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.
Highlights
The most of the fatal injuries from vehicle accidents happen in frontal crashes
We propose the mechanical model consisting of two parallel viscoelastic rods of different lengths, which will not start to deform at the same time
Dynamics and deformations during the impact process are described by systems of differential equations, which includes fractional derivatives of both contact forces and deformations of viscoelastic rods in the case of the fractional viscoelastic model
Summary
Various crash tests are performed in order to improve safety of vehicle occupants. Both offset and full width barrier tests are mainly conducted in the analysis of frontal impacts. Experimental results of a car to pole frontal impact test are presented in the papers of Pawlus et al [6, 7]. In order to achieve better agreement between a model prediction and a crash test experiment than the agreement presented in [6], the classical and the fractional Zener model of a viscoelastic body will be applied to model a deformable
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