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Prediction of high-speed debris motion in the framework of time-fractional model: theory and validation

Malendowski Michał, Sumelka Wojciech, Gajewski Tomasz, Studziński Robert, Peksa Piotr, Sielicki Piotr W.

Archives of Civil and Mechanical Engineering

2023

Vol. 23, no. 1

art. no. e46, 2023

In this work, a newly proposed fractional derivative framework is used for the prediction of high-speed debris motion. The paper focuses on the mathematical formulation of the equation of motion, in which the damping term is generalised using the fractional derivative. The capacity of the proposed approach to predict the motion of debris is justified by the experimental results. Furthermore, the mathematical formulation has been verified by extensive parametric studies on spherical projectiles. The general conclusion is that the elaborated formulation is more reliable compared to the classical approach or, in other words, the fractional viscous damping term (proportional to the fractional velocity of debris) provides a better description of the complexity of the real drag force.