Free Vibration Characteristics of a String with Time-Varying Length

길이가 변하는 현의 자유진동 특성

  • 이승엽 (서강대학교 공과대학 기계공학과) ;
  • 박상규 (서강대학교 대학원 기계공학과)
  • Published : 1999.10.01

Abstract

Time-dependent period and energy of free vibration of a string, whose length varies with time at a constant rate, are investigated by a traveling wave method. When the string length is increased, the vibration period increase, but the free vibration energy decrease with time. However, when the string undergoes retraction, the vibration energy increases with time. String tension together with non-zero instantaneous velocity at the moving boundary results in energy variation. Analytical solutions by the traveling wave method are compared with previous results using the perturbation method and Kotera's approach.

Keywords

References

  1. Nonconsertive Problems of the Theory of Elastic Stability Bolotin, V. V.
  2. Applied Mechanics Reviews v.40 Instability of Dynamically Loaded Structures Simites, G. S.
  3. Journl of Guidance, Control and Dynamics v.9 Traveling Wave Control for Large Spacecraft Structures Von Flotow, A. H.
  4. Journl of Guidance, Control and Dynamics v.8 Distributed Piezoeletric-Polymer Active Vibration Control of a Cantilever Beam Bailey, T.;Hubbard, J. E.
  5. Shock and Vibration Digest v.20 Currunt Research on the Vibration and Stability of Axially Moving Materials Wickert, J. A.;Mote, C. D.
  6. Shock and Vibration Digest v.23 On the Noise and Vibration Chain Drive System Liu, S. P.;Wang, K. W.
  7. Journal of Fluid and Structures v.7 Pipes Conveying Fluid : a Model of Dynamical Problem Li, G. X. ;Paidoussis, M. P.
  8. Journal of Dynamic Systems, Measurement and Control v.118 Vibration Control of an Axially Moving String by Boundary Control Lee, S.-Y.;Mote, C. D.
  9. Journal of sound and Vibration v.204 A Generalized Treatment of the Energetics of Translating Continua, Part I : Strings and Tensioned Pipes Lee, S.-Y.;Mote, C. D.
  10. Journal of sound and Vibration v.212 Traveling Wave Dynamics in a Translating String Coupled to Stationary Constraints: Energy Transfer and Mode Localization Lee, S.-Y.;Mote, C. D.
  11. Nonlinear Oscillations Nafeh, A. H.;Mook, D. T.
  12. Bulletin of JSME v.21 Vibrations of String with Time-varying Length Yamamoto, T.;Yasuda, K.;Kato, M.
  13. Bulletin of JSME v.21 Vibrations of String with Time-varying Length Kotera, T.
  14. Journal of Sound and Vibration v.194 no.1 Free Vibration of a String with Moving Boundary Conditions by the Method of Distorted Images Ram, Y. M.;Caldwell, J.
  15. ASME Winter Annual Meeting v.56 Nonstationary Vibrations of a String with Time-Varying Length and a Mass-Spring System Attached at the Lower End Terumichi, Y.;Ohtsuka, M.(et al.)