Analytic model of an adaptive mirror in the form of a thin plate with discrete actuators

A description is given of a model of an adaptive mirror in the form of a thin plate with discrete piezoelectric actuators. This model is based on the assumptions of a theory of thin plates. Analytic expressions are found for the response functions of an adaptive mirror, for the range of displacements of the substrate under the action of an actuator, and for the efficiency of conversion of the energy of a control signal into the energy of elastic deformation of the substrate. The response functions obtained using the adopted model are in good agreement with the experimental response functions of a cooled mirror with 19 magnetostrictive actuators. The results are given of a numerical modeling of the operation of an actuator acting on an adaptive mirror.