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.
Keywordtethered satellites space elevator longitudinal oscillations transverse vibrations
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