Application of Fractional Calculus to Frontal Crash Modeling

Abstract

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.

A Fractional Derivative-Based Lateral Preview Driver Model for Autonomous Automobile Path Tracking

“…Here, fractional calculus is considered to build the focus point preview model. Although the idea of fractional calculus is as old as the idea of integer calculus, the application of fractional calculus has become more and more popular over the past few decades [15,16]. It covers many research areas, including viscoelastic material, image processing, and automatic control.…”