Geodesic
Nonlinear deformation waves in a geometrically and physically nonlinear viscoelastic cylindrical shell containing viscous incompressible fluid and surrounded by an elastic medium
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 193-202 
A. Yu. Blinkova; Yu. A. Blinkov; S. V. Ivanov; L. I. Mogilevich. Nonlinear deformation waves in a geometrically and physically nonlinear viscoelastic cylindrical shell containing viscous incompressible fluid and surrounded by an elastic medium. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 193-202. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a9/
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     title = {Nonlinear deformation waves in a geometrically and physically nonlinear viscoelastic cylindrical shell containing viscous incompressible fluid and surrounded by an elastic medium},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The present study is devoted to analysis of nonlinear deformation of longitudinal waves in a cylindrical shell surrounded by an elastic medium and containing viscous incompressible fluid inside. The physical properties of the shell are defined by the equations of quadratic theory of viscoelasticity, which takes into account the linear elastic volume strain. The problem of wave propagation in viscoelastic and nonlinear thin-walled structures, including cylindrical shells, without interaction with the viscous incompressible fluid are considered from the perspective of earlier theory of solitons. The presence of fluid requires the development of new mathematical models and computer simulation of the processes occurring in the system.

[1] Zemlyanukhin A. I., Mogilevich L. I., Nonlinear Waves in Cylindrical Shells : Solitons, Symmetry, Evolution, Saratov State Tech. Univ. Press, Saratov, 1999, 132 pp. (in Russian)

[2] Arshinov G. A., Zemlyanukhin A. I., Mogilevich L. I., “Two-dimensional Solitary Waves in Nonlinear Viscoelastic Deformable Environment”, Acoustical Physics, 46:1 (2000), 116–117 (in Russian)

[3] Arshinov G. A., Mogilevich L. I., Static and Dynamic Problems of Viscoelasticity, Saratov State RGM Univ. Press, Saratov, 2000, 152 pp. (in Russian)

[4] Loitsyansky L. G., Fluid Mechanics, Drofa, M., 2003, 840 pp. (in Russian) | DOI

[5] Volmir A. S., Dynamics of Plates and Shells, Nauka, M., 1972, 432 pp. (in Russian) | MR

[6] Moskvitin V. V., Resistance Vyzko-elastic materials, Nauka, M., 1972, 328 pp. (in Russian)

[7] Vlasov V. Z., Leont'ev N. N., Beams, Plates and Shells on Elastic Foundation, Fizmatgiz, M., 1960, 490 pp. (in Russian)

[8] Chivilikhin S. A., Popov I. Yu., Gusarov V. V., “Dynamics of nanotube twisting in a viscous fluid”, Doklady Physics, 52:1 (2007), 60–62 | DOI

[9] Popov I. Y., Rodygina O. A., Chivilikhin S. A., Gusarov V. V., “Soliton in a nanotube wall and stokes flow in the nanotube”, Technical Physics Letters, 36:9 (2010), 852–855 | DOI

[10] Blinkov Yu. A., Mozzhilkin V. V., “Generation of Difference Schemes for the Burgers Equation by Constructing Gröbner Bases”, Programming and Computer Software, 32:2 (2006), 114–117 | DOI | MR | Zbl

[11] Gerdt V. P., Blinkov Yu. A., Mozzhilkin V. V., “Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations”, Symmetry, Integrability and Geometry : Methods and Applications, 2 (2006), 26 pp. (data obrascheniya: 03.03.2015) http://www.emis.de/journals/SIGMA/2006/Paper051/index.html | DOI | MR

[12] Gerdt V. P., Blinkov Yu. A., “Gröbner Bases and Involution and difference schemes for the Navier–Stokes equations”, Computer Algebra in Scientific Computing, Lecture Notes in Computer Science, 5743, 2009, 94–105 | DOI | Zbl

[13] Gerdt V. P., Robertz D., “A Maple Package for Computing Gröbner Bases for Linear Recurrence Relations”, Nuclear Instruments and Methods in Physics Research, A559 (2006), 215–219 | DOI