Vibration Problems ICOVP-2007 pp 281-290 | Cite as

# Elastic Oscillations Of Space Tethers And The Space Elevator

Many tethered satellite systems that have flown so far involve tethers that are several kilometers long. Another thin long structure that might become a reality in the future is the space elevator, which will extend from the surface of the Earth to an altitude beyond the geostationary orbit. For both of these structures, the ratio of the length to any cross-sectional dimension is very high. Hence, their flexural rigidity is negligible and they behave like strings. For both space tethers and the space elevator, an axial tension is generated due to the gravity force gradient and the centrifugal force gradient. This tension varies along the length. An exact solution is presented for the longitudinal oscillations of space tethers. The proposed space elevator is expected to have a variable area of cross-section to nominally maintain uniform stress throughout. For this case, the discretized equations governing elastic oscillations are derived using the assumed modes method. These are solved to obtain the frequencies of longitudinal and transverse oscillations.

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tethered satellites space elevator longitudinal oscillations transverse vibrations## Preview

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## References

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*A Mathematical Model for Long Term Dynamics of Tethered Satellites Systems*, M. Eng. Thesis, Dept. of Mechanical Engineering, McGill Univ., Montreal.Google Scholar - 2.S. S. Cohen, 2006.
*Dynamics of a Space Elevator*, M. Eng. Thesis, Dept. of Mechanical Engineering, McGill Univ., Montreal.Google Scholar - 3.S. E. Patamia, A. M. Jorgensen, 2005.
*Analytical Model of Large Scale Transverse Dynamics of Proposed Space Elevator, 56th International Astronautical Congress of the International Astronautics Federation*, Paper No. IAC-05-D4.2.06, Fukuoka, Japan.Google Scholar