Modeling of tape tether vibration and vibration sensing using smart film sensors Kouta Kunugi a , Hirohisa Kojima a,n , Pavel M. Trivailo b a Department of Aerospace Engineering, Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan b School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora, VIC 3083, Australia article info Article history: Received 16 March 2014 Received in revised form 15 October 2014 Accepted 16 November 2014 Available online 22 November 2014 Keywords: Tape tether Smart film sensor Bending and torsion Vibration sensing abstract Tape-tethered satellite systems use long and flexible tape tethers, the bending and torsional vibrations of which affect the positions and attitude of attached satellites and climbers. Owing to the distribution characteristics of a tape tether, ordinary point sensors and actuators cannot be used easily to control the vibrations. Other types of sensors and actuators are required for this purpose. The flexibility and deformability of smart materials make them particularly suitable for integration into a tape-tethered system. Thus, in this paper, we propose a method for modeling the bending and torsional vibrations of a tape tether, and report our investigation into the feasibility of using smart film sensors to distinguish between the two vibration types. We formulate equations of motion for the tape tether using multibody dynamics techniques, and perform numerical simulations to study the behavior of the bending and torsional vibrations. The results of our experiments show that the bending and torsional vibrations of a tape tether can be measured using smart film sensors attached to the tether. & 2014 IAA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Tethered satellite systems (TSS) are emerging space tech- nologies. A TSS generally comprises a mother satellite, one or more subsatellites, and a very long tether that connects all the satellites. TSSs facilitate satellite orbit transfer, formation sys- tems, transportation, subsatellite attitude control, and other tasks [1]. The space elevator (SE) is the ultimate configuration of a TSS and includes a subsystem for transportation from the ground into space. Electrodynamic tether (EDT) systems, which use the Lorentz force derived from the interaction bet- ween the electric current on the tether and Earth's magnetic field, have the potential to function as space debris removal systems. However, the practical application of the TSSs remains difficult, especially because of the highly complex nonlinear dynamics of the tether. In space, tethers are expected to be deployed over 1 km with the tension in them to vary along their length. Thus, the vibration of the tether cannot be treated as a string vibration. The tether motion is affected by not only external forces such as gravity but also the Coriolis force because the tether of tethered satellite systems moves in the orbital frame that orbits around the Earth with an orbital angular velocity. If the tether is subject to vibrational excitation in space, the damping would be minimal owing to the almost negligible drag force. There is also a possibility of the tether becoming slack, and in such case, it could not be used to control the satellites at its ends. In addition, the vibration of the tether may disturb the attitude of the mother satellite, the subsatellites, and a climber [2–4] traveling along the tether. Thus, the dynamics of a TSS is highly complex and very difficult to model. In particular, flexibility and three-dim- ensional motion must be considered in modeling of the tether. Extensive studies have been conducted on modeling of flexible beams [5–7], cables [6,8,9], plates and membranes [10], using Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/actaastro Acta Astronautica http://dx.doi.org/10.1016/j.actaastro.2014.11.024 0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: þ81 42 585 8653; fax: þ81 42 583 5119. E-mail address: hkojima@tmu.ac.jp (H. Kojima). Acta Astronautica 107 (2015) 97–111