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IssuesArchive of Issues2015-2pp.208-217

Archive of Issues

Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

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D.V. Tarlakovskii and G.V. Fedotenkov, "Nonstationary 3D Motion of an Elastic Spherical Shell," Mech. Solids. 50 (2), 208-217 (2015)
Year 2015 Volume 50 Number 2 Pages 208-217
DOI 10.3103/S0025654415020107
Title Nonstationary 3D Motion of an Elastic Spherical Shell
Author(s) D.V. Tarlakovskii (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr. 1, Moscow, 119192 Russia, tdvhome@mail.ru)
G.V. Fedotenkov (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, Moscow, 125993 Russia, greghome@mail.ru)
Abstract A 3D model of motion of a thin elastic spherical Timoshenko shell under the action of arbitrarily distributed nonstationary pressure is considered. An approach for splitting the system of equations of 3D motion of the shell is proposed. The integral representations of the solution with kernels in the form of influence functions, which can be determined analytically by using series expansions in the eigenfunctions and the Laplace transform, are constructed. An algorithm for solving the problem on the action of nonstationary normal pressure on the shell is constructed and implemented. The obtained results find practical use in aircraft and rocket construction and in many other industrial fields where thin-walled shell structural members under nonstationary working conditions are widely used.
Keywords spatial nonstationary problem, spherical shell, splitting of equations, series in eigenfunctions, integral representation, influence function, numerical-analytical algorithms
References
1.  S. A. Lychev and Yu. V. Sidorov, "Nonstationary Vibrations of Three-Layer Spherical Shells with a Multiple Spectrum," Izv. Vyssh. Uchebn. Zaved. Stroit., No. 4, 31-39 (2001).
2.  Yu. E. Senitskii, "Dynamics of Inhomogeneous Non-Shallow Spherical Shells," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 144-157 (2002) [Mech. Solids (Engl. Transl.) 37 (6), 123-133 (2002)].
3.  Yu. E. Senitskii and A. Yu. Senitskii, "To the Problem of Expansion in Vector Eigenfunctions in Nonstationary Initial Boundary-Value Problems of Dynamics of Shells of Revolution," Vestnik Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, No. 30, 83-91 (2004).
4.  V. D. Kubenko and V. R. Bogdanov, "Axisymmetric Impact of a Shell on an Elastic Halfspace," Prikl. Mekh. 31 (10), 56-63 (1995) [Int. Appl. Mech. (Engl. Transl.) 31 (10), 829-835 (1995)].
5.  A. G. Gorshkov, D. V. Tarlakovskii, and G. V. Fedotenkov, "Plane Problem of Vertical Cylindrical Shell Hit on Elastic Half-Space," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 151-158 (2000).
6.  E. Yu. Mikhailova and G. V. Fedotenkov, "Nonstationary Axisymmetric Problem of the Impact of a Spherical Shell on an Elastic Half-Space (Initial Stage of Interaction)," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 98-108 (2011) [Mech. Solids (Engl. Transl.) 46 (2), 239-247 (2011)].
7.  A. G. Gorshkov, A. L. Medvedskii, L. N. Rabinskii, and D. V. Tarlakovskii, Waves in Continuous Media (Fizmatlit, Moscow, 2004) [in Russian].
8.  E. W. Hobson, The Theory of Spherical and Ellipsoidal Functions (Cambridge Univ. Press, Cambridge, 1931; IL, Moscow, 1952).
9.  Ye. M. Suvorov, D. V. Tarlakovskii, and G. V. Fedotenkov, "The Plane Problem of the Impact of a Rigid Body on a Half-Space Modelled by a Cosserat Medium," J. Appl. Math. Mech. 76 (5), 850-859 (2012) [J. Appl. Math. Mech. 76 (5), 511-518 (2012)].
10.  E. L. Kuznetsova, D. V. Tarlakovskii, and G. V. Fedotenkov, "Propagation of Unsteady Waves in an Elastic Layer," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 144-152 (2011) [Mech. Solids (Engl. Transl.) 46 (5), 779-787 (2011)].
11.  M. A. Lavrentiev and B. V. Shabat, Method of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1973) [in Russian].
Received 20 October 2014
Link to Fulltext http://link.springer.com/article/10.3103/S0025654415020107
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