### 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 |
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Pages (from-to) | 401-422 |

Number of pages | 22 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 16 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1999 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)
- Applied Mathematics

### Cite this

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**Eigenvalue Problems for the Beam and an Upper and Lower Bound for Each Branch of Solutions of Rayleigh-Lamb Frequency Equation.** / Liu, Kang-Man.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Eigenvalue Problems for the Beam and an Upper and Lower Bound for Each Branch of Solutions of Rayleigh-Lamb Frequency Equation

AU - Liu, Kang-Man

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0345895104&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345895104&partnerID=8YFLogxK

U2 - 10.1007/BF03167365

DO - 10.1007/BF03167365

M3 - Article

VL - 16

SP - 401

EP - 422

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 3

ER -