ANALYTICAL SOLUTION OF THE INFLUENCE FUNCTIONS OF ACTUATORS FOR A CIRCULAR DEFORMABLE MIRROR WITH A FREE EDGE UNDER CONCENTRATED LOADS
D. A. Yagnyatinskiy, V. N. Fedoseyev
Federal State Unitarian Enterprise “Scientific Research Institute Scientific Industrial Association “LUCH”, Podolsk, Russia
Keywords: deflection, thin circular plate, deformable mirror, free edge, concentrated load, actuator, integral transforms, kinematic pairs, ANSYS
Abstract
An analytical solution of the problem of deflection of a deformable mirror with a thin circular plate with a free edge under the action of a concentrated load generated by one of the actuators acting on the plate with the other end resting on an infinitely rigid base is derived. The solution is based on the application of integral transforms and takes into consideration the kinematic pairs between the plate and each actuator, which is deformed according to Hooke’s law. The analytical solution is compared to the finite element solution obtained by using the ANSYS software. The results of the study can be used to optimize the actuator positions and to control the circular deformable mirrors in adaptive optics problems.
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