 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 50, Issue 2 / 2015 | Next article >> |
| 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 |
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