MATEC Web Conf.
Volume 129, 2017International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTMTE 2017)
|Number of page(s)||4|
|Section||Other Related Topics|
|Published online||07 November 2017|
Eigenvibrations of a bar with load
Kazan Federal University, 420008, Kazan, 18 Kremlevskaya Street, Russian Federation
* Corresponding Author: firstname.lastname@example.org
The differential eigenvalue problem describing eigenvibrations of an elastic bar with load is investigated. The problem has an increasing sequence of positive simple eigenvalues with limit point at infinity. To the sequence of eigenvalues, there corresponds a complete orthonormal system of eigenfunctions. We formulate limit differential eigenvalue problems and prove the convergence of the eigenvalues and eigenfunctions of the initial problem to the corresponding eigenvalues and eigenfunctions of the limit problems as load mass tending to infinity. The original differential eigenvalue problem is approximated by the finite difference method on a uniform grid. Error estimates for approximate eigenvalues and eigenfunctions are established. Investigations of this paper can be generalized for the cases of more complicated and important problems on eigenvibrations of beams, plates and shells with attached loads.
© The Authors, published by EDP Sciences, 2017
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. (http://creativecommons.org/licenses/by/4.0/).
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