Finite difference approximation of eigenvibrations of a bar with oscillator

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 pr...

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Bibliographic Details
Published inMATEC Web of Conferences Vol. 329; p. 3030
Main Authors Korosteleva, D. M., Koronova, L. N., Levinskaya, K. O., Solov’ev, S. I.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Les Ulis EDP Sciences 2020
Subjects
Approximation
Eigenvalues
Eigenvectors
Finite difference method
Finite element method
Harmonic oscillators
Spectra
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Summary: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.
ISSN:2261-236X
2274-7214
2261-236X
DOI:10.1051/matecconf/202032903030