Active Control of Translating Media With Arbitrarily Varying Length

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

Department of Mechanical Engineering, University of Maryland Baltimore County, Baltimore, MD 21250e-mail: wzhu@umbc.edu

J. Ni

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

J. Huang

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong

J. Vib. Acoust 123(3), 347-358 (Feb 01, 2001) (12 pages) doi:10.1115/1.1375809 History: Received February 01, 2000; Revised February 01, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.


Mote,  C. D., 1971, “Dynamic Stability of Axially Moving Materials,” Shock Vib. Dig., 4, No. 4, pp. 2–11.
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., 6, No. 2, pp. 100–103.
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 Dyn., 12, No. 1, pp. 39–55.
Misra,  A. K, and Modi,  V. J., 1985, “Depolyment and Retrieval of Shuttle Supported Tethered Satellite,” AIAA Journal of Guidance, Control, and Dynamics, 5, No. 3, pp. 278–285.
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.
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.
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.
Sato,  K., and Sakawa,  Y., 1988, “Modelling and Control of a Flexible Rotary Crane,” Int. J. Control, 48, No. 5, pp. 2085–2105.
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.
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, No. 3, pp. 201–220.
Zajaczkowski,  J., and Lipinski,  J., 1979, “Instability of the Motion of a Beam of Periodically Varying Length,” J. Sound Vib. 63, pp. 9–18.
Zajaczkowski,  J., and Yamada,  G., 1980, “Further Results on Instability of the Motion of a Beam of Periodically Varying Length,” J. Sound Vib., 68, No. 2, pp. 173–180.
Zhu,  W. D., and Ni,  J., 2000, “Energetics and Stability of Translating Media with an Arbitrarily Varying Length,” ASME J. Vibr. Acoust., 122, pp. 295–304.
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.
Yang,  B., and Mote,  C. D., 1991, “Active Vibration Control of the Axially Moving String in the S Domain,” ASME J. Appl. Mech., 58, pp. 189–196.
Zhu,  W. D., Mote,  C. D., and Guo,  B. Z., 1997, “Asymptotic Distribution of Eigenvalues of a Constrained Translating String,” ASME J. Appl. Mech., 64, pp. 613–619.
Zhu,  W. D., Guo,  B. Z., and Mote,  C. D., 2000, “Stabilization of a Translating Tensioned Beam Through a Pointwise Control Force,” ASME J. Dyn. Syst., Meas., Control, 122, pp. 322–331.
Yang,  B., and Mote,  C. D., 1990, “Vibration Control of Band Saws: Theory and Experiment,” Wood Sci., 24, pp. 355–373.
Huang,  D., Fan,  Q., and Tan,  C. A., 1998, “Experimental Investigations on the Active Vibration Control of Chain Drives,” Noise Control Eng. J., 46, No. 4, pp. 139–145.
Rahn, C. D., “Parametric Control of Vibration in Flexible and Axially-Moving Materials Systems,” 1992, Ph.D. Dissertation, University of California, Berkeley.
Rahn,  C. D., and Mote,  C. D., 1994, “Parametric Control of Flexible Systems,” ASME J. Vibr. Acoust., 116, pp. 379–385.
Chung,  C. A., and Tan,  C. A.,1995, “Active Vibration Control of the Axially Moving String by Wave Cancellation,” ASME J. Vibr. Acoust., 117, No. 1, pp. 49–55.
Lee,  S. Y., and Mote,  C. D., 1996, “Vibration Control of an Axially Moving String by Boundary Control,” ASME J. Dyn. Syst., Meas., Control, 118, pp. 66–74.
Renshaw,  A. A., Rahn,  C. D., Wickert,  J. A., and Mote,  C. D., 1998, “Energy and Conserved Functionals for Axially Moving Materials,” ASME J. Vibr. Acoust., 120, pp. 634–636.
Rugh, W. J., 1996, Linear System Theory, Prentice Hall, pp. 116–117.
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 mass-spring at x=l(t) subject to a pointwise control force uf(t) and/or moment um(t) at x=θ(t)
Grahic Jump Location
Schematic of a vertically translating string with an attached mass-spring at x=l(t) subject to a pointwise control force uf(t) at x=θ(t)
Grahic Jump Location
The tip responses and energies of vibration of uncontrolled translating beams with and without end mass during extension (a) and retraction (b). Solid, me*=0.2; dashed, me*=0.
Grahic Jump Location
The tip responses and energies of vibration of uncontrolled and controlled translating beams without end mass during extension (a) and retraction (b). Dash-dotted, uncontrolled; dotted, domain force control with Kf*=0.2 and θ*(t*)=l*(t*)−0.1; solid, boundary force control with Kf*=0.2; dashed, boundary moment control with Km*=0.2.
Grahic Jump Location
The effect of the control gain in the boundary force control law (35) on the response of the translating beam without end mass. Dependences of the average energy of vibration on the control gain Kf* during extension and retraction are shown in (a) and (b), respectively. Under various control gains, the energy of vibration and the tip displacement are shown in (c) and (e) during extension, and (d) and (f) during retraction. Solid in (c) and (e), Kf*=1.22 (optimal); solid in (d) and (f), Kf*=1.26 (optimal); dashed in (c)–(f), Kf*=5; dotted in (c)–(f), Kf*=0.2; dash-dotted in (c)–(f), Kf*=1000.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In