The deflection of circular mirrors of linearly varying thickness supported along a central hole and free along the outer edge.
Most cassegrainian mirrors supported along the central hole are designed for deflection tolerances using the theory for solid, constant thickness plates. Where tolerances are critical, the mirror is usually made thicker, thereby reducing the deflection, but also increasing the weight of the mirror. Weight can be reduced by using a honeycomb design; however, manufacturing problems result because of the inherent complexity. To circumvent the disadvantages of excessive weight in the solid, constant thickness design and the complexity of the honeycomb design, a lightweight, yet simple design would be desirable. A possible lightweight, yet simple design would be a solid mirror of linearly varying thickness, decreasing in thickness from the center to the outer edge. As mirrors of linearly varying thickness may provide the best solution under combined deflection and weight restraints, a design basis is required and found in small deflection plate theory. The work of H. Conway was extended to account for pressure loading proportional to mirror density for the case when Poisson's ratio is ?. Closed form solutions for the slope of the linearly varying thickness mirrors were obtained for fixed and simply supported boundary conditions along the central hole. Maximum deflections were obtained by numerical integration and compared with the results for comparable constant thickness mirrors.
Prevenslik
T V
TV