Hybrid Active—passive Damping Treatment of Sandwich Beams in Non-linear Dynamics

Abstract

In the context of large displacement and rotations, this work presents a co-rotational finite element formulation of an adaptive sandwich beam composed of a viscoelastic core constrained by laminated elastic/piezoelectric faces. A classical sandwich theory is used for the face/core/face set, considering transverse shear deformations for the core. The four-parameter fractional Zener model is used in order to take the viscoelastic behavior of the middle layer into account, while a classical linear piezoelectric constitutive law is used for modeling the piezoelectric material. The finite element formulation allows large displacements and rotations with a local small strain measure. Moreover, local electrical degrees-of-freedom are used in order to reproduce sensor configurations. Another particularity consists of approximating the fractional derivative operator by the Grünwald-Letnikov scheme, where the history of the internal memory force is used to take into account the damping effect.