This work is devoted to mathematical and numerical modelling of a coupled system including an elastic thin shell, distributed piezoelectric patches and a distributed electronic circuit. The formulation of the circuit is general, it can take into account passive devices and voltage to voltage amplifiers. Two numerical simulations based on a finite elements method are presented. They are related to two different distributed electronic circuits which are both stabilizing shell vibrations. In our mind, the shell vibration stabilization problem is an intermediary step before to study the question of sound transmission control through a such an thin elastic shell. This last question is a key for noise reduction in all terrestrial and non terrestrial vehicles.