Mechanics Today

Abstract

Formulas are given for initial and residual root-mean-squared (rms) surface shape error and edge moments and force amplitudes for a deformable primary reflecting surface composed of an array of relatively small diameter circular elements. These formulas apply to the reshapement of large shallow primary reflectors in such a way that the center of mass of the reflector at the focus of the primary (the secondary) does not translate. The edge moment and force resultants required to minimize the rms residual surface error of each circular element of the primary are derived for n = 0 and n = 1 circumferential waves from a shallow-shell theory published by Reissner in 1946 and for n ≥ 2 circumferential waves from an inextensional bending theory published by Flügge in 1960. It is found that for reasonable configurations most of the residual rms surface error is axisymmetric and proportional to the square of the diameter-to-thickness ratio of the circular elements. The formulas demonstrate clearly that sandwich wall construction is superior to monocoque, permitting the use of thinner, lighter shells and smaller actuation forces and moments.