Dynamics of Sandwich Curved Beams with Viscoelastic Core Described by Fractional Derivative Operators

Abstract

This paper presents a finite element formulation for transient dynamic analysis of sandwich curved beams with embedded viscoelastic material whose constitutive behavior is modeled by means of fractional derivative operators. The sandwich configuration is composed of a band as a viscoelastic core bonded to elastic metallic strips. The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. The Grünwald definition of the fractional operator is used to implement the viscoelastic model into a finite element formulation. Then, discretized motion equations are solved with a direct time integration scheme based on the Newmark method. A useful aspect of the procedure is that only the anelastic displacements history is kept. This allows an important save of computational resources associated with the non-locality of the operators for fractional derivatives. Numerical studies are presented in order to validate the curved beam model with other approaches (frames of straight beams) as well as to analyze the influence of different parameters in the transient dynamics of naturally curved sandwich beams.