Asymptotic Formulas for the Eigenvalues of the Timoshenko Beam

Asymptotic formulas are derived for the eigenvalues of a free-ended Timoshenko beam which has variable mass density and constant beam parameters otherwise. These asymptotic formulas show how the eigenvalues (and hence how the natural frequencies) of such a beam depend on the material and geometric p...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 253; no. 2; pp. 341 - 380
Main Authors Geist, Bruce, McLaughlin, Joyce R.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.01.2001
Elsevier
Subjects
eigenvalue asymptotics
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematics
Ordinary differential equations
Physics
Sciences and techniques of general use
Solid mechanics
Structural and continuum mechanics
Structural mechanics (beam, string...)
Theory and numerical methods
Timoshenko beam models
Timoshenko beam models
eigenvalue asymptotics
Initial condition
Differential equation
Integrability
Asymptotic behavior
Eigenvalue
Sturm Liouville equation
Boundary condition
Density
Timoshenko beam model
Asymptotic formula
Boundary value problem
Timoshenko differential equation
Beam theory
Integral equation
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Summary:Asymptotic formulas are derived for the eigenvalues of a free-ended Timoshenko beam which has variable mass density and constant beam parameters otherwise. These asymptotic formulas show how the eigenvalues (and hence how the natural frequencies) of such a beam depend on the material and geometric parameters which appear as coefficients in the Timoshenko differential equations.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2000.7125