Dynamics of a Slender Spinning Membrane
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Dynamics of a Slender Spinning Membrane Jer-Nan Juang1,2,3 · Chung-Han Hung1,3 · William K. Wilkie4
Published online: 30 October 2015 © American Astronautical Society 2015
Abstract A novel approach is introduced to conduct dynamic analysis of a spinning, high aspect ratio membrane. In this formulation, an inextensible, long, slender membrane is modeled using a discrete set of lumped masses. Lagranges equations are used to derive the highly coupled ordinary differential equations for in-plane, out-of-plane, and twisting motions for the spinning membrane. The generalized and uncoupled linear equations for small motion are used to compute the vibration mode frequencies which are compared to results from an uncoupled analysis of blade motion using rotor dynamics. Linearized behavior is shown to reduce to the linearized solutions for the spinning membrane blade developed by MacNeal. Numerical simulations along with 3-D animations are used to study the linear and nonlinear uncoupled dynamics of the spinning membrane. Keywords Heliogyro solar sail · Spinning membrane · Structural dynamics
Fellow AAS, AIAA, ASME. Jer-Nan Juang
[email protected] 1
Department of Engineering Science, National Cheng Kung University, Tainan City, Taiwan
2
Aerospace Engineering Department, Texas A & M University, College Station, TX, USA
3
National Institute of Aerospace, Hampton, VA, USA
4
Structural Dynamics Branch, NASA Langley Research Center, Hampton, VA, USA
J of Astronaut Sci (2013) 60:494–516
495
Introduction Spinning membrane structures are of particular interest for solar sail propulsion of spacecraft. Solar sails derive thrust directly from momentum transfer of solar photons, which enables essentially propellantless propulsion for long-duration, continuous thrusting applications, or missions to high delta-V destinations otherwise unreachable via chemical or solar electric propulsion [1]. Science applications for solar sails include solar weather early warning sentinels, high-inclination solar polar observers, and deep space probes that can travel beyond the heliopause and into interstellar space. Gravity tractors for asteroid deflection have also been proposed [2]. Human spaceflight-relevant missions include robotic precursor spacecraft to nearEarth asteroids and Earth-to-Mars cargo prepositioning [3]. As solar radiation pressure is extremely small (4.6 x 10-6 Pa at 1.0 AU) very large reflective surfaces must be used to generate appreciable thrust. Mass of the large reflective surfaces, which, with the mass of any spacecraft bus and scientific payload, is the total sail craft mass, must also be minimized in order to develop overall accelerations sufficient to conduct missions within a reasonable timeframe. The most common solar sail architectures (see Fig. 1) are 1) kite-like, square-rigged solar sails that use rigid beams or spars to tension a usually square membrane sail [4], 2) spinning, low-aspect ratio (disk or square) sails that use centrifugal forces to flatten and stabilize the solar sail membrane reflector [5]
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