Elastic guide rail oscillation due to moving concentrated load
Keywords:
wave equation, cubic spline, moving loadAbstract
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.
References
- Savchuk VP, Titioura OV. A string bend under a moving load. Vestnik BGU. Seriya 1. Fizika. Matematika. Informatika. 2004; 1:75–78. Russian.
- Vesnitskii AI. Volny v sistemakh s dvizhushchimisya granitsami i nagruzkami [Waves in systems with moving boundaries and loads]. Moscow: Fizmatlit; 2001. 320 p. Russian.
- Filippov AP. Kolebaniya deformiruemykh sistem. 2e izdanie [Vibrations of elastic systems. 2 nd editions]. Мoscow: Mashinostroenie; 1970. 734 p. Russian.
- Savchuk VP. Matematicheskoe modelirovanie zadach dinamiki uprugikh sistem [Mathematical modeling of dynamics problems for elastic systems]. Minsk: Belarusian State University; 2018. 111 p. Russian.
- Alevy I. Solutions to the heat and wave equations and the connection to the Fourier series [Internet]. 2010 [cited 2019 January 21]. Available from: http://www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Alevy.pdf.
- Kaya E. Spline interpolation techniques. Journal of Technical Science and Technologies. 2013;2(1):47–52.
Downloads
Published
Issue
Section
License
The authors who are published in this journal agree to the following:
- The authors retain copyright on the work and provide the journal with the right of first publication of the work on condition of license Creative Commons Attribution-NonCommercial. 4.0 International (CC BY-NC 4.0).
- The authors retain the right to enter into certain contractual agreements relating to the non-exclusive distribution of the published version of the work (e.g. post it on the institutional repository, publication in the book), with the reference to its original publication in this journal.
- The authors have the right to post their work on the Internet (e.g. on the institutional store or personal website) prior to and during the review process, conducted by the journal, as this may lead to a productive discussion and a large number of references to this work. (See The Effect of Open Access.)
