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Nonlinear stability of moderately thick functionally graded sandwich shells with double curvature in thermal environment.
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3. Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine1; Pidgorny A. Intsitute of Mechanical Engineering Problems, Kharkiv, Ukraine2

Page: Kosm. teh. Raket. vooruž. 2020, (1); 26-33

DOI: https://doi.org/10.33136/stma2020.01.026

Language: Russian

Annotation: The study of thermal strength of the hold-down bay is considered. The hold-down bay is a cylindrical shell with the load-bearing elements as the standing supports. The case of the hold-down bay consists of the following structural elements: four standing supports and the compound cylindrical shell with two frames along the top and bottom joints. The purpose of this study was the development of a general approach for the thermal strength calculation of the hold-down bay. This approach includes two parts. Firstly, the unsteady heat fields on the hold-down bay surface are calculated by means of the semi-empirical method, which is based on the simulated results of the combustion product flow of the main propulsion system. The calculation is provided by using Solid Works software. Then the unsteady stress-strain behavior of the hold-down bay is calculated, taking into consideration the plastoelastic deformations. The material strain bilinear diagram is used. The finiteelement method is applied to the stress-strain behavior calculation by using NASTRAN software. The thermal field is assumed to be constant throughout the shell thickness. As a result of the numerical simulation the following conclusions are made. The entire part of the hold-down bay, which is blown by rocket exhaust jet, is under stress-strain behavior. The stresses of the top frame and the shell are overridden the breaking strength that caused structural failure. The structure of the hold-down bay, which is considered in the paper, is unappropriated to be reusable. The hold-down bay should be reconstructed by reinforcement in order to provide its reusability.

Key words: stress-strain behavior, finite-element method, plastoelastic deformations, breaking strength, reusability

Bibliography:

1. Elhefny A., Liang G. Stress and deformation of rocket gas turbine disc under different loads using finite element modeling. Propulsion and Power Research. 2013. № 2. P. 38–49. https://doi.org/10.1016/j.jppr.2013.01.002
2. Perakis N., Haidn O. J. Inverse heat transfer method applied to capacitively cooled rocket thrust chambers. International Journal of Heat and Mass Transfer. 2019. № 131. P. 150–166. https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.048
3. Yilmaz N., Vigil F., Height J., et. al. Rocket motor exhaust thermal environment characterization. Measurement. 2018. № 122. P. 312–319. https://doi.org/10.1016/j.measurement.2018.03.039
4. Jafari M. Thermal stress analysis of orthotropic plate containing a rectangular hole using complex variable method. European Journal of Mechanics A /Solids. 2019. № 73. P. 212–223. https://doi.org/10.1016/j.euromechsol.2018.08.001
5. Song J., Sun B. Thermal-structural analysis of regeneratively cooled thrust chamber wall in reusable LOX / Methane rocket engines. Chinese Journal of Aeronautics. 2017. № 30. P. 1043–1053.
6. Ramanjaneyulu V., Murthy V. B., Mohan R. C., Raju Ch. N. Analysis of composite rocket motor case using finite element method. Materials Today: Proceedings. 2018. № 5. P. 4920–4929.
7. Xu F., Abdelmoula R., Potier-Ferry M. On the buckling and post-buckling of core-shell cylinders under thermal loading. International Journal of Solids and Structures. 2017. № 126–127. P. 17–36.
8. Wang Z., Han Q., Nash D. H., et. al. Thermal buckling of cylindrical shell with temperature-dependent material properties: Conventional theoretical solution and new numerical method. Mechanics Research Communications. 2018. № 92. P. 74–80.
9. Duc N. D. Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy’s third-order shear de-formation shell theory. European Journal of Mechanics A /Solids. 2016. № 58. P. 10–30.
10. Trabelsi S., Frikha A., Zghal S., Dammak F. A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells. Engineering Structures. 2019. № 178. P. 444–459.
11. Trinh M. C., Kim S. E. Nonlinear stability of moderately thick functionally graded sandwich shells with double curvature in thermal environment. Aerospace Science and Technology. 2019. № 84. P. 672–685.
12. Лойцянский Л. Г. Механика жидкости и газа. М., 2003. 840 с.
13. Launder B. E., Sharma B. I. Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. International Journal of Heat and Mass Transfer. 1974. № 1. P. 131–138.
14. Михеев М. А., Михеева И. М. Основы теплопередачи. М., 1977. 345 с.
15. Малинин Н. Н. Прикладная теория пластичности и ползучести. М., 1968. 400 с.

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3.1.2020 Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff
3.1.2020 Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff
3.1.2020 Analysis of the unsteady stress-strain behavior of the launch vehicle hold-down bay at liftoff

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13.1.2020 Mathematical models of hydraulic servomechanisms of space technology https://journal.yuzhnoye.com/content_2020_1-en/annot_13_1_2020-en/ Wed, 13 Sep 2023 10:58:26 +0000 https://journal.yuzhnoye.com/?page_id=31045
To calculate the rocket stability regions and to evaluate own stability of servo actuators, a linearized mathematical model of hydraulic servo actuator is used that takes into account the most important parameters having impact on stability of the servo actuator itself and on that of the rocket: hardness of working fluid, stiffness of elastic suspension of the actuator and control element, slope of mechanical characteristic of the actuator in the area of small control signals, which, as full mathematical model analysis showed, is conditioned only by dimensions of initial axial clearances of slide’s throats. Key words: mathematical model , hydraulic actuator , servo actuator , stability , damping , slide Bibliography: 1. mathematical model , hydraulic actuator , servo actuator , stability , damping , slide .
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13. Mathematical models of hydraulic servomechanisms of space technologynt

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2020, (1); 121-132

DOI: https://doi.org/10.33136/stma2020.01.121

Language: Russian

Annotation: Being a final executive element of rocket control systems, a hydraulic actuator is at the same time the main source of various non-linear dependencies in rocket dynamic design whose availability dramatically com plicates theoretical analysis of their dynamics and control systems synthesis. The required accuracy and complexity of mathematical models of hydraulic servo mechanisms are different for different design phases of guided rockets. The paper deals with the simplest models of hydraulic servo actuators intended to calculate rocket controllability and to define requirements to response and power characteristics of the actuators. To calculate the rocket stability regions and to evaluate own stability of servo actuators, a linearized mathematical model of hydraulic servo actuator is used that takes into account the most important parameters having impact on stability of the servo actuator itself and on that of the rocket: hardness of working fluid, stiffness of elastic suspension of the actuator and control element, slope of mechanical characteristic of the actuator in the area of small control signals, which, as full mathematical model analysis showed, is conditioned only by dimensions of initial axial clearances of slide’s throats. The full mathematical model constructed based on accurate calculations of the balance of fluid flow rate through the slide’s throats allows, as early as at designing phase, determining the values of most important static and dynamic characteristics of a future hydraulic actuator, selecting optimal characteristics of slides based on specified degree of stability and response of servo actuator and conducting final modeling of rocket flight on the integrated control system test benches without using real actuators and loading stands. It is correct and universal for all phases of rockets and their control systems designing and testing. Using this mathematical model, the powerful actuators of a line of intercontinental ballistic missiles with swinging reentry vehicle and the main engines actuators of Zenit launch vehicle first stage were developed. The results of their testing separately and in rockets practically fully comply with the data of theoretical calculations.

Key words: mathematical model, hydraulic actuator, servo actuator, stability, damping, slide

Bibliography:
1. Dinamika gidroprivoda / pod red. V. N. Prokofieva. М., 1972. 292 s.
2. Gamynin N. S. Gidravlicheskii privod system upravleniia. М., 1972. 376 s.
3. Chuprakov Yu. I. Gidroprivod i sredstva gidroavtomatiki. М., 1979. 232 s.
4. Kozak L. R. Geometriia zolotnika i dinamicheskie kharakteristiki gidroprivoda // Visnyk Dnipropetrovskoho universytetu. Vyp. 13, Tom 1. 2009.
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13.1.2020  Mathematical models of hydraulic servomechanisms of space technology
13.1.2020  Mathematical models of hydraulic servomechanisms of space technology
13.1.2020  Mathematical models of hydraulic servomechanisms of space technology

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11.1.2020 Some results of strength calculations relying on analytical and FEM approaches. Trends of using contemporary machine learning strategies https://journal.yuzhnoye.com/content_2020_1-en/annot_11_1_2020-en/ Wed, 13 Sep 2023 10:51:08 +0000 https://journal.yuzhnoye.com/?page_id=31040
This article also discusses analytical solutions that apply asymptotic approaches and a method of initial parameters in a matrix form for solving a problem of equal stability of reinforced compartments of combined shell systems of the rocket and space technology within the scope of the research being carried out jointly by teams of Yuzhnoye State Design Office and Zaporizhzhya National University. Key words: numerical and analytical methods , stress-strain state , rocket structures , shell system , reinforcing load-bearing elements , local and general stability , machine learning technology Bibliography: 1. numerical and analytical methods , stress-strain state , rocket structures , shell system , reinforcing load-bearing elements , local and general stability , machine learning technology .
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11. Some results of strength calculations relying on analytical and FEM approaches. Trends of using contemporary machine learning strategies

Organization:

Zaporizhzhia National University, Zaporizhzhia, Ukraine

Page: Kosm. teh. Raket. vooruž. 2020, (1); 107-113

DOI: https://doi.org/10.33136/stma2020.01.107

Language: Russian

Annotation: This article analyzes the results of studies, which are based on numerical methods of analysis, of the stress-strain state of thin-walled shell structures. This article also discusses analytical solutions that apply asymptotic approaches and a method of initial parameters in a matrix form for solving a problem of equal stability of reinforced compartments of combined shell systems of the rocket and space technology within the scope of the research being carried out jointly by teams of Yuzhnoye State Design Office and Zaporizhzhya National University. The primary attention is paid to the use of FEM-based direct numerical methods and the research results for which analytical methods can be useful for making a preliminary assessment of the bearing capacity of load-bearing structures, and in some cases for their rational design. This article does not contrast numerical and analytical approaches but about the possibility of using them effectively. The article talks about possible ways of using the up-to-date technique of machine learning (Machine Learning Technology) in the calculation and experimental methods for determining the characteristics of the rocket and space technology.

Key words: numerical and analytical methods, stress-strain state, rocket structures, shell system, reinforcing load-bearing elements, local and general stability, machine learning technology

Bibliography:
1. Jean-Jacques Rousseau. URL: https://www.sdamesse.ru/2019/03/blog-post_14.html.
2. Akimov D. V., Gristchak V. Z., Gomenjuk S. I., Grebenyk S. N., Lisniak А. А., Choporov S. V., Larionov I. F., Klimenko D. V., Sirenko V. N. Matematicheskoe modelirovanie i issledovanie prochnosti silovykh elementov konstruktsij kosmicheskikh letatelnykh apparatov. Visn. Zaporiz’koho nats. un-tu. Fiz.-mat. nauky. 2015. № 3. S. 6–13.
3. Akimov D. V., Gristchak V. Z., Gomenjuk S. I., Larionov I. F., Klimenko D. V., Sirenko V. N. Finite-element analysis and experimental investigation on the strength of a three-layered honeycomb sandwich structure of spacecraft adapter module. Strength of Materials. 2016. № 3. P. 52–57. https://doi.org/10.1007/s11223-016-9775-y
4. Akimov D. V., Larionov I. F., Klimenko D. V., Gristchak V. Z., Gomenjuk S. I. Matematicheskoe modelirovanie i issledovanie napriazhenno-deformirovannogo sostoianiia otsekov raket kosmicheskogo naznacheniia. Kosmicheskaya tekhnika. Raketnoe vooruzhenie: sb. nauch.-tekhn. st. GP «KB «Yuzhnoye». Dnipro, 2019. Vyp. 1. S. 21–27. https://doi.org/10.33136/stma2019.01.021
5. Yarevskii Ye. А. Teoreticheskie osnovy metodov kompiuternogo modelirovaniia: ucheb.-metod. posobie. Sankt-Peterburg, 2010. 83 S.
6. Klovanich S. F. Metod konechnykh elementov v nelineinykh zadachakh inzhenernoi mekhaniki. Zaporozhie, 2009. 394 S.
7. Akimov D. V., Gristchak V. Z., Larionov I. F., Gomenjuk S. I., Klimenko D. V., Choporov S. V., Grebenyk S. N. Matematicheskoe obespechenie analiza prochnosti silovykh elementov raketno-kosmicheskoi techniki. Problemy obchysliuvalnoi mekhaniky i mitsnosti konstruktsii: zb. nayk. prats. 2017. Vyp. 26. S. 5–21.
8. Akimov D. V., Gristchak V. Z., Gomenjuk S. I., Larionov I. F., Klimenko D. V., Sirenko V. N. Eksperimentalnoe issledovanie deformirovannogo sostoianiia i prochnosti mezhstupenchatogo otseka raketonositelia pri staticheskom vneshnem nagruzhenii. Novi materialy i technolohii v metalurhii ta mashynobuduvanni. 2016. №1. S. 82–89.
9. Akimov D. V., Gristchak V. Z., Grebenyk S. N., Gomenjuk S. I. Sravnitelnyi analiz metodik rascheta napriazhenno-deformirovannogo sostoianiia elementov konstruktsii raketonositelia. Novi materialy i technolohii v metalurhii ta mashynobuduvanni. 2016. № 2. S. 116–120.
10. Gristchak V. Z., Gomeniuk S. I., Grebeniuk S. N., Larionov I. F., Degtiarenko P. G., Akimov D. V. An Investigation of a Spacecraft’s Propellant Tanks Shells Bearing Strength. Aviation in XXI-st Century. Safety in Aviation and Space Technologies: Proccedings the Sixth world congress. Kiev, 2014. Vol. 1. Р. 1.14.49–1.14.51.
11. Gristchak V. Z., Manievich А. I. Vliianiie zhestkosti shpangoutov na izgib iz ploskosti na ustoichivost podkreplennoi tsilindricheskoi obolochki. Gidroaeromechanika i teoriia uprugosti. 1972. Vyp. 14. S. 121–130.
12. Gristchak V. Z., Diachenko N. M. Opredelenie oblastei ustoichivosti konicheskoi obolochki pri kombinirovanom nagruzhenii na baze gibridnogo asimptoticheskogo podkhoda. Visn. Zaporiz’koho nats. un-tu. Fiz.-mat. nauky. 2017. №2. S. 32–46. URL: http:// nbuv.gov.ua/UJRN/Vznu_mat_2017_2_6.
13. Dehtiarenko P. H., Gristchak V. Z., Gristchak D. D., Diachenko N. M. K probleme ravnoustojchivosti podkreplenoi obolochechnoi konstruktsii pri kombinirovannom nagruzhenii. Kosmicheskaia nauka I technologiia. 2019. Т. 25, № 6(121). S. 3–14.
14. Kononiuk А. Е. Fundamentalnaia teoriia oblachnykh technologij: v 18 kn. Kyiv, 2018. Kn. 1. 620 s.
15. URL: http://datareview.info/article/vse-modeli-mashinnogo-obucheniya-imeyut-svoi-nedostatki
16. Choporova О. V., Choporov S. V., Lysniak А. О. Vykorystannia mashynnoho navchannia dlia prohnozuvannia napruzheno-deformovannoho stanu kvadratnoi plastyny. Matematychne modeliuvannia fizychnykh I tekhnolohichnykh system. Visnyk KhNTU. 2019. № 2(69). S. 192–201.
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11.1.2020  Some results of strength calculations relying on analytical and FEM approaches. Trends of using contemporary machine learning strategies
11.1.2020  Some results of strength calculations relying on analytical and FEM approaches. Trends of using contemporary machine learning strategies
11.1.2020  Some results of strength calculations relying on analytical and FEM approaches. Trends of using contemporary machine learning strategies

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5.1.2020 Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep https://journal.yuzhnoye.com/content_2020_1-en/annot_5_1_2020-en/ Wed, 13 Sep 2023 06:15:53 +0000 https://journal.yuzhnoye.com/?page_id=31026
Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep Authors: Hudramovych V. The article deals with various aspects of solving the problem of strength and stability of space rocket objects with consideration for the impact of plasticity and creeping deformations. Plastic and creep instability of shells with initial imperfections. (2020) "Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep" Космическая техника. "Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep" Космическая техника. quot;Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep", Космическая техника. Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep Автори: Hudramovych V.
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5. Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine1; The Institute of Technical Mechanics, Dnipro, Ukraine2; Oles Honchar Dnipro National University, Dnipro, Ukraine3

Page: Kosm. teh. Raket. vooruž. 2020, (1); 44-56

DOI: https://doi.org/10.33136/stma2020.01.044

Language: Russian

Annotation: The shell structures widely used in space rocket hardware feature, along with decided advantage in the form of optimal combination of mass and strength, inhomogeneities of different nature: structural (different thicknesses, availability of reinforcements, cuts-holes et al.) and technological (presence of defects arising in manufacturing process or during storage, transportation and unforseen thermomechanical effects). The above factors are concentrators of stress and strain state and can lead to early destruction of structural elements. Their different parts are deformed according to their program and are characterized by different levels of stress and strain state. Taking into consideration plasticity and creeping of material, to determine stress and strain state, the approach is effective where the calculation is divided into phases; in each phase the parameters are entered that characterize the deformations of plasticity and creeping: additional loads in the equations of equilibrium or in boundary conditions, additional deformations or variable parameters of elasticity (elasticity modulus and Poisson ratio). Then the schemes of successive approximations are constructed: in each phase, the problem of elasticity theory is solved with entering of the above parameters. The problems of determining the lifetime of space launch vehicles and launching facilities should be noted separately, as it is connected with damages that arise at alternating-sign thermomechanical loads of high intensity. The main approach in lifetime determination is one that is based on the theory of low-cycle and high-cycle fatigue. Plasticity and creeping of material are the fundamental factors in lifetime substantiation. The article deals with various aspects of solving the problem of strength and stability of space rocket objects with consideration for the impact of plasticity and creeping deformations.

Key words: shell structures, stress and strain state, structural and technological inhomogeneity, thermomechanical loads, low-cycle and high-cycle fatigue, lifetime

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29. Hudramovich V. S., Konovalenkov V. S. Deformirovanie i predelnoie sostoianie neuprugikh obolochek s uchetom istorii nagruzheniia. Izv. AN SSSR. Mekhanika tverdogo tela. 1987. №3. S. 157 – 163.
30. Нudramovich V. S. Plastic and creep instability of shells with initial imperfections. Solid mechanics and its applications / Ed. G. M. L. Gladwell V. 64. Dordrecht, Boston, London, 1997. P. 277–289. https://doi.org/10.1007/0-306-46937-5_23
31. Нudramovich V. S., Lebedev A. A., Mossakovsky V. I. Plastic deformation and limit states of metal shell structures with initial shape imperfections. Light-weight steel and aluminium structures: proceedings Int. Conf. (Helsinki, Finland, 1999) / Ed. P. Makelainen. Amsterdam, Lousanne, New York, Tokyo, 1999. P. 257–263. https://doi.org/10.1016/B978-008043014-0/50133-5
32. Kushnir R. M., Nikolyshyn М. М., Osadchuk V. А. Pruzhnyi ta pruzhnmoplastychnyi hranychnyi stan obolonok z defectamy. Lviv, 2003. 320 s.
33. Hudramovich V. S. Predelnyi analiz – effektivnyi sposob otsenki konstruktsionnoi prochnosti obolochechnykh system. III Mizhnar. konf. «Mekhanika ruinuvannia i mitsnist konstruktsii» (Lviv, 2003) / pid red. V. V. Panasiuka. Lviv, 2003. S.583–588.
34. Herasimov V. P., Hudramovich V. S., Larionov I. F. i dr. Plasticheskoe razrushenie sostavnykh obolochechnykh konstruktsii pri osevom szhatii. Probl. prochnosti. 1979. №11. S. 58 – 61.
35. Hudramovich V. S. Herasimov V. P., Demenkov A. F. Predelnyi analiz elementov konstruktsii / otv. red. V. S. Budnik. Kiev, 1990. 136 s.
36. Druker D. Makroskopicheskie osnovy teorii khrupkogo razrusheniia. Razrushenie. М., 1973. Т. 1. S. 505 – 569.
37. Galkin V. F., Hudramovich V. S., Mossakovsky V. I., Spiridonov I. N. O vliianii predela tekuchesti na ustoichivost tsilindricheskikh obolochek pri osevom szhatii. Izv. AN SSSR. Mekhanika tverdogo tela. 1973. №3. С 180 – 182.
38. Hudramovich V. S., Dziuba A. P., Selivanov Yu. М. Metody golograficheskoi interferometrii v mechanike neodnorodnykh tonkostennykh konstruktsii. Dnipro, 2017. 288 s.
39. Hudramovich V. S., Skalskii V. R., Selivanov Yu. М. Holohrafichne te akustyko-emisiine diahnostuvannia neodnoridnykh konstruktsii i materialiv / vidpovid. red. Z. Т. Nazarchuk. Lviv, 2017. 488 s.
40. Pisarenko G. S., Strizhalo V. А. Eksperimentalnye metody v mekhanike deformiruemogo tverdogo tela. Kiev, 2018. 242 s.
41. Guz’ A. N., Dyshel M. Sh., Kuliev G. G., Milovanova O. B. Razrushenie i lokalnaia poteria ustoichivosti tonkostennykh tel s vyrezami. Prikl. mekhanika. 1981. Т. 17, №8. S. 3 – 24. https://doi.org/10.1007/BF00884086
42. Hudramovich V. S., Diskovskii I. A., Makeev E. M. Tonkostennye element zerkalnykh antenn. Kiev, 1986. 152 s.
43. Hudramovich V. S., Hart E. L., Klimenko D. V., Ryabokon’ S. A. Mutual influence of openings on strength of shell-type structures under plastic deformation. Strength of Materials. 2013. V. 45, Iss. 1. P. 1 – 9. https://doi.org/10.1007/s11223-013-9426-5
44. Hudramovich V. S., Klimenko D. V., Hart E. L. Vliianie vyrezov na prochnost tsilindricheskikh otsekov raket-nositelei pri neuprugom deformirovanii materiala. Kosmichna nauka i tekhnolohiia. 2017. Т. 23, № 6. S. 12 – 20.
45. Hart E. L., Hudramovich V. S. Proektsiino-iteratsiini skhemy realizatsii variatsiino-sitkovykh metodiv u zadachakh pruzhno-plastychnoho deformuvannia neodnoridnykh tonkostinnykh konstruktsii. Matematychni metody I fizyko-mechanichni polia. 2019. Т. 51, № 3. S. 24 – 39.
46. Nikitin P. I., Hudramovich V. S., Larionov I. F. Ustoichivost obolochek v usloviiakh polzuchesti. Polzuchest v konstruktsiakh: tez. dokl. Vsesoiuzn. Simpoziuma (Dniepropetrovsk, 1982 g.). Dniepropetrovsk, 1982. S. 3 – 5.
47. Hudramovich V. S. Ob issledovaniiakh v oblasti teorii polzuchesti v Institute tekhnicheskoi mekhaniki NANU i GKAU. Tekhn. mekhanika. 2016. №4. S. 85 – 89.
48. Hoff N. J., Jahsman W. E., Nachbar W. A. A study of creep collapse of a long circular shells under uniform external pressure. J. Aerospace Sci. 1959. Vol. 26, No 10. P. 663 – 669. https://doi.org/10.2514/8.8243
49. Barmin I. V. Tekhnologicheskiie obiekty nazemnoi infrastruktury raketno-kosmicheskoi tekhniki. V 2-kh kn. M., 2005. Kn. 1. 412 s. М., 2005. Kn. 2. 376 s.
50. Makhutov N. А., Matvienko D. G., Romanov А. N. Problemy prochnosti, tekhnogennoi bezopasnosti i konstruktsionnogo materialovedenia. М., 2018. 720 s.
51. Gokhfeld D. А., Sadakov О. S. Plastichnost i polzuchest elementov konstruktsii pri povtornykg nagruzheniiakh. М., 1984. 256 s.
52. Troshchenko V. Т., Sosnovskii L. А. Soprotivlenie ustalosti metallov i splavov: spravochnik v 2-kh t. Kiev, 1987. Т. 1. 510 s. Kiev, 1987. Т. 2. 825 s.
53. Manson S. S. and Halford G. R. Fatigue and durability of structural materials. ASM International Material Park. Ohio, USA, 2006. 456 p.
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5.1.2020 Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep
5.1.2020 Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep
5.1.2020 Strength and stability of inhomogeneous structures of space technology, consid-ering plasticity and creep

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23.2.2018 On the Role of Space in Origination of Inertia Force Field, Earth Gravity Force Field and Zero Gravity of Material Body https://journal.yuzhnoye.com/content_2018_2-en/annot_23_2_2018-en/ Thu, 07 Sep 2023 12:35:25 +0000 https://journal.yuzhnoye.com/?page_id=30813
On Stability of Compressed Rod. On the Impact of Initial Imperfections on Rod Stability Loss in Conditions of Axial Compression.
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23. On the Role of Space in Origination of Inertia Force Field, Earth Gravity Force Field and Zero Gravity of Material Body

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2018 (2); 190-206

DOI: https://doi.org/10.33136/stma2018.02.190

Language: Russian

Annotation: Presented is the theoretical justification of the phenomenon of the inertia initiation under accelerated motion of the body, and gravity origin in the circumterrestrial space. There is no description of the physical nature of the inertia and gravity in the scientific publications. In the phenomenological approach under study, allowing for reflection properties of the space, earlier unknown interdependent information-physical link of the body and its mechanical particles with space under the accelerated motion was determined in the state of rest of the gravitation field as well as in the state of weightlessness. Alongside with the environment, eigenspace, i.e. configuration space of the body and corresponding metric lines of the space are considered. Idea of metric lines agrees with the concept of F. Wilczek, the American physicist, Nobel-Prize laureate, on the existence of the unobservable metric field in the real space. Solution of the problem rests on the example of the cantilever beam and mathematical model of the information reflection process, which for the first time takes into consideration previously unknown property of space reflection. Under the accelerated motion of the body reflection gains the acceleration vector dt d а     . In this case reflection manifests itself in the initiation of the beam of polarization vector under study   ~ in every point of the configuration space and is expressed as     ~ а . Value of the polarization vector equals the value of acceleration vector with negative sign. As a result metric lines of the configuration space under conditions of beam acceleration become polarized lines, generating vector information inertia field. Interaction of mechanical particles with the information inertia field in the configuration space generates physical inertia field of force, providing the real inertia under accelerated motion of the beam. (Relatively slow motion of bodies is studied as compared to the speed of light). According to the set forth unconventional approach the nature of the earth gravity is conditioned by the polarization of the radial metric lines of the circumterrestrial space. And polarization vector is directed to the center of the Earth and equals acceleration vector of the free fall with the same sign. Interaction of the body with specific mass with the vector information field of the Earth generates the physical force field of gravity. Article deals with the fundamental issues of theoretical physics and other fields of natural science. Materials of the conducted research are regarded as a potential scientific discovery.

Key words: configuration space, modified method of sections, information and vacuum environment, metric lines, property of space reflection, polarization, scalar information field, vector information field

Bibliography:
1. Vilchek F. Fine Physics. Mass, Ester and Unification of World Forces. Collection of publications, 2018. 336 p.
2. Sivukhin D. V. General Course of Physics. Vol. 1. М., 1989. 576 p.
3. Logunov А. А. Lectures on Relativity Theory and Gravitation. Modern Analysis of Problem. М., 1987. 272 p.
4. Feinman R., Layton R., Sands M. Feinman Lectures in Physics. Vol. 1. Modern Natural Science. The Laws of Mechanics. Vol. 2. Space. Time. Motion / Translation from English. М., 1976. 439 p.
5. Mulyar Y. M. On Stability of Compressed Rod. Technical mechanics. Dnepropetrovsk, 2000. No. 2. P. 51-57.
6. Mulyar Y. M., Perlik V. I. On Mathematical Model Representation of Information Field in Loaded Deformed System. Information and Telecommunication Technologies. М., 2012. No. 15. P. 61-74.
7. Vernadsky V. I. Reflections of Natural Scientist. Space and Time in Inanimate and Animate Nature. М., 1975. 173 p.
8. Ursul A. D. Reflection and Information. М., 1973. 231 p.
9. Vladimirov Y. S. Metaphysics. М., 2002. 550 p.
10. Author’s Certificate 181066 USSR. Energy Absorber / А. М. Buyanovsky, Y. М. Mulyar. Discoveries. Inventions. 1993. No. 15. P. 101.
11. Cacku M. Physics of Impossible / Translation from English. М., 2016. 456 p.
12. Proceedings of the International Scientific Conference “Problems of Ideality in Science”. М., 2001. 352 p.
13. Mulyar Y. M., Fyodorov V. M., Tryasuchev L. M. On the Impact of Initial Imperfections on Rod Stability Loss in Conditions of Axial Compression. Space Technology. Missile Armaments: Collection of scientific-technical articles. 2017. Issue 1 (113). P. 48-58.
14. Dyomin A.I. Paradigm of Dualism. Space – Time, information – energy. М., 2007. 320 p.
15. Lisin A.I. Paradigm of Dualism. Ide: Reality of ideality. Part 1. М., 1999. 382 p.
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23.2.2018 On the Role of Space in Origination of Inertia Force Field, Earth Gravity Force Field and Zero Gravity of Material Body
23.2.2018 On the Role of Space in Origination of Inertia Force Field, Earth Gravity Force Field and Zero Gravity of Material Body
23.2.2018 On the Role of Space in Origination of Inertia Force Field, Earth Gravity Force Field and Zero Gravity of Material Body

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18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis https://journal.yuzhnoye.com/content_2018_2-en/annot_18_2_2018-en/ Thu, 07 Sep 2023 12:20:49 +0000 https://journal.yuzhnoye.com/?page_id=30799
Spinning significantly increases stability of a moving object and partially evens out the negative impact of external and internal disturbing factors (skewness and eccentricities of propulsion system and control elements, wind).
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18. Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2018 (2); 151-156

DOI: https://doi.org/10.33136/stma2018.02.151

Language: Russian

Annotation: Contemporary trends in developing space-rocket hardware indicate the increased demand for light and ultra-light rockets. The first trend in developing the up-to-date light and ultra-light rocket hardware includes improving accuracy of cargo delivery to the specified area; the second trend covers the enhancement of energetic properties and the reduction of production and operational costs. Spinning about the longitudinal axis of symmetry may be one of the ways to improve the light and ultra-light rocket hardware in these trends. Spinning significantly increases stability of a moving object and partially evens out the negative impact of external and internal disturbing factors (skewness and eccentricities of propulsion system and control elements, wind). Refusal to use systems that provide stabilization about the longitudinal axis of symmetry leads to reduction in mass of the control system equipment, thus increasing energetic perfection of the rocket hardware. Hence, rotation of the rocket about the longitudinal axis may be caused by the spinning elements on purpose as well as by disturbing impacts in case of control failure in the roll channel. This article considers suggestions on algorithmic realization of light rocket control methods under conditions of rapid rotation about the longitudinal axis for each of the options mentioned above. This article offers control methods for the rocket, rotating about the longitudinal axis, that provide angular stabilization, improve the transient quality, and determine the angle of roll after program stop of rotation about the longitudinal axis.

Key words: angular stabilization, spinning, rotation about the longitudinal axis of symmetry, light rocket, drive delay, determination of the angle of roll, aerodynamic control surfaces, algorithm for maneuver determination of the angle of roll

Bibliography:
1. Shunkov V. N. Encyclopedia of Rocket Artillery / Under the general editorship of A. E. Taras. Minsk, 2004. 544 p.
2. Igdalov I. M. et al. Rocket as Control Object: Tutorial / Under the editorship of S. N. Konyukhov. Dnepropetrovsk, 2004. 544 p.
3. Pugachyov V. S. et al. Rocket Control Systems and Flight Dynamics. М., 1965. 610 p.
4. Sikharulidze Y. G. Flying Vehicles Dynamics. М., 1982. 352 p.
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18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis
18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis
18.2.2018 Angular Stabilization of an Object Rapidly Rotating around Longitudial Axis

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7.2.2018 Theoretical Models of Sound Speed Increase Effects in Gas Duct with Corrugated Wall https://journal.yuzhnoye.com/content_2018_2-en/annot_7_2_2018-en/ Thu, 07 Sep 2023 11:12:23 +0000 https://journal.yuzhnoye.com/?page_id=30754
The spiral shape of the corrugation ensures also axial rotation, which increases vortexes stability.
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7. Theoretical Models of Sound Speed Increase Effects in Gas Duct with Corrugated Wall

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine1; National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine2

Page: Kosm. teh. Raket. vooruž. 2018 (2); 57-67

DOI: https://doi.org/10.33136/stma2018.02.057

Language: Russian

Annotation: During experimental investigation of the dynamic characteristics of a pneumatic test bench for testing liquid rocket engine high-flowrate automatic units, the effect was detected of 20-35% sound speed increase in the gas flow moving along the channel with corrugated wall (metal hose) which is a part of test bench drain system. The article presents the results of experiments and the task of theoretical justification of the effect is solved. It is indicated that its causes may be two mutually complementary factors – a decrease of gas compressibility at eddy motion and oscillations of metal hose wall. The physical model is considered that describes variation of gas elasticity and density in the conditions of high flow vorticity. It is supposed that in the near-wall layer of the channel, toroidal vortexes (vortex rings) are formed, which move into turbulent core of the flow where their size decreases and the velocity of rotation around the ring axis of torus increases. The spiral shape of the corrugation ensures also axial rotation, which increases vortexes stability. The intensive rotation around the ring axis creates considerable centrifugal forces; as a result, the dependence of pressure on gas density and the sound speed increase. The mathematical model has been developed that describes coupled longitudinal-lateral oscillations of gas and channel’s corrugated shell. It is indicated that in the investigated system, two mutually influencing wave types are present – longitudinal, which mainly transfer gas pressure pulses along the channel and lateral ones, which transfer the shell radial deformation pulses. As a result of modeling, it has been ascertained that because of the lateral oscillations of the wall, the propagation rate of gas pressure longitudinal waves (having the same wave length as in the experiments at test bench) turns out to be higher than adiabatic sound speed.

Key words: rocket engine automatic units, pneumatic test bench, metal hose, corrugated shell, toroidal vortex, longitudinal-lateral oscillations

Bibliography:
1. Shevchenko S. A. Experimental Investigation of Dynamic Characteristics of Gas Pressure Regulator in Multiple Ignition LRE Starting System. Problems of Designing and Manufacturing Flying Vehicle Structures: Collection of scientific works. 2015. Issue 4 (84). P. 49-68.
2. Shevchenko S. A., Valivakhin S. A. Results of Mathematical Modeling of Transient Processes in Gas Pressure Regulator. NTU “KhPI” News. 2014. No. 39 (1082). P. 198-206.
3. Shevchenko S. A., Valivakhin S. A. Mathematical Model of Gas Pressure Regulator. NTU “KhPI” News. 2014. No. 38 (1061). P. 195-209.
4. Shevchenko S. A., Konokh V. I., Makoter A. P. Gas Dynamic Resistance and Sound Speed in Channel with Corrugated Wall. NTU “KhPI” News. 2016. No. 20 (1192). P. 94-101.
5. Flexible Metal Hoses. Catalogue. Ufimsky Aggregate Company “Hydraulics”, 2001.
6. Loytsyansky L.G. Liquid and Gas Mechanics. М., 1978. 736 p.
7. Prisnyakov V. F. et al. Determination of Gas Parameters at Vessel Emptying Taking into Account Compressibility and Manifold Resistance. Problems of High-Temperature Engineering: Collection of scientific works. 1981. P. 86-94.
8. Kirillin V. A., Sychyov V. V., Sheydlin A. E. Technical Thermodynamics. М., 2008. 486 p.
9. Grekhov L. V., Ivashchenko N. A., Markov V. A. Propellant Equipment and Control Systems of Diesels. М., 2004. 344 p.
10. Sychyov V. V., Vasserman A. A., Kozlov A. D. et al. Thermodynamic Properties of Air. М., 1978. 276 p.
11. Shariff K., Leonard A. Vortex rings. Annu. Rev. Fluid Mech. 1992. Vol. 24. P. 235-279. https://doi.org/10.1146/annurev.fl.24.010192.001315
12. Saffman F. Vortex Dynamics. М., 2000. 376 p.
13. Akhmetov D. G. Formation and Basic Parameters of Vortex Rings. Applied Mechanics and Theoretical Physics. 2001. Vol. 42, No 5. P. 70–83.
14. Shevchenko S. A., Grigor’yev A. L., Stepanov M. S. Refinement of Invariant Method for Calculation of Gas Dynamic Parameters in Rocket Engine Starting Pneumatic System Pipelines. NTU “KhPI” News. 2015. No. 6 (1115). P. 156-181.
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7.2.2018 Theoretical Models of Sound Speed Increase Effects in Gas Duct with Corrugated Wall
7.2.2018 Theoretical Models of Sound Speed Increase Effects in Gas Duct with Corrugated Wall
7.2.2018 Theoretical Models of Sound Speed Increase Effects in Gas Duct with Corrugated Wall

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5.2.2018 Electromagnetic Valves Developed by Yuzhnoye SDO Liquid Rocket Engines Design Office https://journal.yuzhnoye.com/content_2018_2-en/annot_5_2_2018-en/ Thu, 07 Sep 2023 11:01:49 +0000 https://journal.yuzhnoye.com/?page_id=30749
Increase of Action Stability of Electric Pneumatic Valve with Boost in the System with Increased Inlet Hydraulic Resistance.
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5. Electromagnetic Valves Developed by Yuzhnoye SDO Liquid Rocket Engines Design Office

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2018 (2); 34-48

DOI: https://doi.org/10.33136/stma2018.02.034

Language: Russian

Annotation: In the pneumohydraulic systems of liquid rocket engines and propulsion systems, electromagnetic valves that allow making the pneumohydraulic systems more simple and ensuring multiple ignition of liquid rocket engines have found wide application. The Yuzhnoye-developed electromagnetic valves are designed according to two schemes – of direct and indirect action. In the direct-action electromagnetic valves, the shutting-off device opens (closes) the throat with the force developed by electric magnet. They have gained acceptance in the pneumohydraulic systems with the working medium pressure of ~8.5 MPa, they are of simple design and have high operating speed (0.001…0.05 s). In the electromagnetic valves with amplification, the electromagnet armature is connected with control valve and the main shutting-off device moves due to the force from working medium pressure drop on it. They are used in the operating pressure range of 0.5…56 MPa, at that, the action time is 0.025…0.15 s. For the European Vega launch vehicle fourth stage main engine assembly that has pressure propellant feeding system, the electrohydraulic valve with amplification and drainage was developed. The dependence of this electrohydraulic valve high speed from the line’s output length is decreased to the maximum due to the installation of Venturi nozzle at the output connecting branch. This electrohydraulic valve is operable at the pressure below 8 MPa, the action time is 0.08…0.12 s. The present-day spacecraft gas-jet orientation and stabilization systems use as propulsion devices the electromagnetic valves with nozzles whose thrust is, as a rule, not more than 30 N and the working medium pressure is up to 24 MPa. Yuzhnoye State Design Office developed for 15B36 gas-jet system the electropneumatic valve with amplification and nozzle, which is operable at the pressure below 45 MPa, ensures the action frequency of up to 10 Hz and is capable of creating the thrust of 100 N on gaseous argon. To solve the task of decreasing the dependence of operability and high speed of electromagnetic valves with drainage and amplification on geometry of lines in which a valve is installed, the electropneumatic valve was developed that has spool elements ensuring reliable and quick action with long input lines of 0.004 m diameter. Its mass is 2…2.5 times lower than the mass of analogs. Recently, Yuzhnoye State Design Office develops the apogee RD840 LRE with 400 N thrust, for the conditions of which the direct-action electrohydraulic valve was developed and tested with the following characteristics: pressure – up to 2.15 MPa, consumed power in operation mode – less than 7.1 W, action time – not more than 0.02 s, mass – 0.19 kg. The presented electromagnetic valves by their technical and operational characteristics meet the highest world requirements and have found wide utility in liquid rocket engines and propulsion systems.

Key words: electrohydraulic valve, electropneumatic valve, pneumohydraulic system, direct-action electric valve, electric valve with amplification, action time

Bibliography:
1. Electric Hydraulic Valve: Patent 89948 Ukraine: MPK F 16K 32/02 / Shnyakin V. M., Konokh V. I., Kotrekhov B. I., Troyak A. B., Boiko V. S.; Applicant and patent holder Yuzhnoye State Design Office. а 2006 02543; claimed 09.03.2006; published 25.03.2010, Bulletin No. 6.
2. Boiko V. S., Konokh V. I. Stabilization of Opening Time of Electric Hydraulic Valve with Boost in Liquid Rocket Engine Hydraulic System. Problems of Designing and Manufacturing Flying Vehicle Structures: Collection of scientific works. 2015. Issue 4 (84). P. 39-48.
3. Electric Valve: Patent 97841, Ukraine: MPK F 16K 32/02 / Shnyakin V. M., Konokh V. I., Kotrekhov B. I., Troyak A. B., Boiko V. S., Ivashura A. V.; Applicant and patent holder Yuzhnoye State Design Office. а 2009 12002; claimed 23.11.2009; published 26.03.2012, Bulletin No. 6.
4. Boiko V. S., Konokh V. I. Increase of Action Stability of Electric Pneumatic Valve with Boost in the System with Increased Inlet Hydraulic Resistance. Aerospace Engineering and Technology: Scientific-Technical Journal. 2013. Issue 3 (100). P. 90-95.
5. Flying Vehicles Pneumatic Systems Units / Lyaskovsky I. F., Shishkov A. I., Romanenko N. T., Romanenko M. T., Chernov M. T., Yemel’yanov V. V. / Under the editorship of N. T. Romanenko. М., 1976. 176 p.
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5.2.2018 Electromagnetic Valves Developed by Yuzhnoye SDO Liquid Rocket Engines Design Office
5.2.2018 Electromagnetic Valves Developed by Yuzhnoye SDO Liquid Rocket Engines Design Office
5.2.2018 Electromagnetic Valves Developed by Yuzhnoye SDO Liquid Rocket Engines Design Office

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8.1.2017 Initial Imperfection Effect on Loss of Rod Stability under Axial Compression Conditions https://journal.yuzhnoye.com/content_2017_1/annot_8_1_2017-en/ Tue, 27 Jun 2023 12:02:02 +0000 https://journal.yuzhnoye.com/?page_id=29430
Initial Imperfection Effect on Loss of Rod Stability under Axial Compression Conditions Authors: Muliar Yu. 2017 (1); 48-58 Language: Russian Annotation: The experimental and theoretical justification is presented for the phenomenon of sudden buckling with dynamic effect at stability loss of a rectilinear rod with real existing imperfections. The interdependent connection is established between the initial imperfections and buckling intensity in the effect of zero rigidity of an utmost compressed rod at stability loss in the large. Nonconservative Problems of Elastic Stability Theory. Investigation of Minor Disturbing Actions on Shell Stability. Synergetics: Instability Hierarchies in Self-Organizing Systems and Devices / Translation from English. Stability of Deformed Systems. Investigation of Local Raising of Shell Structures at Stability Loss of their Bays. Longitudinal Bending and Stability.
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8. Initial Imperfection Effect on Loss of Rod Stability under Axial Compression Conditions

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2017 (1); 48-58

Language: Russian

Annotation: The experimental and theoretical justification is presented for the phenomenon of sudden buckling with dynamic effect at stability loss of a rectilinear rod with real existing imperfections. The interdependent connection is established between the initial imperfections and buckling intensity in the effect of zero rigidity of an utmost compressed rod at stability loss in the large.

Key words:

Bibliography:
1. Feodos’yev V. I. Selected Tasks and Problems of Materials Strength. М., 1973. 400 p.
2. Trusdell K. Primary Course of Rational Mechanics of Continuous Media / Translation from English. М., 1975. 522 p.
3. Bolotin V. V. Nonconservative Problems of Elastic Stability Theory. М., 1961. 339 p.
4. Rabotnov Y. N. Mechanics of Deformed Solid Body. М., 1979. 744 p.
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8.1.2017 Initial Imperfection Effect on Loss of Rod Stability under Axial Compression Conditions
8.1.2017 Initial Imperfection Effect on Loss of Rod Stability under Axial Compression Conditions
8.1.2017 Initial Imperfection Effect on Loss of Rod Stability under Axial Compression Conditions
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2.1.2017 Ultimate Stability Stresses in Smooth Cylindrical Skins. Dynamic Problem https://journal.yuzhnoye.com/content_2017_1/annot_2_1_2017-en/ Tue, 27 Jun 2023 11:52:29 +0000 https://journal.yuzhnoye.com/?page_id=29361
Ultimate Stability Stresses in Smooth Cylindrical Skins. 2017 (1); 8-17 Language: Russian Annotation: This work deals with the problem of cylindrical shell stability within Donnel-Vlasov linear theory based on updated equilibrium equations and dynamic approach to their solution. Stability of Elastic Systems. Nonconservative Problems of Elastic Stability Theory. Stability of Rods, Plates and Shells. (2017) "Ultimate Stability Stresses in Smooth Cylindrical Skins. "Ultimate Stability Stresses in Smooth Cylindrical Skins. quot;Ultimate Stability Stresses in Smooth Cylindrical Skins. Ultimate Stability Stresses in Smooth Cylindrical Skins. Ultimate Stability Stresses in Smooth Cylindrical Skins. Ultimate Stability Stresses in Smooth Cylindrical Skins. Ultimate Stability Stresses in Smooth Cylindrical Skins.
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2. Ultimate Stability Stresses in Smooth Cylindrical Skins. Dynamic Problem

Organization:

Yangel Yuzhnoye State Design Office, Dnipro, Ukraine

Page: Kosm. teh. Raket. vooruž. 2017 (1); 8-17

Language: Russian

Annotation: This work deals with the problem of cylindrical shell stability within Donnel-Vlasov linear theory based on updated equilibrium equations and dynamic approach to their solution. The new theoretical results of critical stress determination that are well agreed with experimental data are presented here. The plot of critical stress as a function of dynamic behavior of specific shell is shown here. The wave generation parameters for the moment of equilibrium loss for each specific case are also presented in this work.

Key words:

Bibliography:
1. Volmir A. S. Stability of Elastic Systems. М., 1963. P. 463-471, 491-495.
2. Bolotin V. V. Nonconservative Problems of Elastic Stability Theory. М., 1961. P. 335.
3. Gladky V. F. Flying Vehicle Structural Dynamics. М., 1969. P. 129-134.
4. Kiselyov V. A. Structural Mechanics. М., 1969. P. 35-40.
5. Kaplya P. G., Pinyagin V. D. On Dynamics of Stiffened Cylindrical Shells. Space Technology. Missile Armaments: Collection of scientific-technical articles. 2009. Issue 2. P. 59–73.
6. Rabotnov Y. N. Strength of Materials. М., 1967. P. 88-89.
7. Timoshenko S. P. Stability of Rods, Plates and Shells. М., 1971. P. 257-259, 457-472.
8. Galaka P. I. Investigation of Impact of Axial Compressive Forces on Oscillation Frequencies and Modes of Ribbed Cylindrical Shells / P. I. Galaka, V. A. Zarutsky, P. G. Kaplya, V. I. Matsner, A. M. Nosachenko. Kyiv, 1975. Vol. XI, Issue 8. P. 41–48.
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2.1.2017 Ultimate Stability Stresses in Smooth Cylindrical Skins. Dynamic Problem
2.1.2017 Ultimate Stability Stresses in Smooth Cylindrical Skins. Dynamic Problem
2.1.2017 Ultimate Stability Stresses in Smooth Cylindrical Skins. Dynamic Problem
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