| Non-linear vibration of a spinning tether is studied in this thesis. The tether is thought to be a part of a spinning tethered satellite system in the station-keeping phase so that the tether has a constant nominal length and is forced to spin at a constant rate about its nominal axis. Using the extended Hamilton's principle the governing equations of motion are derived retaining non-linear terms up to the third order that originate from geometric non-linearity. They are discretized by the assumed-modes method, truncated to one-mode equations, and transformed to the phase-space form. Then the method of averaging is applied.;When the tether has high nominal tension, averaging with two variables results in a closed form solution, which shows dependence of the frequency contents on the initial amplitude parameters of the system. In the case of very low nominal tension, averaging with a single variable is useful to obtain the steady state and the limit steady state solutions, both of which result in a circular whirling motion like a skip-rope. Without damping, a general transverse mode appears to be quasi-periodic but it can be periodic under certain initial conditions. Numerical investigations reveal that the material damping through the longitudinal mode derives the steady state to the limit steady state. Also, several interesting shapes are observed in phase plots. |
