Eigenvalue Problems for the Beam and an Upper and Lower Bound for Each Branch of Solutions of Rayleigh-Lamb Frequency Equation

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Abstract

The Rayleigh-Lamb frequency equation is derived in studying eigenvalues and eigenfunctions for the beam problem in a domain (-a, a) × (-d, d). It is shown that there is an upper bound and a lower bound for each branch of the frequency spectrum which consists of all roots of the frequency equation.

Original languageEnglish
Pages (from-to)401-422
Number of pages22
JournalJapan Journal of Industrial and Applied Mathematics
Volume16
Issue number3
DOIs
Publication statusPublished - 1999 Jan 1

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Eigenvalues and eigenfunctions
Rayleigh
Eigenvalue Problem
Upper and Lower Bounds
Branch
Eigenvalues and Eigenfunctions
Frequency Spectrum
Roots
Lower bound
Upper bound

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

Cite this

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abstract = "The Rayleigh-Lamb frequency equation is derived in studying eigenvalues and eigenfunctions for the beam problem in a domain (-a, a) × (-d, d). It is shown that there is an upper bound and a lower bound for each branch of the frequency spectrum which consists of all roots of the frequency equation.",
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