Modeling and Controllability of Coupled Plate-Beam Systems

Abstract

In this chapter we shall develop a distributed parameter models for two dynamic elastic plate-beam configurations. The first consists of a thin plate to which a thin beam is rigidly and orthogonally attached to the edge of the plate in such a manner that the centerline of the beam is coplanar with the middle plane of the plate (in the equilibrium state). The second model is that of a thin plate to which a thin beam is attached orthogonally to a face of the plate (i.e., the centerline of the beam is orthogonal to a face of the plate in the equilibrium configuration). In the case of the configuration in which the beam is orthogonal to the edge of the plate, it will be proved that the dynamical system obtained is exactly controllable by means of controls applied along an appropriate portion of the edge of the plate that excludes the junction region between the plate and beam. We shall also consider a simplified model of that system obtained by passing to the limit in the original model as the shear moduli go to infinity.