MATEC Web Conf.
Volume 329, 2020International Conference on Modern Trends in Manufacturing Technologies and Equipment: Mechanical Engineering and Materials Science (ICMTMTE 2020)
|Number of page(s)||6|
|Published online||26 November 2020|
Eigenvibrations of a beam with two mechanical resonators attached to the ends
1 Kazan Federal University, 18 Kremlevskaya Street, Kazan, 420008, Russian Federation
2 Kazan State Power Engineering University, 51 Krasnoselskaya Street, Kazan, 420066, Russian Federation
* Corresponding author: email@example.com
The fourth-order ordinary differential spectral problem describing vertical eigenvibrations of a beam with two mechanical resonators attached to the ends is studied. This problem has positive simple eigenvalues and corresponding eigenfunctions. We define limit differential spectral problem and establish the convergence of the eigenvalues and eigenfunctions of the original spectral problem to the eigenvalues and eigenfunctions of the limit spectral problem as parameters of the attached resonators tending to infinity. The initial fourth-order ordinary differential spectral problem is approximated by the finite difference method. Theoretical error estimates for approximate eigenvalues and eigenfunctions are derived. Obtained theoretical results are illustrated by computations for model problem with constant coefficients. Theoretical and experimental results of this paper can be developed for the problems on eigenvibrations of complex mechanical constructions with systems of resonators.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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