Bounds on natural frequencies of composite circular plates

Integral equation methods

W. B. Bickford, S. Y. Wu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The problem of finding upper and lower bounds to the natural frequencies of free vibration of a circular plate with stepped radial density has been investigated. Such problems, involving discontinuous coefficients in the governing differential equation, are formulated with an integral equation by using a Green function and the basic theory of linear integral equations. It is shown that eigenvalue estimation techniques based on the integral equation formulation are more effective than those based on the traditional differential equation formulation. By using the Galerkin method, the integral equation formulation is shown to provide more accurate upper bounds than the differential equation formulation for both the clamped and simply supported plates. Additionally, it is shown that the corresponding Green functions can be used to supply improvable lower bounds.

Original languageEnglish
Pages (from-to)19-35
Number of pages17
JournalJournal of Sound and Vibration
Volume126
Issue number1
DOIs
Publication statusPublished - Oct 8 1988
Externally publishedYes

Fingerprint

circular plates
Integral equations
integral equations
resonant frequencies
Natural frequencies
formulations
Differential equations
differential equations
composite materials
Composite materials
Green's function
Green's functions
Galerkin method
free vibration
Galerkin methods
Vibrations (mechanical)
eigenvalues
coefficients

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

Cite this

Bounds on natural frequencies of composite circular plates : Integral equation methods. / Bickford, W. B.; Wu, S. Y.

In: Journal of Sound and Vibration, Vol. 126, No. 1, 08.10.1988, p. 19-35.

Research output: Contribution to journalArticle

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