Nonlinear Free Vibration of a Spinning Tether
- PDF / 3,373,476 Bytes
- 23 Pages / 496.08 x 722.88 pts Page_size
- 53 Downloads / 264 Views
Nonlinear Free Vibration of a Spinning Tether 1 Byung No Min,2 Arun K. Misra,' and
v. J. Modi
4
Abstract This paper considers nonlinear free vibration of a spinning tether. The tether is a part of a tethered satellite system spinning at a constant rate about its nominal longitudinal axis. Using Hamilton's principle, the governing equations of motion are derived for the stationkeeping phase retaining the nonlinear terms up to the third order. These equations are discretized by the assumed-modes method and then analyzed by applying the method of averaging. When the tether has moderately high nominal tension, averaging with two time variables leads to a closed-form solution, which describes the dependence of the frequency content on the initial amplitude parameters. In the case of very low nominal tension, averaging with only one of the two time variables is permissible to obtain accurate solutions. One can then obtain the steady state and the limit steady state solutions, both of which represent circular whirling motion like a skip-rope. Analytical expressions governing the amplitudes of the whirling motions are presented in the paper. In the absence of damping, the general transverse motion is quasi-periodic, but it can be periodic if the initial conditions are chosen correctly. Numerical investigations reveal that the material damping associated
with longitudinal motion drives the steady state to the limit steady state.
Introduction The simple concept of tethered satellite systems, connecting satellites or space structures with long thin tethers, has led to a large number of proposals for practical application [1, 2]. Several tethered systems have been flown in space, which can be categorized into two types: one is the non-spinning type such as the SEDS (Small Expendable Deployer System) and TSS (Tethered Satellite System) missions, while
'Presented as paper AAS 97-141 at the AAS/AIAA Space Flight Mechanics Meeting, Huntsville, Alabama, February 1997. 2Graduate student, Department of Mechanical Engineering, McGill University, Montreal, Quebec, H3A 2K6, Canada. Email: [email protected]. 3 p rofe ssor, Department of Mechanical Engineering, McGill University, Montreal, Quebec, H3A 2K6, Canada. Email: [email protected]. "Professor, Department of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada.
2
Min, Misra, and Modi
the other is the spinning type such as Gemini XI and OEDIPUS (Observation of Electric field Distribution in Ionospherica Plasma-a Unique Strategy) missions. There is a need to understand the dynamics of tethered systems in order to design successful missions. In spite of the simple configuration, the system dynamics can be quite complex, more so for spinning systems. A survey of earlier works on the dynamics and control of tethered systems was done by Misra and Modi [3]. A more recent work by Beletsky and Levin [4] presents many interesting results on space tether dynamics. In conjunction with the TSS and SEDS missions, a lot of rese
Data Loading...
