Longitudinal-radial vibrations of a elastic cylindrical shell filled with a viscous compressible liquid

Kh. Kh. Khudoynazarov   ; R. I. Khalmuradov   ; B. F. Yalgashev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 69 (2021), pp. 139-154

Résumé

In this paper, the longitudinal-radial vibrations of the elastic cylindrical shell filled with a viscous compressible fluid are studied using the mathematical model proposed. The general equations for the longitudinal-radial vibrations of the shell made of the homogeneous and isotropic material are derived. These equations can be used to obtain refined equations of vibrations. The proposed algorithm allows one to uniquely determine the stress-strain state of points in any section of the considered hydroelastic system using the field of the required functions in coordinates and time. The benchmark problem of harmonic oscillations in a cylindrical shell with a viscous fluid is solved. The dependences of the frequency on the wave number are obtained for various shell- fluid interaction cases.

Détail

Keywords: cylindrical shell, refined equations, stresses, displacements.
Mots-clés : viscous fluid, vibrations

Bibliographie

[1] Vlasov V. Z., Obschaya teoriya obolochek, GITTL, M.–L., 1949, 784 pp. | MR

[2] Novozhilov V. V., Finkelshtein R. M., “O pogreshnosti gipotez Kirkhgofa v teorii obolochek”, PMM, 7:5 (1943), 331–340

[3] Mushtari Kh. M., “Ob oblasti primenimosti priblizhennoi teoriya obolochek Kirkhgoffa–Lyava”, PMM, 11:5 (1947), 517–520 | Zbl

[4] Darevskii V. M., “Ob osnovnykh sootnosheniyakh teorii tonkikh obolochek”, PMM, 25:3 (1961), 519–535 | MR | Zbl

[5] Nigul U. K., “Asimptoticheskaya teoriya statiki i dinamiki uprugikh krugovykh tsilindricheskikh obolochek i analiz tochnosti razlichnykh variantov v teorii Kirkhgofa - Lyava”, Teoriya plastin i obolochek, Erevan, 1964, 738–742

[6] Grigolyuk E. I., Selezov I. T., “Neklassicheskie teorii kolebanii sterzhnei, plastin i obolochek”, Itogi nauki i tekhniki. Ser. Mekhanika tverd. deformir. tel, 5, VINITI, M., 1973, 272 pp. | Zbl

[7] Ambartsumyan S. A., “K voprosu postroeniya priblizhennykh teorii rascheta pologikh tsilindricheskikh obolochek”, PmM, 18:3 (1954), 303–312 | MR | Zbl

[8] Yi-Yuan Yu, “Vibrations of cylindrical shells analyzed by means of Donnell-type equations”, Aero/Space Sci, 11 (1958), 699–715 | MR

[9] Nigul U. K., “Lineinye uravneniya dinamiki uprugoi krugovoi tsilindricheskoi obolochki, svobodnye ot gipotez”, Tr. Tallinsk. politekhn. in-ta. Seriya A, 1960, no. 7, 67–76

[10] Petrashen G. I., “Problemy inzhenernoi teorii kolebanii vyrozhdennykh sistem”, Issledovaniya po uprugosti i plastichnosti, 5, Izd-vo LGU, L., 1966, 3–33

[11] Herrmann G., Mirsky I., “Three-dimensional and shell theory analysis of axially symmetric motions of cylinders”, J. Appl. Mech., 23:4 (1956), 563–568 | DOI | MR | Zbl

[12] Khudoinazarov Kh. Kh., Yalgashev B. F., “Osesimmetrichnye kolebaniya vyazkouprugogo tsilindricheskogo sloya, zapolnennogo vyazkoi szhimaemoi zhidkostyu”, Problemy arkhitektury i stroitelstva, 2016, no. 1, 119–125

[13] Filippov I. G., Kudainazarov K., “General transverse vibrations equations for a circular cylindrical viscoelastic shell”, Soviet Applied Mechanics, 26:4 (1990), 351–357 | DOI | Zbl

[14] Khudoynazarov Kh., Khudoyberdiyev Z. B., “Unsteady vibrations of a three-layer plate with an asymmetric structure”, IOP Conf. Ser.: Earth Environ. Sci, 614 (2020), 012061 | DOI

[15] Khudoinazarov Kh. Kh., Abdirashidov A., Burkutboev Sh. M., “Modelirovanie krutilnykh kolebanii vyazkouprugogo kruglogo sterzhnya, vraschayuschegosya s postoyannoi uglovoi skorostyu”, Matematicheskoe modelirovanie i chislennye metody, 2016, no. 1 (9), 38–51

[16] Khudoynazarov Kh., Yaxshiboyev Sh.R., “The mathematical model of transverse vibrations of the three-layer plate”, IOP Conf. Ser.: Earth Environ. Sci, 614 (2020), 012062 | DOI

[17] Khudoinazarov Kh. Kh., Burkutboev Sh. M., “Matematicheskaya model krutilnykh kolebanii tsilindricheskogo sloya s uchetom protekayuschei zhidkosti i vrascheniya”, Matematicheskoe modelirovanie i chislennye metody, 2017, no. 4, 38–56

[18] Netrebko A. V., Pshenichnov S. G., “Nekotorye zadachi dinamiki lineino-vyazkouprugikh tsilindricheskikh obolochek konechnoi dliny”, Problemy prochnosti i plastichnosti, 77:1 (2015)

[19] Khalmuradov R. I., Yalgashev B. F., “Frequency analysis of longitudinal-radial vibrations of a cylindrical shell”, IOP Conf. Ser.: Earth Environ. Sci, 614 (2020), 012087 | DOI

[20] Bespalova E. I., Boreiko N. P., “Opredelenie sobstvennykh chastot sostavnykh anizotropnykh obolochechnykh sistem s ispolzovaniem razlichnykh modelei deformatsii”, Int. Appl. Mech., 55 (2019), 41–54 | DOI

[21] Kubenko V. D., “Opredelenie dinamicheskikh kharakteristik vyazkoi zhidkosti v tsilindricheskoi polosti pod deistviem sfericheskogo izluchatelya”, Int. Appl. Mech., 55 (2019), 296–304 | DOI

[22] Akulenko L. D., Gavrikov A. A., Nesterov S. V., “Sobstvennye kolebaniya truboprovoda na uprugom osnovanii, transportiruyuschego zhidkost”, Izv. RAN. MTT, 2018, no. 1, 123–133

[23] Khudayarov B. A., Komilova Kh. M., “Chislennoe modelirovanie kolebanii vyazkouprugikh truboprovodov, transportiruyuschikh dvukhfaznuyu sredu v rezhime probkovogo techeniya”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2019, no. 61, 95–110 | DOI | MR

[24] Guz A. N., “Rasprostranenie voln v tsilindricheskoi obolochke s vyazkoi szhimaemoi zhidkostyu”, Prikl. mekh. Kiev, 16:10 (1980), 10–20 | Zbl

[25] Khudoinazarov Kh. Kh., Yalgashev B. F., “O nestatsionarnykh zadachakh gidrouprugosti dlya tsilindricheskogo sloya s vyazkoi szhimaemoi zhidkostyu”, Problemy arkhitektury i stroitelstva, 2007, no. 2, 119–125

[26] Khudoynazarov K., Yalgashev B. F., Mavlonov T., “Mathematical modelling of torsional vibrations of the three-layer cylindrical viscoelastic shell”, IOP Conf. Ser.: Earth Environ. Sci, 1030 (2021), 012098 | DOI

[27] Khudoinazarov Kh. Kh., Nestatsionarnoe vzaimodeistvie krugovykh tsilindricheskikh obolochek i sterzhnei s deformiruemoi sredoi, Izd-vo im. Abu Ali ibn Sino, Tashkent, 2003, 325 pp.

[28] Filippov I. G., Kudainazarov K., “Refinement of equations describing longitudinal-radial vibrations of a circular cylindrical viscoelastic shell”, Soviet Applied Mechanics, 26:2 (1990), 161–168 | DOI | Zbl

[29] Filippov I. G., Kudainazarov K., “Boundary-value problems of longitudinal vibrations of circular cylindrical shells”, International Applied Mechanics, 34:12 (1998), 1204–1210 | DOI | Zbl