 2767–2789.
Perkins,  N. C., 1992, “Modal Interactions in the Non-Linear Response of Elastic Cables Under Parametric/External Excitation,” Int. J. Non-Linear Mech., 27, No. 2, pp. 233–250.
Lee,  C. L., and Perkins,  N. C., 1995, “Experimental Investigation of Isolated and Simultaneous Internal Resonances in Suspended Cables,” ASME J. Vibr. Acoust., 117, pp. 385–391.
Irvine,  H. M., and Caughey,  T. K., 1974, “The Linear Theory of Free Vibrations of a Suspended Cable,” Proc. R. Soc. London, Ser. A, A341, pp. 299–315.

Figures

Grahic Jump Location
Schematic diagram of a ballooning string system
Grahic Jump Location
The dependence on the nondimensional rotation speed ω on the nondimensional balloon height h and eyelet length d. Theoretical solid (d=0.01), dashed (d=0.038) and dash-dotted (d=0.1) curves and experimental data (* ) are shown.
Grahic Jump Location
Theoretical (dash-dotted and experimental data (* ) and best fit line (solid) steady-state in-plane displacement: (a) ω=0.6π,d=0.038,γ=400; (b) ω=0.9π,d=0.038,γ=400. Experimental data correspond to circled points in Fig. 3.
Grahic Jump Location
Theoretical (solid) and experimental (* ) natural frequencies (d=0.038,γ=400). Mode shapes (1st solid, 2nd dash-dotted, 3rd dashed): (a) ω=0.3π, (b) ω=0.6π, (c) ω=0.9π.
Grahic Jump Location
Theoretical (dash-dotted) and experimental (solid) mode shapes (ω=0.9π,d=0.038,γ=400): (a) first mode in-plane, (b) second mode in-plane, (c) first mode out-of-plane, (d) second mode out-of-plane. Experimental mode shapes correspond to the circled points in Fig. 5.

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