Geodesic
Elastic guide rail oscillation due to moving concentrated load
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2019), pp. 62-66

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

This article illustrates the solution of a differential equation describing oscillations of an elastic tensioned guide rail, which consist of string bundle enclosed in an elastic cylindrical shell, while concentrated load, simulated by a material point, moves along it. The oscillatory system is considered in such way that the guide rail supports freely. The existing external and internal forces of resistance to movement of the guide rail are also taken into account. Initial and boundary conditions are zero. In article «A string bend under a moving load», published in the journal «Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika» (2004, No. 1), the deflection of a flexible guide rail under load was obtained by solving an equation with deviating argument. In this article, an algorithm is constructed for finding deflection of an elastic tensioned guide rail in the form of a cubic splines. All the results of calculations are presented in a dimensionless form.
Keywords: wave equation; cubic spline; moving load. 
V. P. Savchuk; P. A. Savenkov. Elastic guide rail oscillation due to moving concentrated load. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2019), pp. 62-66. http://geodesic.mathdoc.fr/item/BGUMI_2019_2_a6/
@article{BGUMI_2019_2_a6,
     author = {V. P. Savchuk and P. A. Savenkov},
     title = {Elastic guide rail oscillation due to moving concentrated load},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {62--66},
     year = {2019},
     volume = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2019_2_a6/}
}
TY  - JOUR
AU  - V. P. Savchuk
AU  - P. A. Savenkov
TI  - Elastic guide rail oscillation due to moving concentrated load
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2019
SP  - 62
EP  - 66
VL  - 2
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2019_2_a6/
LA  - ru
ID  - BGUMI_2019_2_a6
ER  - 
%0 Journal Article
%A V. P. Savchuk
%A P. A. Savenkov
%T Elastic guide rail oscillation due to moving concentrated load
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2019
%P 62-66
%V 2
%U http://geodesic.mathdoc.fr/item/BGUMI_2019_2_a6/
%G ru
%F BGUMI_2019_2_a6

[1] V. P. Savchuk, O. V. Tityura, “Progib struny pod dvizhuscheisya nagruzkoi”, Vestnik BGU. Fizika. Matematika. Informatika, 1 (2004), 75–78 | Zbl

[2] A. I. Vesnitskii, “Volny v sistemakh s dvizhuschimisya granitsami i nagruzkami”, Moskva: Fizmatlit, 2001, 320

[3] A. P. Filippov, “Kolebaniya deformiruemykh sistem”, Moskva: Mashinostroenie, 1970, 734

[4] V. P. Savchuk, “Matematicheskoe modelirovanie zadach dinamiki uprugikh sistem”, Minsk: BGU, 2018, 111

[5] I. Alevy, “Solutions to the heat and wave equations and the connection to the Fourier series [Internet]”, 010 | DOI

[6] E. Kaya, “Spline interpolation techniques”, Journal of Technical Science and Technologies, 2(1) (2013), 47–52