0
BRIEF NOTES

A New Wave Technique for Free Vibration of a String With Time-Varying Length

[+] Author and Article Information
S.-Y. Lee

Department of Mechanical Engineering, Sogang University, Sinsudong, Mapoku, Seoul 121-742, Korea e-mail: sylee@sogang.ac.kr. Mem. ASME

M. Lee

Department of Mechanical Engineering, Sejong University, Kunjadong, Kwanjinku, Seoul 143-747, Korea.

J. Appl. Mech 69(1), 83-87 (Aug 08, 2001) (5 pages) doi:10.1115/1.1427337 History: Received August 29, 2000; Revised August 08, 2001
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.

References

Downer,  J. D., and Park,  K. C., 1993, “Formulation and Solution of Inverse Spaghetti Problem: Application to Beam Deployment Dynamics,” AIAA J., 31, pp. 339–347.
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.
Carrier,  G. F., 1949, “The Spagetti Problem,” Am. Math. Monthly, 56, pp. 669–672.
Renshaw,  A. A., 1997, “Energetics of Winched Strings,” ASME J. Vibr. Acoust., 119, No. 4, pp. 643–644.
Wickert,  J. A., and Mote,  C. D., 1988, “Current Research on the Vibration and Stability of Axially Moving Materials,” Shock Vib. Dig., 20, pp. 3–13.
Li,  G. X., and Paidoussis,  M. P., 1993, “Pipes Conveying Fluid: A Model of Dynamical Problem,” J. Fluids Struct., 7, pp. 137–204.
Lee,  S.-Y., and Mote,  C. D., 1997, “A Generalized Treatment of the Energetics of Translating Continua, Part I: Strings and Tensioned Pipes,” J. Sound Vib., 204, pp. 735–753.
Lee,  S.-Y., and Mote,  C. D., 1998, “Traveling Wave Dynamics in a Translating String Coupled to Stationary Constraints: Energy Transfer and Mode Localization,” J. Sound Vib., 212, pp. 1–22.
Yamamoto,  T., Yasuda,  K., and Kato,  M., 1978, “Vibrations of a String With Time-Variable Length,” Bull. JSME, 21, pp. 1677–1684.
Kotera,  T., 1978, “Vibrations of String With Time-Varying Length,” Bull. JSME, 21, pp. 1469–1474.
Ram,  Y. M., and Caldwell,  J., 1996, “Free Vibration of a String With Moving Boundary Conditions by the Method of Distorted Images,” J. Sound Vib., 194, No. 1, pp. 35–47.
Terumichi, Y., and Ohtsuka, M., et al., 1993, “Nonstationary Vibrations of a String With Time-Varying Length and a Mass-Spring System Attached at the Lower End,” Dynamics and Vibration of Time-Varying Systems and Structures, DE-Vol. 56, ASME, New York, pp. 63–69.
Cremer, L., Heckel, M., and Ungar, E. E., 1988, Structure-Borne Sound, Springer–Verlag, Berlin.
Mead,  D. J., 1994, “Waves and Modes in Finite Beams: Application of the Phase-Closure Principle,” J. Sound Vib., 171, pp. 695–702.

Figures

Grahic Jump Location
String with length varying at a constant velocity v
Grahic Jump Location
Traveling wave pattern of the fundamental vibration mode over a period
Grahic Jump Location
Time-varying vibration periods of the fundamental mode when the string length changes at v=0.1c/l0
Grahic Jump Location
String motion history during a period when v=0.2c/l0 for the initial displacement of the fundamental mode; (a) increasing length, (b) decreasing length
Grahic Jump Location
Power flow by string tension at the moving boundary; (a) increasing length, (b) decreasing length
Grahic Jump Location
Free vibration energy when the length increases at v=0.1c/l0
Grahic Jump Location
Free vibration energy when the length decreases at v=0.1c/l0
Grahic Jump Location
Free vibration energy when v=0.2c/l0; (a) increasing length, (b) decreasing length

Tables

Errata

Discussions

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