Energetics and Stability of Translating Media with an Arbitrarily Varying Length

[+] Author and Article Information
W. D. Zhu

Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250

J. Ni

Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030

J. Vib. Acoust 122(3), 295-304 (Jun 01, 1999) (10 pages) doi:10.1115/1.1303003 History: Received June 01, 1999
Copyright © 2000 by ASME
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Terumichi,  Y., Ohtsuka,  M., Yoshizawa,  M., Fukawa,  Y., and Tsujioka,  Y., 1997, “Nonstationary Vibrations of a String with Time-Varying Length and a Mass-Spring System Attached at the Lower End,” Nonlinear Dynam., 12, No. 1, pp. 39–55.
Misra,  A. K., and Modi,  V. J., 1985, “Deployment and Retrieval of Shuttle Supported Tethered Satellites,” AIAA J. Guid., 5, No. 3, pp. 278–285.
Yuh,  J., and Young,  T., 1991, “Dynamic Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment,” ASME J. Dyn. Syst., Meas., Control, 113, pp. 34–40.
Tsuchiya,  K., 1983, “Dynamics of a Spacecraft During Extension of Flexible Appendages,” AIAA J. Guid., 6, No. 2, pp. 100–103.
Stolte,  J., and Benson,  R. C., 1992, “Dynamic Deflection of Paper Emerging from a Channel,” ASME J. Vibr. Acoust., 114, No. 2, pp. 187–193.
Kumaniecka,  K., and Niziok,  J., 1994, “Dynamic Stability of a Rope with Slow Variability of the Parameters,” J. Sound Vib., 178, No. 2, pp. 211–226.
Roberts, R., 1998, “Control of High-Rise/High-Speed Elevators,” Proceedings of the American Control Conference, FM16-1, Philadelphia.
Venkatesh, S. R., and Cho, Y. M., 1998, “Identification and Control of High Rise Elevators,” Proceedings of the American Control Conference, FM16-3, Philadelphia.
Carrier,  G. F., 1949, “The Spaghetti Problem,” Am. Math. Monthly, 56, pp. 669–672.
Tabarrok,  B., Leech,  C. M., and Kim,  Y. I., 1974, “On the Dynamics of an Axially Moving Beam,” J. Franklin Inst., 297, pp. 201–220.
Zajaczkowski,  J., and Lipinski,  J., 1979, “Instability of the Motion of a Beam of Periodically Varying Length,” J. Sound Vib., 63, No. 1, pp. 9–18.
Yamamoto,  T., Yasuda,  K., and Koto,  M., 1978, “Vibration of a String with Time-Variable Length,” Bull. J. Soc. Mech. Eng., 21, No. 162, pp. 1677–1684.
Mansfield,  L., and Simmonds,  J. G., 1987, “The Reverse Spaghetti Problem: Drooping Motion of an Elastica Issuing from a Horizontal Guide,” ASME J. Appl. Mech., 54, pp. 147–150.
Tadikonda,  S. K., and Baruh,  H., 1992, “Dynamics and Control of a Translating Flexible Beam with a Prismatic Joint,” ASME J. Dyn. Syst., Meas., Control, 114, pp. 422–427.
Stolte,  J., and Benson,  R. C., 1993, “An Extending Dynamic Elastica—Impact with a Surface,” ASME J. Vibr. Acoust., 115, No. 3, pp. 308–313.
Vu-Quoc,  L., and Li,  S., 1995, “Dynamics of Sliding Geometrically-Exact Beams: Large Angle Maneuver and Parametric Resonance,” Comput. Methods Appl. Mech. Eng., 120, pp. 65–118.
Cooper,  J., 1993, “Asymptotic Behavior for the Vibrating String with a Moving Boundary,” J. Math. Anal. Appl., 174, pp. 67–87.
Wickert,  J. A., and Mote,  C. D., 1989, “On the Energetics of Axially Moving Continua,” J. Acoust. Soc. Am., 85, pp. 1365–1368.
Wang,  P. K. C., and Wei,  J. D., 1994, “Correction and Remarks on Vibration in a Moving Flexible Robot Arm,” J. Sound Vib., 172, No. 3, pp. 413–414.
Miranker,  W. L., 1960, “The Wave Motion in a Medium in Motion,” IBM J. Res. Dev., 4, pp. 36–42.
White, F. M., 1994, Fluid Mechanics, McGraw-Hill, pp. 114–122.
Meirovitch, L., 1970, Methods of Analytical Dynamics, McGraw-Hill, pp. 14–17.
Wang,  P. K. C., and Wei,  J. D., 1987, “Vibrations in a Moving Flexible Robot Arm,” J. Sound Vib., 116, pp. 149–160.


Grahic Jump Location
Schematic of a horizontally (a) or vertically (b) translating beam with an attached spring-inertia-damper at x=l(t)
Grahic Jump Location
Schematic of a vertically translating string with an attached spring-mass-damper at x=l(t)
Grahic Jump Location
The nondimensionalized dynamic response of a flexible arm during uniformly accelerated extension (–) and retraction ([[dashed_line]]). The tip deflection and velocity are shown in (a) and (b), respectively. The energy of vibration of the arm is shown in (c).
Grahic Jump Location
The prescribed position (a), velocity (b), acceleration (c), and jerk (d) functions for a hoist cable in a high-rise, high-speed elevator
Grahic Jump Location
The dynamic response of the hoist cable under motion profiles shown in Fig. 4 and initial conditions y(x,0)=0.1 sin(πx/180) and yt(x,0)=0. The displacement and velocity of a fixed point on the cable, located at x=l(t)−25, are shown in (a) and (b), respectively. The energy of vibration of the cable is shown in (c).




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