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Mathematical Problems in Engineering
Volume 2017, Article ID 7419602, 10 pages
Research Article

Application of Fractional Calculus to Frontal Crash Modeling

Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, Novi Sad, Serbia

Correspondence should be addressed to Miodrag Zigic;

Received 22 February 2017; Revised 16 May 2017; Accepted 1 June 2017; Published 4 July 2017

Academic Editor: J.-C. Cortés

Copyright © 2017 Miodrag Zigic and Nenad Grahovac. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Fractional derivative viscoelastic model is used in the analysis of a frontal impact of a vehicle against a rigid obstacle. The frontal part of the vehicle is first modeled as a viscoelastic fractional rod and then it is modeled as two different viscoelastic fractional rods with a different length. In the second model also the friction is taken into account. A motion is analyzed during several phases because of both different lengths of the rods and the presence of a dry friction force in the later model. Governing systems of differential equations together with the corresponding initial conditions are derived. Parameter identification is done on the basis of the existing experimental results using the solution of a posed impact problem. What makes the problem more complex, regarding the second model, is the fact that it belongs to the class of nonsmooth fractional order systems, which require special treatment when dealing with deformation history during different motion phases.