Geodesic
A mathematical investigation of one problem of the longitudinal impact on an elastic rod with an elastic attachment at the end
Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 81-87 
V. I. Korzyuk; J. V. Rudzko. A mathematical investigation of one problem of the longitudinal impact on an elastic rod with an elastic attachment at the end. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 81-87. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a9/
@article{TIMB_2023_31_1_a9,
     author = {V. I. Korzyuk and J. V. Rudzko},
     title = {A mathematical investigation of one problem of the longitudinal impact on an elastic rod with an elastic attachment at the end},
     journal = {Trudy Instituta matematiki},
     pages = {81--87},
     year = {2023},
     volume = {31},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a9/}
}
TY  - JOUR
AU  - V. I. Korzyuk
AU  - J. V. Rudzko
TI  - A mathematical investigation of one problem of the longitudinal impact on an elastic rod with an elastic attachment at the end
JO  - Trudy Instituta matematiki
PY  - 2023
SP  - 81
EP  - 87
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a9/
LA  - ru
ID  - TIMB_2023_31_1_a9
ER  - 
%0 Journal Article
%A V. I. Korzyuk
%A J. V. Rudzko
%T A mathematical investigation of one problem of the longitudinal impact on an elastic rod with an elastic attachment at the end
%J Trudy Instituta matematiki
%D 2023
%P 81-87
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a9/
%G ru
%F TIMB_2023_31_1_a9

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

The present work is devoted to the construction and the rigorous justification of the solution of a boundary value problem of the longitudinal impact on a homogeneous elastic rod of a constant cross-section in the case when one of its ends is rigidly fixed, and the other end has a linear elastic element at the end and was subjected to the impact by some load.

[1] V. A. Lazaryan, “O dinamicheskikh usiliyakh v upryazhnykh priborakh odnorodnykh poezdov pri soprotivleniyakh otnositelnym peremescheniyam ekipazhei”, Tr. Dnepropetr. in-ta inzhenerov zh. d. transporta, 20, 1950, 3–32

[2] A. N. Tveritin, “Matematicheskoe rassmotrenie prosteishei kraevoi zadachi, svyazannoi s teoriei prodolnogo udara po uprugovyazkomu sterzhnyu s opertymi kontsami”, Tr. Dnepropetr. in-ta inzhenerov zh. d. transporta, 23, 1953, 24–60

[3] C. I. Gaiduk, “O nekotorykh zadachakh, svyazannykh s teoriei prodolnogo udara po sterzhnyam”, Differents. uravneniya, 26:5 (1976), 865–880

[4] C. I. Gaiduk, “Matematicheskoe rassmotrenie odnoi zadachi o prodolnom udare po relaksiruyuschemu sterzhnyu”, Differents. uravneniya, 26:4 (1976), 668–685

[5] M. L. Rasulov, Metod konturnogo integrala i ego primenenie k issledovaniyu zadach dlya differentsialnykh uravnenii, Nauka, M., 1964, 464 pp.

[6] A. N. Tveritin, “Issledovanie transtsendentnogo uravneniya $\mu\ctg \mu=\alpha \mu^2-\gamma$”, Tr. Dnepropetr. in-ta inzhenerov zh. d. transporta, 1958, no. 26, 349–367

[7] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979, 320 pp. | MR

[8] A. N. Tveritin, “Rassmotrenie ryadov, svyazannykh s uravneniem $\mu\ctg \mu=\alpha \mu^2-\gamma$”, Podvizhnoi sostav i energeticheskoe khozyaistvo zheleznykh dorog, Tr. Dnepropetr. in-ta inzhenerov zh.-d. transporta, 26, 1958, 368–411