Use of a recurrence based fractional derivative model in the analysis of the influence of geometrical parameters in the transient response of viscoelastic beams

Resumo

This paper aims to analyze the influence of geometrical parameters on the dynamical behavior of
viscoelastic beams. Viscoelastic materials are widely used in vibration control of dynamic systems. Usually, a
viscoelastic layer is applied on the surface of the structure and a second layer with elastic properties is used to
restrict viscoelastic displacements. This restrictive layer intensifies energy dissipation once it introduces shear
deformation in the viscoelastic material. Naturally, geometrical parameters, mainly the width of the viscoelastic
layer may influence the shear deformation and the efficiency of the vibration control treatment. For this analysis,
a recurrence based fractional derivative model is used, the system is discretized in finite elements and solved
using Newmark's method. This procedure makes it possible to compare the mechanical behavior of several
viscoelastic beams with different geometries, and determine how they affect vibration control treatment.