Integral identities for Bi-laplacian problems and their application to vibrating plates

Guang Tsai Lei, George Pan

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we derive boundary integral identities for the bi-Laplacian eigenvalue problems under Dirichlet, Navier and simply-supported boundary conditions. By using these integral identities, we prove that the first eigenvalue of the eigenvalue problem under the simply-supported boundary conditions strictly increases with Poisson's ratio. In addition, we establish the boundary integral expressions for the strain energy calculation of the vibrating plates under the three types of boundary conditions.

Original languageEnglish (US)
Pages (from-to)425-443
Number of pages19
JournalHokkaido Mathematical Journal
Volume42
Issue number3
DOIs
StatePublished - 2013

Keywords

  • Bi-Laplacian eigenvalue problems
  • Dirichlet boundary conditions
  • Pohozaev's identity
  • Poisson's ratio
  • Rayleigh's conjecture
  • Rellich's identity
  • Simplysupported boundary conditions
  • Vibrating plates

ASJC Scopus subject areas

  • Mathematics(all)

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