Piezoelectric structural acoustic problems: Symmetric variational formulations and finite element results

This paper presents an original symmetric finite element formulation for piezoelectric structural acoustic coupled problems. First, an unsymmetric variational formulation in terms of structure displacement, electric potential and fluid pressure field is proposed. Then, through the introduction of an additional variable, namely fluid displacement potential, a symmetric finite element formulation is presented. Finally, after a rigorous condensation procedure and using the fluid added mass and piezoelectric added stiffness concepts, a reduced symmetric formulation is obtained. Some numerical examples concerning axisymmetric elastic/piezoelectric structures filled with internal compressible fluid are presented in order to validate the proposed formulation.