Free Oscillations of a Toroidal Viscoelastic Shell with a Flowing Liquid
American Journal of Mechanics and Applications
Volume 6, Issue 2, June 2018, Pages: 37-49
Received: Mar. 20, 2018; Accepted: Mar. 30, 2018; Published: May 7, 2018
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Safarov Ismail Ibrahimovich, Department of Mathematics, Tashkent Chemcal - Technological Institute, Tashkent, Republic of Uzbekistan
Teshaev Muhsin Khudoyberdiyevich, Department of Mathematics, Вukhara Engineering - Technological Institute, Bukhara, Republic of Uzbekistan
Akhmedov Maqsud Sharipovich, Department of Mathematics, Вukhara Engineering - Technological Institute, Bukhara, Republic of Uzbekistan
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On the basis of the method of orthogonal sweep and the Mueller method, the solution of the problem of intrinsic oscillation of a Toroidal shell with a flowing liquid is discussed. The problem of determining the frequencies and forms of intrinsic bending vibrations in the plane of curvature of curvilinear sections of thin-walled Toroidal shells of large diameter with a flowing liquid, with different conditions for fixing the end sections is solved. The behavior of complex Eigen frequencies as a function of the curvature of the shell axis is studied.
Toroidal Shell, Liquid, Sweep, Mueller Method, Natural Frequency, Oscillation
To cite this article
Safarov Ismail Ibrahimovich, Teshaev Muhsin Khudoyberdiyevich, Akhmedov Maqsud Sharipovich, Free Oscillations of a Toroidal Viscoelastic Shell with a Flowing Liquid, American Journal of Mechanics and Applications. Vol. 6, No. 2, 2018, pp. 37-49. doi: 10.11648/j.ajma.20180602.11
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Bozorov M. B., Safarov I. I., Shokin Yu. I. Numerical simulation of oscillations of dissipative homogeneous and inhomogeneous mechanical systems. Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 1966-188 p.
Safarov I. I., Akhmedov M., Umarov A. Own vibrations of toroidal shell with flowing liquid. Lambert Academic Publishing (Germany). 2017. 177p. hhtp:// dnb.d – ISBN: 978-3-330-06423-2
Vlasov V. Z. General theory of shells and its applications in engineering. - Moscow-Leningrad. Gostekhizdat Press., 1949-784 p.
Volmir AS, Grach M. S. Fluctuations of a shell with a flowing fluid, Izvestiya USSR Academy of Sciences, Mechanics of Solid State, No. 6, 1973.-p. 162-166.
Vol'mir AS, Shells in a stream of liquid and gas. Problems of aeroelasticity. - Moscow: Nauka, 1976.-416 p.
Galiev Sh. U. Dynamics of the interaction of structural elements with the pressure wave in the liquidity. - Kiev: Nauka Dumka press. 1977 172 p.
Gladkikh P. A, Khachaturyan S. A. Vibration in pipelines and methods for their elimination. Moscow, Mashgiz press, 1969. 170 p.
Gol'denveizer A. L. The theory of elastic thin shells. –Moscow, Gostehizdat press. 1953, -544 p.
Kayumov S. S., Safarov I. I. Propagation and diffraction of waves in dissipative - inhomogeneous cylindrical deformable mechanical systems. Tashkent, Publishing house: Science, 2004, 214 p.
Safarov I. I., Nuriddinov B. Z., Shodiyev Z. O. Dynamic stress-Deformed condition layer cylindrical layer from the harmonic wave. World Wide Journal of Multidisciplinary Research and Development (WWJMRD). 25, 2017, 3(7) P.277-286
SNIP 2.05.06-85 *. Migratory pipelines.- M.: Gosstroy of Russia, 1997. 60 p.
Safarov I. I., Teshayev M. K., Boltayev Z. I., Akhmedov M. Sh. Damping Properties of Vibrations of Three-Layer VIscoelastic Plate. International Journal of Theoretical and Applied Mathematics 2017; 3(6): 191-198
Safarov I. I., Teshaev M. X. Akhmedov M. Sh., Ruziyev T. R Application Of The Method Of Finite Element For Investigation Of The Dynamic Stress- deformed Condition Of Pipeline Sides When Exposed External Loods. // Case Studies Journal -Volume 6, Issue-5-May-2017. Р.38-4514.
Safarov I. I., Teshaev M. KH, Boltaev Z. I.. Mathematical modeling of wave process in a mechanical waveguide taking into account the internal friction. Germany. LAP. 2013. 243p.
Safarov I. I, Akhmedov M. Sh., Boltaev. Z. I. Dissemination Sinusoidal Waves in of A Viscoelastic Strip. Global Journal of Science Frontier Research: F Mathematics & Decision Sciences. 2015. Volume 15 Issue 1 (Ver.1.0). P.39-60.
Safarov I. I, Akhmedov M. Sh., Boltaev. Z. I. Ducting in Extended Plates of Variable Thickness. Global Journal of Science Frontier Research: F Mathematics & Decision Sciences. 2016. Volume 16 Issue 2 (Ver.1.0). P.33-66.
Koltunov M. A.. Creep and relaxation. - M.: Higher School press, 1976.-276p.
Safarov I. I., Teshaev M. KH., Boltaev Z. I. Distribution of linear waves in extended lamellar bodies. LAP, Lambert Academic Publishing (Germany). 2016. 315 p.
Safarov I. I., Akhmedov M. Sh., Boltaev Z. I.. Proper waves in layered media. Lambert Academic Publishing (Germany). 2016. 192p.
Safarov I. I, Boltaev Z. I., Akhmedov M. Sh. Properties of wave motion in a fluid-filled cylindrical shell/ LAP, Lambert Academic Publishing. 2016 -105 р.
Safarov I. I, Akhmedov M. Sh., Qilichov O. Dynamics of underground hiheline from the flowing fluid.. Lambert Academic Publishing (Germany). 2016. 345р.
S. K. Godunov. On the numerical solution of boundary value problems for systems of linear ordinary differential equations. - Successes of Mathematical Sciences, 1061, Т. 16, № 3, 171-174 p.
Bolotin V. V. Oscillations and stability of an elastic cylindrical shell in a flow of a compressible fluid. -Inzh. sb., 1956, v. 24, p. 331
Bolotin V. V. Dynamic stability of elastic systems. –Moscow, Gostekhizdat press, 1956.-600 p.
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