In some applications, moment actuators provide a competitive
alternative approach to the conventional piston type of actuators. A piezoelectric
or similar device placed between two posts on the back surface
of a deformable mirror constitutes one type of moment actuator. A closed
form solution of the biharmonic equation of Kirchhoff's thin plate theory
is obtained by the classical method of boundary value problems of linear
elastomechanics and presented in this paper for the influence function of
an arbitrarily located and oriented moment actuator of the above type on
the back of a flat circular deformable mirror. The solution covers both
radial and tangential moments. The results clearly show their global character
in contrast to those for the piston type actuators with high stiffness.
An application of these functions to the design of a 30-actuator circular
deformable mirror with moment actuators, related hardware, and test
results has been reported elsewhere.