Mathematical Notes

, Volume 79, Issue 3–4, pp 342–355 | Cite as

On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a viscoelastic rod

  • A. A. Vladimirov


In this paper, we study the problem of the boundary accumulation of a discrete spectrum, which is essential for a boundary-value problem of fourth order arising in the theory of small transverse vibrations in an inhomogeneous viscoelastic rod (a Kelvin—Voigt body). We establish conditions for such an accumulation and its asymptotics, which are expressed in terms of the coefficients defining the problem posed by the differential expression. The results obtained are illustrated by numerical computation data.

Key words

operator pencil small vibrations in a viscoelastic rod Kelvin—Voigt body accumulation of eigenvalues quadratic form index of inertia of a quadratic form 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. A. Vladimirov
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityRussia

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