| Issue |
MATEC Web Conf.
Volume 224, 2018
International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTMTE 2018)
|
|
|---|---|---|
| Article Number | 04012 | |
| Number of page(s) | 6 | |
| Section | Modelling of Technical Systems. CAD/CAM/CAE Systems | |
| DOI | https://doi.org/10.1051/matecconf/201822404012 | |
| Published online | 30 October 2018 | |
Eigenvibrations of a simply supported beam with elastically attached load
Kazan Federal University, 18 Kremlevskaya Street, Kazan 420008, Russian Federation
* Corresponding author: sergei.solovyev@kpfu.ru
The nonlinear differential eigenvalue problem describing eigenvibrations of a simply supported beam with elastically attached load is investigated. The existence of an increasing sequence of positive simple eigenvalues with limit point at infinity is established. To the sequence of eigenvalues, there corresponds a system of normalized eigenfunctions. To illustrate the obtained theoretical results, the initial problem is approximated by the finite difference method on a uniform grid. The accuracy of approximate solutions is studied. Investigations of the present paper can be generalized for the cases of more complicated and important problems on eigenvibrations of plates and shells with elastically attached loads.
© The Authors, published by EDP Sciences, 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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