Refined Finite Element Model for Vibration Analysis of Sandwich Beams with Shear Piezoelectric Actuators and Sensors

High stresses and possible impacts of surface-mounted piezoelectric actuators can be alleviated by embedding axially poled piezoceramic actuators between two elastic layers. In this case, the application of a transverse electric field induces shear deformation of the actuator thus generating the desired sandwich structure deflection. Although this so-called shear actuation mechanism seems quite promising for structural control, its modelling is still an open issue. For piezoelectric shear actuated sandwich beams, either the classical sandwich theory (CST) or first and higher-order equivalent single layer (ESL) theories were used. However, ESL theories fail to model localized core shear deformations, which are determinant to correctly evaluate the shear actuation of the sandwich beam.

This work extends a previously presented refined sandwich beam finite element (FE) model [

1

] for vibration analysis. The mechanical model is a refinement of CST, for which the core is modelled with a third-order shear deformation theory [

2

]. The FE model is developed considering, through the beam length, electrically: constant electric difference of potentials for the piezoelectric facing and core layers and quadratic third-order variable of the electric potential in the core, while mechanically: linear axial displacement and quadratic bending rotation of the core, and cubic transverse displacement of the sandwich beam. Despite the refinement of mechanical and electrical behaviours of the piezoelectric core, the model leads to the same number of degrees of freedom (dof) as the previous CST one due to a two-step static condensation of the internal dof (bending rotation and core electric potential third-order variable). The proposed FE model is validated through the comparison with numerical and experimental results [

3

]. Results confirm that the TSDT and the induced cubic electric potential yield an extra stiffness to the sandwich beam.