- Volume 12 Issue 4
The time-dependent frequency and energy of free vibration of the spagetti problem, that is the axially moving continuum with time-varying length, are investigated. Exact expressions for the natural frequency and time-varying vibration energy are derived by dealing with traveling waves. The vibration period increases with increasing length, but the free vibration energy decreases. When the string undergoes retraction, the vibration energy increases with time. The free response of the time-varying string is represented by superposing two traveling waves.
- Carrier, G. F., 1949, "The Spaghetti Problem," American Mathematical Monthly, Vol 56, pp. 669-672. https://doi.org/10.2307/2305560
- Tsuchiya, K., 1983, "Dynamics of a Space-craft during Extension of Flexible Appendages," Journal of Guidance, Control and Dynamics, Vol. 6, pp. 100-103. https://doi.org/10.2514/3.56343
- Janice D. Downer and K. C. Park, 1993. "Formulation and Solution of Inverse Spaghetti Problem: Application to Beam Deployment Dynamics," AIAA Journal. Vol. 31, pp. 339-347. https://doi.org/10.2514/3.61535
- Ehud N. and Thomas R. K., 1993, "Deployment and Retrieval Optimization of a Tethered Satellite System," Journal of Guidance, Control and Dynamics, Vol. 6. pp. 1085-1091.
- Yuh. J. and Young, T., 1991, "Dynamics Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment," Journal of Mechanical Systems, Measurement and Control, Vol. 113, pp.34-40. https://doi.org/10.1115/1.2896355
- Terumichi, Y., Ohtsuka, M., et al., 1993, 'Nonstationary Vibrations of a String with Time-varying Length and a Mass-spring System Attached at the Lower End.", ASME Winter Annual Meeting, DE-Vol. 56, pp. 63-69.
- Wickert, J. A. and Mote. C. D., 1988, 'Currunt Research on the Vibration and Stability of Axially Moving Materials." Shock and Vibration Digest, Vol. 20, pp. 3-13.
- Liu, S. P. and Wang, K. W., 1991, "On the Noise and Vibration Chain Drive System." Shock and Vibration Digest, Vol. 23. pp. 8-13.
- Yamamoto, T., Yasuda, K. and Kato, M., 1978. "Vibrations of a String with Time-variable Length." Bulletin of JSME, Vol. 21. pp. 1677-1684. https://doi.org/10.1299/jsme1958.21.1677
- Kotera, T., 1978. "Vibrations of String with Time-varying Length." Bulletin of JSME, Vol. 21, pp. 1469-1474 https://doi.org/10.1299/jsme1958.21.1469
- Lee, S.Y., and Mote, C. D., 1996, "Vibration Control of an Axially Moving String by Boundary Control." Mechanical Engineers. Journal of Dynamic Systems, Measurement and Control, Vol. 118. pp. 66-74. https://doi.org/10.1115/1.2801153
- Lee, S.Y., and Mote, C. D., 1997. "A Generalized Treatment of the Energetics of Translating Continua, Part I: Strings and Tensioned Pipes." Journal of Sound and Vibration, Vol. 204, pp. 735-753. https://doi.org/10.1006/jsvi.1996.0946
- Lee, S.Y., and Mote C. D., 1998, "Traveling Wave Dynamics in a Translating String Coupled to Stationary Constraints: Energy Transfer and Mode Localization," Journal of Sound and Vibration, Vol. 212, pp. 1-22. https://doi.org/10.1006/jsvi.1997.1285
- 이승엽, 박상규, 1999, "길이가 변하는 현의자유진동 특성," 한국소음진동공학회지, 제 9권 제 5호, pp. 906-913.
- Lee, S.Y. and Lee, M., 2002, "A New Wave Technique for Free Vibration of a String with Time-varying Length," Journal of Applied Mechanics, Vol, 69. No. 1, (to be published).
- Nafeh, A. H.. and Mook, D. T., 1979. Nonlinear Oscillations, John Wiley & Sons.
- Cremer, L., Heckel M. and Ungar, E. E., 1988, Structure-borne Sound, Berlin: Springer-verlag.
- Mead, D. J., 1994, "Waves and Modes in Finite Beams: Application of the Phase-closure Principle," Journal of Sound and Vibration. Vol. 171, pp. 695-702. https://doi.org/10.1006/jsvi.1994.1150