Alternative technologies of composite highly loaded aircraft structures: a qualitative method of making multi-criteria decisions. Comprehensive presentation: Part IV. Equilibrium and stability of the dynamic model of the ADS

Authors

  • Volodymyr Zabashta Ukrainian Research Institute of Aviation Technology, JCS, Ukraine

DOI:

https://doi.org/10.20535/2521-1943.2024.8.3(102).302969

Keywords:

SA, AK, PKM, ADS, alternative TPs, manifolds, criterion estimates, phase space, separatrix equilibrium points, stability, bifurcations, transitions, topology tools

Abstract

The main direction of the fourth part of the work is the study of an autonomous dynamic system in the field of aviation technology, based on the provisions of the qualitative theory of differential equations with the involvement of the phase portrait method. The materials and results of the article are based on the starting points in the decision-making problem (DPR), specified [1], [3] empirically - the formalized direction of research in the comparison of preprego - autoclaved (surfactant) and non-autoclaved VARTM technologies in the manufacture of carbon-plastic aircraft structures according to the prevalence (first of all - quality) (AK) type of highly loaded stringer panels of the wing caisson (VSP) of mainline aircraft. That is, we are talking about a large multi-stage (based on ChTP) technological system. The research as a whole is based on systems analysis (SA) and interpreted structure-functional modeling of ATP. The evaluation toolkit and criterion-evaluation apparatus based on the macro-level ADS and a number of technological structures and other configurations are used [2]. Special points, stability and phase portrait of ADS (quadratic function) were investigated, with the involvement of interpreted elements of the topology of many species, as well as bifurcation points of the system.

References

  1. D. Kiva and V. Zabashta, "Alternative technologies of composite high-loaded aircraft constructions: a qualitative method of making multicriterial decisions. Part I. Initial stages in the problem of decision-making", Mechanics and Advanced Technologies, vol. 5, no. 2, pp. 203-211, 2021. DOI: https://doi.org/10.20535/2521-1943.2021.5.2.245000.
  2. V. Zabashta, "Alternative technologies of composite highly loaded of aircraft structures: a qualitative method of making multi-criteria decisions. Part II. Modeling in multi-criteria evaluation of alternatives", Mechanics and Advanced Technologies, vol. 6, no. 2, pp. 203-220, 2022. DOI: https://doi.org/10.20535/2521-1943.2022.6.2.265371.
  3. V. Zabashta, "Alternative technologies of composite of highly loaded aircraft structures: a qualitative method for making multicriteria decisions. Part III. Research of the methodological basis in decision-making: technological constructions in the assessment toolkit", Mechanics and Advanced Technologies, vol. 7, no. 3 (99), pp. 374-388, 2023. DOI: https://doi.org/10.20535/2521-1943.2023.7.3.293231.
  4. S. A. Smotrova and Y. D. Symonov-Emelianov, "Effektyvnye tekhnolohyy formovanyia vysokonahruzhennykh avyatsyonnykh konstruktsyi yz polymernykh kompozytsyonnykh materyalov", Konstruktsyy yz kompozytsyonnykh materyalov, no. 3, pp. 15-24, 2016.
  5. Ye. A. Veshkin, V. Yu. Postnov, M. V. Postnova and A. A. Barannikov, "Opyt primeneniya vakuum–infuzionnykh tekhnologiy v proizvodstve konstruktsiy iz PKM", Izvestiya Samarskogo nauchnogo tsentra Rossiyskoy akademii nauk, vol. 20, no. 4 (3), pp. 16-28, 2018.
  6. V. V. Batrakov and R. I. Petrushenko, "Vliyaniye rezhimov avtoklavnogo formovaniya i konstruktsii tekhnologicheskogo paketa na poristost konstruktsii iz kompozitnykh materialov", Izv. vuzov "Aviatsionnaya tekhnika", vol. 1, pp. 68-92, 2018.
  7. O. V. Andrieiev, Naukovi osnovy pidvyshchennia efektyvnosti stvorennia konstruktsii transportnykh litakiv z polimernykh kompozytsiinykh materialiv na etapakh zhyttievoho tsyklu vyrobu. Kyiv, 2020, 333 p.
  8. Vliyaniye poristosti polimernykh kompozitsionnykh materialov na osnovu epoksidnoy matritsy i nepreryvnykh uglerodnykh volokon na yego fiziko–mekhanicheskiye svoystva. Elektronnyy resurs.
  9. M. Yu. Dushin, A. V. Khrulkov and R. Yu. Karavayev, "Parametry, vliyayushchiye na obrazovaniye poristosti iz polimernykh kompozitsionnykh materialov, izgotavlivayemykh bezavtoklavnymi metodami (obzor)", Trudy VIAM, no. 2, pp. 58-61, 2015.
  10. A. V. Khrulkov, R. Yu. Karavlev, Yu. A. Gorodkova and K. Yu. Donetskiy, "Nekotoryye prichiny obrazovaniya por v polimernykh kompozitsionnykh materialakh (obzor)", Trudy VIAM, 2023.
  11. N.A. Verbitskaya, Nauchnyye osnovy tekhnologii termoreaktivnykh polimernykh kompozitnykh materialov s zadannymi strukturoy i svoystvami (avtoreferat). Saratov: STU, 2000.
  12. Kh. A. Krivov, Yu. M. Tarasov, A. Kh. Khromoshev and V. F. Zabashta, "Tekhnologiya bezavtoklavnogo formirovaniya silovykh konstruktsiy samoleta iz polimernykh kompozitsionnykh materialov", Tekhnologicheskiye sistemy, no. 5, pp. 47–76, 2009.
  13. V. Ye. Yonov, "Upravleniye ryskom protsessov ispolzovaniya kompozitnykh materialov", Trudy VIAM, pp. 46-50, 2018.
  14. K. O. Antoshyna, Homotopichni vlastyvosti topolohichnykh prostoriv y fundamentalni hrupy skinchenykh CW-kompleksiv. Kyiv: NaUKMA, 2021, 50 p.
  15. Yu. H. Masikevych, O. V. Shestopalov, A. A. Nehadaylo et al., "Liniyni systemy. Typy osoblyvykh tochok: vuzol, sidlo, fokus, tsentr", in Teoriya system v ekolohiyi. Sumy: SumDU, 2015, pp. 240-248.
  16. N. O. Sliepinina, "Asotsiatsii: vid teorii do praktyky", Mova i kultura, vol 1, no. 16, pp. 71-79, 2013.
  17. N. M. Ausheva, "Modeliuvannia hladkykh poverkhon pry ekolohichnykh rozrakhunkakh", Prykladna heometriia ta inzhenerna hrafika, no. 63, pp. 217-219, 1998.
  18. A. T. Fomenko, Nahlyadnaya heometryya y topolohyya. Matematycheskye obrazy v realnom myre. Moskva: MHU, 1998, 416 p.
  19. A. O. Ivanov and A. A. Tuzhinlin, Lektsii po klassicheskoy differentsialnoy geometrii. Moskva: Logos, 2009, 217 p.
  20. B. V. Atamaniuk, Konspekt lektsiy do spetskursu “Teoriya retraktiv”. Ivano-Frankivsk: PNU, 2011, 214 p.
  21. N. M. Harmatiy, Metodychni rekomendatsiyi po opornomu konspektu lektsiy z dystsypliny "Modeli ekonomichnoyi dynamiky" dlya studentiv napryamu pidhotovky 6.030502 "Ekonomichna kibernetyka" dennoyi ta zaochnoyi formy navchannya. Ternopil: TNTU, 2017, 65 p.
  22. Kachestvennyy analiz dinamicheskikh sistem. Postroyeniye fazovykh portretov D.S. Elektronnyy resurs.
  23. O. M. Hladka, I. M. Karpovych and A. M. Savchuk, Modeli ekonomichnoyi dynamiky dlya fakhivtsiv z informatsiynykh tekhnolohiyi. Rivne: RDHU, 2019, 138 p.
  24. Lektsiya 1. Elementy kachestvennogo analiza dinamicheskikh sistem s nepreryvnym vremenem na samoy pervoy. Lektsiya 2. Dinamicheskiye sistemy s parametrami bifurkatsiy v D.S. Tipy bifurkatsiy v odnoparametricheskikh DS. Elektronnyy resurs.
  25. Yu. A. Khazova, Elementy teorii bifurkatsii. Chast 1. Dinamicheskiye sistemy. Simferopol: KTU, 2019, 54 p.
  26. V. I. Arnold, V. S. Afraymovich, Yu. S. Ilyashenko and L. P. Shilnikov, Teoriya bifurkatsiy. Moskva: VINITI, 1985, 218 p.
  27. O. O. Pryshliak, Diferentsialnaya topologiya. Kyiv: KNU, 2009, 40 p.
  28. O. O. Pryshlyak, Topolohiya mnohovydiv. Kyiv: KNU, 2013, 83 p. Available: https://www.mechmat.univ.kiev.ua/wp-content/uploads/2018/03/topolog_pryshljak.pdf.
  29. B. Khessard, Yu. Kazarinov and Yu. Van, Teoriya i prilozheniya bifurkatsii rozhdeniya tsikla. Moskva: Mir, 1985, 210 p.
  30. V. A. Kadiyevskyy, L. P. Perkhun, S. M. Bratushko and O. O. Synyavska, Stiykyst dynamichnykh system z neperervnym chasom. Sumy: M. Vinnuchenko, E. Lutovchenko, 2014, 120 p.
  31. Shchurov Yu. Obyknovennyye differentsialnyye uravneniya i osobyye tochki nelineynykh sistem na ploskosti. Elektronnyy resurs.
  32. V .I. Urmanchev, Yakisna teoriya zvichainykh dyferentsialnykh rivnyan (lokalnyy analiz). Kyiv: NASOA, 2018, 41 p.
  33. Kachestvennyy analyz dynamycheskykh system. Elektronnyy resurs.
  34. V. A. Danylenko, "Synerhetychnyy pidkhid v doslidzhenni stiykosti ekonomichnykh system", Teoretychni ta prykladni pytannya ekonomiky, no. 20, pp. 257-265. Available: http://tppe.econom.univ.kiev.ua/data/2009_20/Zb20_37.pdf.
  35. A. Ye. Kononyuk, Diskretno-nepreryvnaya matematika. Kniga 8, chast 3: Topologicheskiye prostranstva. Kyiv: Osvita Ukrainy, 2016, 900 p.
  36. L. P. Mironenko and Yu. V. Petrenko, "Matrichnyy metod klassifikatsii krivykh vtorogo poryadka", Iskusstvennyy intellekt, no. 4, pp. 335-342, 2011.
  37. Y. G. Borisevich, N. M. Bliznyakov, Ya. A. Izraylevich and T. Yu. Fomenko, Vvedenye v topologiyu. Moskva: Vysshaya shkola, 1980, 295 p.
  38. T. V. Boyarishcheva, T. V. Hudyvok and O. O. Pohorilyak, Funktsionalnyy analiz. Uzhgorod: Invazor, 2013, 120 p.
  39. O. Hutik, Zahalna topolohiya v teoremakh, prykladakh i zadachakh, 2020, 169 p. Available: https://new.mmf.lnu.edu.ua/wp-content/uploads/2017/11/Topology_PR.pdf.
  40. V. A. Vasylev, Vvedenie v topologiyu. Moskva: Fazis, 1997, 132 p.
  41. T. Ye. Panov, Lektsii 4, 5, 6. Vveden'ye v gomotopicheskuyu topologiyu. Gomotopiya. Retraktsiya. Elektronnyy resurs.
  42. Gomotopiya. Moskva: BRE, 2022.
  43. Tsylindr vidobrazhennya. Elektronnyy resurs.
  44. Ches Kosnevski, Nachalnyy kurs algebraicheskoy topologii. Moskva: Mir, 1983, 304 p.

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Published

2024-09-30

How to Cite

[1]
V. Zabashta, “Alternative technologies of composite highly loaded aircraft structures: a qualitative method of making multi-criteria decisions. Comprehensive presentation: Part IV. Equilibrium and stability of the dynamic model of the ADS”, Mech. Adv. Technol., vol. 8, no. 3(102), pp. 316–331, Sep. 2024.

Issue

Vol. 8 No. 3(102) (2024)

Section

Aviation Systems and Technologies

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Copyright (c) 2024 Володимир Забашта

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