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

Kang Man Liu

doi:10.1007/BF03167365

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

Kang Man Liu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	401-422
Number of pages	22
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/BF03167365
Publication status	Published - 1999 Oct

All Science Journal Classification (ASJC) codes

Engineering(all)
Applied Mathematics

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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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