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Eigenvibrations of a beam with elastically attached load

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Abstract

The nonlinear eigenvalue problem describing eigenvibrations of a 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. The problem is approximated by the finite element method with Hermite finite elements of arbitrary order. The convergence and accuracy of approximate eigenvalues and eigenfunctions are investigated.

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Authors and Affiliations

  1. Department of Computational Mathematics, Institute of Computational Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kremlevskaya ul. 35, Kazan, 420008, Russia

    S. I. Solov’ev

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  1. S. I. Solov’ev
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Correspondence to S. I. Solov’ev.

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Submitted by A. V. Lapin

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Solov’ev, S.I. Eigenvibrations of a beam with elastically attached load. Lobachevskii J Math 37, 597–609 (2016). https://doi.org/10.1134/S1995080216050115

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  • DOI: https://doi.org/10.1134/S1995080216050115

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