<title>Implementation of a distributed control law for thin shell vibrations by a distributed electronic circuit</title>

Abstract

In this paper, we first formulate the equations of the electrical network. This network is composed of resistors, current sources, voltage sources and voltage to voltage amplifiers. It has an arbitrary shape. It is connected to piezoelectrical patches which are distributed transducers on the elastic thin shell. A 2D Reisner-Mindlin model of piezoelectrical thin shell is obtained under coupled to electronic network. A second model is derived under co- localization assumption. The two models are written under the form of a global variational formulation. Sufficient conditions on the network are stated in order to insure existence and uniqueness of the solution of the coupling. They are based on a graph interpretation of abstract conditions stated in the framework of functional analysis. Finally, numerical simulations of the Reisner-Mindlin shell in vibrations are presented for a particular choice of electric circuit. This last is designed in order to act as a stabilizer of the shell vibrations.