539.3

hydroelasticity, gas cavity, spherical wave, elastic spherical shell, interaction of environments, liquid separation, shell surface movement.

Investigations of the dynamics of the system consisting of elastic spherical shell filled with ideal compressible fluid and gas cavity in the center of the system are presented in this paper. The excitation pulse-modulated source is introduced into the gas cavity in the center of the system. The effect of the shell thickness on its dynamics and the stress-state during the pulsations is investigated. The results for radial displacements changes of the middle surface, the thickness of the fluid separation from the shell, the stress intensity in the shell during its free pulsations are obtained. The comparison of calculations for the separation thickness in cases of free and partially fixed shell is carried out.

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11. Fazelzadeh S. Ahmad, Esmaeal Ghavanloo Coupled axisymmetric vibration of nonlocal fluid-filled closed spherical membrane shell. Acta MechanicaSeptember. 2012. Vol. 223. Issue 9, pp 2011–2020.
12. Mingsion R. B., Kuorung W. Free vibration of a thin spherical shell containing a compressible fluid.J. Acoust. Soc. Amer. 1994. Vol. 95. No. 6. P. 3300–3310.
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17. Xi L., Cen Z., Chen J. A Second-order Finite Difference Scheme for a Type of Black-Scholes Equation. Journal of Nonlinear Sciencs. 2008. Vol. 6. No. 3. P. 238–245.
18. Sheptylevskyi A. V., Kosenkov V. M. Pulsatsyy sferycheskoi obolochky s zhydkostiu pry vvode эnerhyy v tsentre. Prykladnaia hydromekhanyka. 2014. No. 1. 16 (88). P. 70–77.
19. Sheptylevskyi A. V, Selezov Y. T., Kosenkov V. M. Dynamycheskoe kontaktnoe vzaymodeistvye upruhoi sferycheskoi obolochky y zapolniaiushchei eё zhydkosty s uchёtom kavytatsyy. Prykladnaia hydromekhanyka. 2013. No. 2. 15 (87). P. 73–84.

1.   Yasniy P. V., Pyndus Y. I., Hud M. I. Analiz chastot s form vlasnyh kolyvan pydsylenyh cylyndrychnyh. Vysnyk ТNТU. Т.: ТNТU, 2016. Тоm 83. No. 3. P. 7–15.
2.   Yasniy P., Pyndus Y., Hud M. Methodology for the experimental research of reinforced cylindrical shell forced oscillations. Vysnyk ТNТU. Т.: ТNТU, 2017. Тоm 86. No. 2. P. 7–13.
3.   Mikulich O., Shvabjuk V. Investigation of the shock waves impact on the dynamic stress state of medium with the system of tunnel cavities. Vysnyk ТNТU. Т.: ТNТU, 2017. Тоm 87. 3. P. 7–15.
4.   Sheptilevskiy А. V., Коsenkov V. М., Selezov I. T. Three-dimensional model of a hydroelastic system bounded by a spherical shell. Journal of Mathematical Sciences. Vol. 190. No. 6. 2013.
5.   Krakovskaia E. V. O prylozhenyy teoryy obolochek k nekotorыm zadacham oftalmolohyy. Rossyiskyi zhurnal byomekhanyky. 2006. No. 1, pp. 52–58.
6.   Typiasev A. S. O deformatsyy sferycheskoi obolochky, zapolnennoi neszhymaemoi zhydkostiu, pry vozdeistvyy kruhovoho rastiazhenyia po эkvatoru. Rossyiskyi zhurnal byomekhanyky. 2008, tom 12, no. 2 (40), pp. 60–65.
7.   Charalambopoulos A., Dassios G., Fotiadis D. I., Massalas C. V. Dynamic characteristics of the human skull-brain system. Mathematical and computer modelling. 27 (2). P. 81–101.
8.   Kuropatenko V. F., Andreev Yu. N. O modelyrovanyy dynamycheskykh protsessov v sferycheskykh y tsylyndrycheskykh obolochkakh. Vichyslytelnaia mekhanyka sploshnykh sred. 2010. T. 3. No. 4.
P. 53–67.
9.   Advani S. H., Lee Y. C. Free vibrations of fluid-filled spherical shells. J. Sound and Vibr. 1970. 12. No. 4. P. 453–462.
10. Ali E. Vibrations of fluid-filled spherical shells. J. Acoust. Soc. Amer. 1969. Vol. 46. No. 1. Pt. 2. P. 186–190.
11. Fazelzadeh S. Ahmad, Esmaeal Ghavanloo Coupled axisymmetric vibration of nonlocal fluid-filled closed spherical membrane shell. Acta MechanicaSeptember. 2012. Vol. 223. Issue 9, pp 2011–2020.
12. Mingsion R. B., Kuorung W. Free vibration of a thin spherical shell containing a compressible fluid.J. Acoust. Soc. Amer. 1994. Vol. 95. No. 6. P. 3300–3310.
13. Shah S. A., Tajuddin M. On axially symmetric vibration of fluid filled poroelastic spherical shells. Open Journal of Acoustics. 2011. 1. P. 15‑26.
14. Naugolnih K. A., Roy N. A. Elektrycheskye razryadi v vode. M.: Nauka, 1977. 151 p.
15. Prasad C. On vibrations of spherical shells. J. Acoust. Soc. Amer. 1964. 36. No. 3. P. 489–494.
16. Sheptylevskyi A. V., Selezov Y. T., Kosenkov V. M. Chyslennoe modelyrovanye nelyneinoi dynamyky gazovoi sferycheskoi polosty pry ee nachalnykh pulsatsyiakh v zhydkosty. Prykladnaia hydromekhanyka. 2015. No. 2. 17 (89). P. 70–77.
17. Xi L., Cen Z., Chen J. A Second-order Finite Difference Scheme for a Type of Black-Scholes Equation. Journal of Nonlinear Sciencs. 2008. Vol. 6. No. 3. P. 238–245.
18. Sheptylevskyi A. V., Kosenkov V. M. Pulsatsyy sferycheskoi obolochky s zhydkostiu pry vvode эnerhyy v tsentre. Prykladnaia hydromekhanyka. 2014. No. 1. 16 (88). P. 70–77.
19. Sheptylevskyi A. V, Selezov Y. T., Kosenkov V. M. Dynamycheskoe kontaktnoe vzaymodeistvye upruhoi sferycheskoi obolochky y zapolniaiushchei eё zhydkosty s uchёtom kavytatsyy. Prykladnaia hydromekhanyka. 2013. No. 2. 15 (87). P. 73–84.