Effects of Tension upon the Surface Accuracy of a Rectangular Membrane Element of a Space Reflector
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概要
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The surrface accuracy of a rectangular membrane element subjected to anisotropic tension in a faceted reflector surface is investigated. The rectangular membrane element is assumed to be placed at an arbitrary place on the reflector surface with an arbitrary rotation angle between the side of the membrane and the direction of the principal curvature of the reflector surface. Rectangular membranes with two kinds of boundaries are considered. One is a coincident-edge membrane whose boundary coincides with the approximate parabolic surface at the local point where the membrane is placed. The other membrane is a coincident-optimum-edge membrane, which is obtained by minimizing the rms error using normal translation of the coincident-edge membrane. The deflection and the surface error of the membrane are calculated based on an analytical solution of the linear membrane equation. In a certain range of parameters, it is found that the appropriate tension ratio reduces the surface error of a membrane element as compared with isotropic tension. The surface error of a slender membrane becomes lower if the longer side of the membrane is loaded with higher tension. The more slender the membrane, the smaller the surface error. The minimum surface error is obtained when the longer side is placed parallel to the direction of the larger principal curvature at the location and the longer side is loaded with higher tension. The ratio of the surface error of a coincident-optimum-edge to that of a coincident-edge membrane is approximately 0.4 - 0.5 and depends only on the ratio of the aspect ratio of the membrane and the tension ratio parameter.
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THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES | 論文
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