A shell finite element for active-passive vibration control of composite structures with piezoelectric and viscoelastic layers

This paper presents an accurate shell finite element (FE) formulation to model composite shell structures with embedded viscoelastic and piezoelectric layers and an integrated active damping control mechanism. The five-layered finite element introduced in this paper uses the first order shear deformation theory in the viscoelastic core and Kirchoff theory for the elastic and piezoelectric layers. The corresponding coupled FE formulation is derived starting from the shell kinematic and electromechanical governing equations. Assuming a linear strain field through each layer and exactly the same transverse displacement and the rotations in the elastic and piezoelectric layers, the number of degree of freedoms (dof) per node is reduced to 8. All the eight of these dofs are mechanical in nature. Constant velocity and constant displacement feedback control algorithms are used to actively control the dynamic response of the adaptive structure. Based on this formulation, a finite element code is implemented and the obtained results are compared to those in the literature analytical model and to the numerical results obtained using a commercial finite element code.