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

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

Identyfikatory

DOI

10.1007/s43452-022-00568-5

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

high speed debris motion; fractional derivatives; equation of motion

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2023
• Tom: Vol. 23, no. 1
• Strony: art. no. e46, 2023
• Opis fizyczny: Bibliogr. 35 poz., rys., tab., wykr.

Twórcy

autor

Malendowski Michał

• Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60‑965 Poznań, Poland

autor

Sumelka Wojciech

• Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60‑965 Poznań, Poland

• https://orcid.org/0000-0002-8317-748X

autor

Gajewski Tomasz

• Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60‑965 Poznań, Poland

autor

Studziński Robert

• Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60‑965 Poznań, Poland
• Institute of Building Engineering, Poznan University of Technology, Piotrowo 5, 60‑965 Poznań, Poland

autor

Peksa Piotr

• Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60‑965 Poznań, Poland

autor

Sielicki Piotr W.

• Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60‑965 Poznań, Poland

Bibliografia

• 1. van der Voort M, Weerheijm J. A statistical description of explosion produced debris dispersion. Int J Impact Eng. 2013;59:29-37. https://doi.org/10.1016/j.ijimpeng.2013.03.002.
• 2. Mébarki A, Nguyen Q, Mercier F. Structural fragments and explosions in industrial facilities: Part ii - projectile trajectory and probability of impact. J Loss Prev Process Ind. 2009;22(4):417-25. https://doi.org/10.1016/j.jlp.2009.02.005.
• 3. Wang M, Hao H, Ding Y, Li Z-X. Prediction of fragment size and ejection distance of masonry wall under blast load using homogenized masonry material properties. Int J Impact Eng. 2009;36(6):808-20. https://doi.org/10.1016/j.ijimpeng.2008.11.012.
• 4. van der Voort M, Radtke FKF, van Amelsfort R, Khoe YS, Stacke I, Voss M, Häring I. Recent developments of the kg software, In: 34th DoD Explosives Safety Seminar 2010, Portland, Oregon: DDESB. 2010.
• 5. Price MA, Nguyen V-T, Hassan O, Morgan K. An euler-lagrange particle approach for modeling fragments accelerated by explosive detonation. Int J Numer Methods Eng. 2016;106(11):904-26. https://doi.org/10.1002/nme.5155.
• 6. Price MA, Nguyen V-T, Hassan O, Morgan K. An approach to modeling blast and fragment risks from improvised explosive devices. Appl Math Model. 2017;50:715-31. https://doi.org/10.1016/j.apm.2017.06.015.
• 7. Loth E. Compressibility and rarefaction effects on drag of a spherical particle. AIAA J. 2008;46(9):2219-28. https://doi.org/10.2514/1.28943.
• 8. Sielicki PW, Stewart MG, Gajewski T, Malendowski M, Peksa P, Al-Rifaie H, Studziński R, Sumelka W. Field test and probabilistic analysis of irregular steel debris casualty risks from a person-borne improvised explosive device. Def Technol. 2020. https://doi.org/10.1016/j.dt.2020.10.009.
• 9. Miller K, B R. An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, 1993.
• 10. Kilbas A, Srivastava H, Trujillo J. Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier; 2006.
• 11. Sumelka W. Fractional viscoplasticity. Mech Res Commun. 2014;56:31-6.
• 12. Sun Y, Gao Y, Zhu Q. Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential. Int J Plast. 2018;102:53-69.
• 13. Sun Y, Chen C, Gao Y. Stress-fractional model with rotational hardening for anisotropic clay. Comput Geotech. 2020;126:103719.
• 14. Sun Y, Gao Y, Shen Y. Mathematical aspect of the state-dependent stress-dilatancy of granular soil under triaxial loading. Geotechnique. 2019;69(2):158-65.
• 15. Lu D, Liang J, Du X, Ma C, Gao Z. Fractional elastoplastic constitutive model for soils based on a novel 3d fractional plastic flow rule. Comput Geotech. 2019;105:277-90.
• 16. Sumelka W. Thermoelasticity in the framework of the fractional continuum mechanics. J Therm Stresses. 2014;37(6):678-706.
• 17. Patnaik S, Semperlotti F. A generalized fractional-order elastodynamic theory for non-local attenuating media. Proc R Soc A Math Phys Eng Sci. 2020;476(2238):20200200.
• 18. Patnaik S, Jokar M, Semperlotti F. Variable-order approach to nonlocal elasticity: theoretical formulation, order identification via deep learning, and applications. Comput Mech. 2021;69:267-98.
• 19. Pang G, Chen W, Fu Z. Space-fractional advection-dispersion equations by the kansa method. J Comput Phys. 2015;293:280-96.
• 20. Béda P. Dynamic stability and bifurcation analysis in fractional thermodynamics. Continuum Mech Thermodyn. 2018;30(6):1259-65.
• 21. Failla G, Santini A, Zingales M. A non-local two-dimensional foundation model. Arch Appl Mech. 2013;83(2):253-72.
• 22. Di Paola M, Alotta G, Burlon A, Failla G. A novel approach to nonlinear variable-order fractional viscoelasticity. Philos Trans R Soc A Math Phys Eng Sci. 2020;378(2172):20190296.
• 23. Sumelka W, Łuczak B, Gajewski T, Voyiadjis G. Modelling of aaa in the framework of time-fractional damage hyperelasticity. Int J Solids Struct. 2020;206:30-42.
• 24. Kukla S, Siedlecka U. Fractional heat conduction in a sphere under mathematical and physical robin conditions. J Theor Appl Mech (Poland). 2018;56(2):339-49.
• 25. Shariyat M, Mohammadjani R. Three-dimensional dynamic stress and vibration analyses of thick singular-kernel fractional-order viscoelastic annular rotating discs under nonuniform loads. Int J Struct Stab Dyn 0 (0) (0) 2050007.
• 26. Podlubny I. Fractional Differential Equations, Vol. 198 of Mathematics in Science and Engineering, Academin Press, 1999.
• 27. Sumelka W, Voyiadjis G. A hyperelastic fractional damage material model with memory. Int J Solids Struct. 2017;124:151-60.
• 28. Voyiadjis GZ, Sumelka W. Brain modelling in the framework of anisotropic hyperelasticity with time fractional damage evolution governed by the caputo-almeida fractional derivative. J Mech Behav Biomed Mater. 2019;89:209-16.
• 29. Malinowska A, Odzijewicz T, Torres D. Advanced Methods in the Fractional Calculus of Variations, Springer Briefs in Applied Sciences and Technology, Springer, 2015.
• 30. Odibat Z. Approximations of fractional integrals and caputo fractional derivatives. Appl Math Comput. 2006;178(2):527-33. https://doi.org/10.1016/j.amc.2005.11.072.
• 31. Reddy J. An Introduction to Nonlinear Finite Element Analysis. Oxford: OUP; 2004.
• 32. Feinstein D. Casualty prediction comparisons. IIT RESEARCH INST CHICAGO IL: Tech. rep; 1968.
• 33. AASTP-1. Manual of NATO Safety Principles for the Storage of Military Ammunition and Explosives, Allied Ammunition Storage and Transport Publication (AASTP), Edition B, Version 1., 2015.
• 34. Grisaro HY, Turygan S, Sielicki PW. Concrete slab damage and hazard from close-in detonation of weaponized commercial unmanned aerial vehicles. J Struct Eng. 2021;147(11):04021190. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003158.
• 35. Schlichting H, Gersten K. Boundary-Layer Theory. 9th ed. Berlin Heidelberg: Springer-Verlag; 2017.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)