Propagating waves and end modes in pretwisted beams

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

A method is presented for studying propagating waves and end modes in a uniformly pretwisted beam. The variationally derived equations of motion are based on three-dimensional elasticity and finite element modelling of the cross-section. This discretization procedure accommodates arbitrarily shaped cross-sections of inhomogeneous, anisotropic material properties that follow the pretwist rotation rate. An harmonic solution form in both time t and axial co-ordinate ζ is introduced, i.e., exp{i(kζ - ωt)}, resulting in a two-parameter algebraic eigensystem. By specifying the axial wavenumber k, the eigenproblem permits real frequencies of propagating modes to be determined. By specifying real frequency ω, both real and complex axial wavenumbers can be extracted, where real values pertain to propagating modes and the complex ones to edge vibrations or end modes. Due to pretwist, the effect of extension, torsion and flexural are coupled. Examples of homogeneous, isotropic beams with rectangular and square cross-sections are given to illustrate the method of analysis and the physical behavior.

Original languageEnglish (US)
Pages (from-to)313-330
Number of pages18
JournalJournal of Sound and Vibration
Volume195
Issue number2
DOIs
StatePublished - Aug 15 1996

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Torsional stress
Equations of motion
Elasticity
Materials properties
cross sections
torsion
equations of motion
elastic properties
harmonics
vibration

All Science Journal Classification (ASJC) codes

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

Cite this

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abstract = "A method is presented for studying propagating waves and end modes in a uniformly pretwisted beam. The variationally derived equations of motion are based on three-dimensional elasticity and finite element modelling of the cross-section. This discretization procedure accommodates arbitrarily shaped cross-sections of inhomogeneous, anisotropic material properties that follow the pretwist rotation rate. An harmonic solution form in both time t and axial co-ordinate ζ is introduced, i.e., exp{i(kζ - ωt)}, resulting in a two-parameter algebraic eigensystem. By specifying the axial wavenumber k, the eigenproblem permits real frequencies of propagating modes to be determined. By specifying real frequency ω, both real and complex axial wavenumbers can be extracted, where real values pertain to propagating modes and the complex ones to edge vibrations or end modes. Due to pretwist, the effect of extension, torsion and flexural are coupled. Examples of homogeneous, isotropic beams with rectangular and square cross-sections are given to illustrate the method of analysis and the physical behavior.",
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Propagating waves and end modes in pretwisted beams. / Onipede, Jr., Oladipo; Dong, S. B.

In: Journal of Sound and Vibration, Vol. 195, No. 2, 15.08.1996, p. 313-330.

Research output: Contribution to journalArticle

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