Boundary Control of Physical Fields in a Piezoceramic Layer Having a Tunnel Hole with a System of Electrodes

Abstract

An approach to the optimal (from the viewpoint of minimum energy consumption) control of the characteristics of coupled fields is illustrated with the example of an antiplane dynamic problem of electroelasticity for a piezoceramic layer with a tunnel hole. The vibrations in the layer are excited by time-dependent harmonic loads of two types: by the difference of electric potentials applied to a pair of infinitely long electrodes located on the surface of the hole and by shear forces or electric charges continuously distributed on the given sections of the layer base, which are assumed as control actions. The inverse problem is solved by using the solution of the corresponding direct mixed antiplane problem of electroelasticity, with the help of which the optimization problem is reduced to the -problem of moments. The functions of optimal control allowing one, for example, to disconnect the external circuit of the generator of electric voltage are given.