Modelling of a thin piezoelectric shell coupled with a distributed electronic circuit by distributed piezoelectric transducers (Q2725533)

A formulation is given for the mathematical and numerical modelling of a coupled system which consists of a thin elastic shell, distributed piezoelectric paths and distributed electronic circuits. A variational formulation of electric circuit, including passive and voltage to voltage amplifiers coupling with electronic network and piezoelectric shell, is presented.NEWLINENEWLINENEWLINESufficient conditions for the existence and uniqueness of the 3D thin shell solutions are proven, using the weak formulation of the coupled system. A Reissner-Mindlin type two-dimensional shell model of a coupled elastic-electric system is also developed. This model is based on Mindlin kinematics for displacements and a similar assumption for the electric potential. The conditions of existence and uniqueness for the solution of the 2D model prove to be the same as for the 3D model. The numerical simulation is based on the degenerate finite element model extended to the multilayer piezoelectric network.NEWLINENEWLINENEWLINEThe presented numerical method is illustrated on a quarter cylinder subjected to uniform and oscillating pressure on its side. Two cases of electric network are considered, a local one and a nonlocal one. Comparison of the effect of the local and the nonlocal controllers to the displacements show that the nonlocal controller is more efficient than the local one.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00045].