Time domain finite element analysis of structures with fractional viscoelastic damping using time-diffusive scheme

Jean-François Deü (1) , Lucie Rouleau (1) , Denis Matignon (2)

1 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
2 DISC - Département d'Ingénierie des Systèmes Complexes

This work aims at simulating the time response of a structure damped by viscoelastic materials. The structure is discretised by finite elements and a 4-parameter fractional derivative model is used to describe the frequency-dependency of the mechanical properties of the viscoelastic material. The proposed approach combines a classical Newmark time-integration scheme to solve the semi-discretised equation of motion with a diffusive representation of fractional derivatives. This approach is applied to a finite element model, and validated on a single degree-of-freedom system for which an analytical solution can be derived.

Mots clés: Fractional damping; Viscoelastic damping; Diffusive representation; Finite element method

Domaines: Mathématiques générales [math.GM]

Jean-François Deü, Lucie Rouleau, Denis Matignon. Time domain finite element analysis of structures with fractional viscoelastic damping using time-diffusive scheme. 2nd Euro-Mediterranean Conference on Structural Dynamics and Vibroacoustics (MEDYNA 2017), Apr 2017, Sevilla, Spain. pp. 130-133. ⟨hal-01814693⟩