Dynamic Finite Element analysis of fractionally damped structural systems in the time domain

Abstract

Visco-elastic material models with fractional characteristics have been used for several decades. This paper provides a simple methodology for Finite-Element-based dynamic analysis of structural systems with viscosity characterized by fractional derivatives of the strains. In particular, a re-formulation of the wellknown Newmark method taking into account fractional derivatives discretized via the Grünwald–Letnikov summation allows the analysis of structural systems using standard Finite Element technology.