Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme

Authors:
J. -F. Deü;D. Matignon
Affiliations:
Conservatoire National des Arts et Métiers (Cnam), Structural Mechanics and Coupled Systems Laboratory, Case 353, 292 rue Saint Martin, F-75141 Paris Cedex03, France;Université de Toulouse, ISAE, Applied Mathematics Training Unit, 10 avenue Edouard Belin, B.P. 54032, F-31055 Toulouse Cedex 4, France
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model.