Low-order actuator influence functions for piezoelectric in-plane actuated tensioned circular deformable mirrors

摘要

Future space-based optical reflectors will be driven by the desire for large apertures versus the constraints of low weight and compactness of packaging. One possible way to satisfy these competing factors is through the use of piezoelectric in-plane actuated, tensioned, deformable mirrors. These configurations typically exhibit both plate-like and membrane-like behavior. Proposed is a new approximation method for the solution to this class of mirror, where the normalized plate stiffness to tension ratio is small. The approximation function is based on the exact analytical solution to this class of problems. The approximation method allows the problem to be reduced to a simple pressure forced membrane equation, a geometry which may be more readily analyzed. A case study comparing the results of the approximation method to a high fidelity finite element model constructed in MSC.Nastran is provided.