Analytical Modeling of the Flexible Rim of Reflectors of Space Antennas
K. G. Okhotkin1,2, A. Yu. Vlasov3, Yu. V. Zakharov3, B. D. Annin4
1Reshetnev Information Satellite Systems, Zheleznogorsk, 662972 Russia
2Krasnoyarsk Scientific Center, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
3Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, 660014 Russia
4Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: гибкая пластина, геометрическая нелинейность, рефлектор антенны, композиционный материал, flexible plate, geometric nonlinearity, antenna reflector, composite material
Abstract
This paper presents of an geometrically nonlinear analytical model of a flexible cylindrical frame (rim) of the transformable precision large-size reflector of space antennas made using polymer composite materials with form memory. A nonlinear boundary-value problem for the frame in a deformed (collapsed) state is formulated and exact analytic solutions in elliptic functions and integrals which describe the deformation modes of the rim. A geometrically nonlinear model us used to obtain exact analytical solutions which allow preliminary determination of the geometric dimensions and the optimal shape of the flexible frame and estimate the stored energy.
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