EXACT TRANSIENT VIBRATION OF NONUNIFORM BARS, SHAFTS AND STRINGS GOVERNED BY WAVE EQUATIONS

A new analytical method is developed for transient solutions for bars in longitudinal vibration, shafts in torsional vibration and strings in transverse vibration. These vibrating continua have nonuniform distributions of geometric and material properties, and are governed by second-order partial di...

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Bibliographic Details
Published inInternational journal of structural stability and dynamics Vol. 12; no. 4; pp. 1250022 - 1250020
Main Authors YANG, B., NOH, K.
Format Journal Article
LanguageEnglish
Published World Scientific Publishing Company 01.07.2012
Subjects
Bars
Exact solutions
Mathematical analysis
Mathematical models
Nonuniform
Strings
Vibration
Wave equations
Distributed vibrating systems
Green's functions
strings
Laplace transform
distributed transfer function method
nonuniform systems
shafts
analytical methods
bars
transient vibration
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ISSN0219-4554
1793-6764
DOI10.1142/S0219455412500228

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Summary:A new analytical method is developed for transient solutions for bars in longitudinal vibration, shafts in torsional vibration and strings in transverse vibration. These vibrating continua have nonuniform distributions of geometric and material properties, and are governed by second-order partial differential equations (wave equations). Based on a transfer function formulation and a residue formula, the proposed method delivers exact solutions for several types of nonuniform systems subject to external, boundary and initial disturbances. The proposed method does not need system eigenfunctions, and is numerically efficient as it only involves simple operations of two-by-two matrices.
Bibliography:ObjectType-Article-2
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ISSN:0219-4554
1793-6764
DOI:10.1142/S0219455412500228