| Issue |
MATEC Web Conf.
Volume 329, 2020
International Conference on Modern Trends in Manufacturing Technologies and Equipment: Mechanical Engineering and Materials Science (ICMTMTE 2020)
|
|
|---|---|---|
| Article Number | 03030 | |
| Number of page(s) | 6 | |
| Section | Mechanical Engineering | |
| DOI | https://doi.org/10.1051/matecconf/202032903030 | |
| Published online | 26 November 2020 | |
Finite difference approximation of eigenvibrations of a bar with oscillator
1 Kazan State Power Engineering University, 51 Krasnoselskaya Street, Kazan, 420066, Russian Federation
2 Kazan Federal University, 18 Kremlevskaya Street, Kazan, 420008, Russian Federation
* Corresponding author: sergey.solovev.kpfu@mail.ru
The second-order ordinary differential spectral problem governing eigenvibrations of a bar with attached harmonic oscillator is investigated. We study existence and properties of eigensolutions of formulated bar-oscillator spectral problem. The original second-order ordinary differential spectral problem is approximated by the finite difference mesh scheme. Theoretical error estimates for approximate eigenvalues and eigenfunctions of this mesh scheme are established. Obtained theoretical results are illustrated by computations for a model problem with constant coefficients. Theoretical and experimental results of this paper can be developed and generalized for the problems on eigenvibrations of complex mechanical constructions with systems of harmonic oscillators.
© The Authors, published by EDP Sciences, 2020
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