Averaged Controllability Of Transversely Isotropic Ambartsumyan Plate

Abstract

In this paper we study the averaged controllability of Ambartsumyan plate made of a transversely isotropic material. Governing equations are based on assumptions of particular theory of anisotropic plates developed by S. A. Ambartsumyan specifically for describing the deformation of anisotropic plates made of material with isotropy plane which, at each point of the plate, is parallel to its middle plane. The Green’s function approach is applied to express the plate normal displacement by means of material parameters (density, Young moduli in both directions of isotropy) which are assumed to be uniformly distributed random variables. Eventually, the averaged controllability condition is reduced to an infinite system of linear constraints with respect to the control action. Three types of particular (heuristic) solutions of the truncated version of the infinite system are discussed. Determination of control parameters is reduced to the solution of a problem of nonlinear programming.