Geodesic
The parametric oscillations of heterogeneous round cylindrical shell of~variable density on different boundary conditions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 210-215.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider an isotropic cylindrical shell of varying thickness and density along the generatrix. Let the shell be under pressure, which is symmetric and also varying along the generatrix. We follow the polupostamenty theory by V. Z. Vlasov and consider the problem of the dynamical stability of the shell. We obtain the exact solution corresponding to the certain relation between thickness, pressure and density. Such kind of shells of extent medium is important in mechanical and aerospace engineering for optimal mass obtaining. In the paper we obtain minimum values of the excitation coefficients for five boundary value problems, which are of great importance in engineering. We give the accuracy estimation of the WKB method for these problems. Numerical results are summarized in the table. 
@article{ISU_2015_15_2_a11,
     author = {A. A. Mochalin},
     title = {The parametric oscillations of heterogeneous round cylindrical shell of~variable density on different boundary conditions},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {210--215},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a11/}
}
TY  - JOUR
AU  - A. A. Mochalin
TI  - The parametric oscillations of heterogeneous round cylindrical shell of~variable density on different boundary conditions
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2015
SP  - 210
EP  - 215
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a11/
LA  - ru
ID  - ISU_2015_15_2_a11
ER  - 
%0 Journal Article
%A A. A. Mochalin
%T The parametric oscillations of heterogeneous round cylindrical shell of~variable density on different boundary conditions
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2015
%P 210-215
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a11/
%G ru
%F ISU_2015_15_2_a11
A. A. Mochalin. The parametric oscillations of heterogeneous round cylindrical shell of~variable density on different boundary conditions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 210-215. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a11/

[1] Belov S. V., Porous metals applications in mechanical engineering, Mashinostroenie, M., 1981, 248 pp. (in Russian)

[2] Boldyrev A. B., “Application of models of solid deformable body of variable density in problems of optimization and prediction of the mass of the airframe”, Collection of scientific papers Science and technology. The results of the dissertation research, v. 1, Ser. Selected works of the Russian school, Russian Academy of Sciences, M., 2009, 177–200 (in Russian)

[3] Vlasov V. Z., General theory of shells, GITTL, M., 1949, 784 pp. (in Russian)

[4] Mochalin A. A., “Stability of non-homogeneous cylindrical about-shell from the uneven radial Noi load”, Problems of machine engineering companies and reliability, 2014, no. 1, 12–17 (in Russian)

[5] Salnikov G. M., “Dynamic stability of cylindrical and conical shells of circular and non-circular cross-section with various boundary conditions”, The Collection Research on the theory of PLA-plates and shells, 5, Kazan, 1967, 469–479 (in Russian)

[6] Bolotin V. V., Dynamic us-persistence of elastic systems, GITTL, M., 1956, 600 pp. (in Russian)