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Closed-form solutions for the free longitudinal vibration of inhomogeneous rods
Published in Academic Press
2005
Volume: 283
   
Issue: 3-5
Pages: 1015 - 1030
Abstract
This paper aims at presenting a family of exact solutions for the longitudinal vibration of variable area rods. Area variations that give solutions in terms of the confluent hypergeometric function are being sought for and the governing differential equation is appropriately reduced to the confluent hypergeometric differential equation, using a generic transformation. The eigenfrequencies of rods with certain area variations, subjected to classical boundary conditions, are obtained and the parametric space of the solutions obtained is studied. These solutions are also highly useful in other topics of study such as torsional vibration of rods and wave propagation in ducts with variable cross-sectional areas, since the governing differential equations are very similar. © 2004 Elsevier Ltd. All rights reserved.
About the journal
JournalJournal of Sound and Vibration
PublisherAcademic Press
ISSN0022460X
Open AccessNo
Concepts (12)
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    Differential equations
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    Ducts
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    Geometry
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    Harmonic analysis
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    Mathematical transformations
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    Problem solving
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    Wave propagation
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    Closed-form solutions
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    HYPERGEOMETRIC FUNCTIONS
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    INHOMOGENEOUS RODS
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    LONGITUDINAL VIBRATION
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    Vibrations (mechanical)