Modeling of Ritz's method of piecewise-inhomogeneous rod system near the critical speed
Matematičeskoe modelirovanie, Tome 23 (2011) no. 9, pp. 57-64.

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

The mathematical modeling of longitudinal elastic central impact of the step and homogeneous rod with a rigid obstacle, at not hard ties by the solutions of the wave equation by d'alembert is realized. On the basis of the law of conservation of energy it is calculated the value of the critical compressive load Ritz's method, in accordance with which further it is calculated the value of the critical speed during the strike, leading to the loss of stability of the rod system.
Keywords: sustainability, impact, modeling, speed, rod.
@article{MM_2011_23_9_a4,
     author = {A. A. Bityurin},
     title = {Modeling of {Ritz's} method of piecewise-inhomogeneous rod system near the critical speed},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {57--64},
     publisher = {mathdoc},
     volume = {23},
     number = {9},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_9_a4/}
}
TY  - JOUR
AU  - A. A. Bityurin
TI  - Modeling of Ritz's method of piecewise-inhomogeneous rod system near the critical speed
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 57
EP  - 64
VL  - 23
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_9_a4/
LA  - ru
ID  - MM_2011_23_9_a4
ER  - 
%0 Journal Article
%A A. A. Bityurin
%T Modeling of Ritz's method of piecewise-inhomogeneous rod system near the critical speed
%J Matematičeskoe modelirovanie
%D 2011
%P 57-64
%V 23
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_9_a4/
%G ru
%F MM_2011_23_9_a4
A. A. Bityurin. Modeling of Ritz's method of piecewise-inhomogeneous rod system near the critical speed. Matematičeskoe modelirovanie, Tome 23 (2011) no. 9, pp. 57-64. http://geodesic.mathdoc.fr/item/MM_2011_23_9_a4/

[1] Lavrentev M. A., Ishlinskii A. Yu., “Dinamicheskie formy poteri ustoichivosti uprugikh sistem”, Doklady AN SSSR, 65:6 (1949)

[2] Malyi V. I., “Dlinnovolnovoe priblizhenie v zadachakh o potere ustoichivosti pri udare”, Izvestiya AN SSSR. MTT, 1972, no. 4, 138–144

[3] Malyi V. I., “Vypuchivanie sterzhnya pri prodolnom udare. Malye progiby”, Izvestiya AN SSSR. MTT, 1973, no. 4, 181–186

[4] Malyi V. I., “Vypuchivanie sterzhnya pri prodolnom udare. Bolshie progiby”, Izvestiya AN SSSR. MTT, 1975, no. 1, 52–61

[5] Volmir A. S., Kildibekov I. G., “Issledovanie protsessa vypuchivaniya sterzhnei pri udare”, Doklady AN SSSR, 2:10 (1966)

[6] Volmir A. S., Ustoichivost uprugikh sistem, GITTL, M., 1967, 880 pp.

[7] Malyshev B. M., “Ustoichivost sterzhnya pri udarnom szhatii”, Izvestiya AN SSSR. MTT, 1966, no. 4, 137–142

[8] Bityurin A. A., “Poterya ustoichivosti odnorodnogo sterzhnya pri prodolnom udare o sterzhen, vzaimodeistvuyuschii s zhestkoi pregradoi”, YuUrGU, Seriya “Matematika. Mekhanika. Fizika”, 3:30(206) (2010), 38–44

[9] Darkov A. V., Shpiro G. S., Soprotivlenie materialov, Vysshaya shkola, M., 2003, 641 pp.

[10] Pisarenko G. S., Yakovlev A. P., Matveev V. V., Spravochnik po soprotivleniyu materialov, Naukova dumka, Kiev, 1989, 732 pp.

[11] Panovko Ya. G., Gubanova I. I., Ustoichivost i kolebaniya uprugikh sistem, Nauka, M., 1987, 352 pp. | MR | Zbl

[12] Alimov O. D., Manzhosov V. K., Eremyants V. E., Rasprostranenie voln deformatsii v udarnykh sistemakh, Nauka, M., 1985, 354 pp.

[13] Bityurin A. A., Prodolnyi udar neodnorodnogo sterzhnya o zhestkuyu pregradu, eds. A. A. Bityurin, V. K. Manzhosov, UlGTU, Ulyanovsk, 2009, 164 pp.