Axial vibration confinement in nonhomogenous rods

S. Choura, Sami El-Borgi, A. H. Nayfeh

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A design methodology for the vibration confinement of axial vibrations in nonhomogenous rods is proposed. This is achieved by a proper selection of a set of spatially dependent functions characterizing the rod material and geometric properties. Conditions for selecting such properties are established by constructing positive Lyapunov functions whose derivative with respect to the space variable is negative. It is shown that varying the shape of the rod alone is sufficient to confine the vibratory motion. In such a case, the vibration confinement requires that the eigenfunctions be exponentially decaying functions of space, where the notion of spatial domain stability is introduced as a concept dual to that of the time domain stability. It is also shown that vibration confinement can be produced if the rod density and/or stiffness are varied with respect to the space variable while the cross-section area is kept constant. Several case studies, supporting the developed conditions imposed on the spatially dependent functions for vibration confinement in vibrating rods, are discussed. Because variation in the geometric and material properties might decrease the critical buckling loads, we also discuss the buckling problem.

Original languageEnglish
Pages (from-to)177-195
Number of pages19
JournalShock and Vibration
Volume12
Issue number3
Publication statusPublished - 2005
Externally publishedYes

Fingerprint

vibration
rods
Buckling
buckling
Lyapunov functions
Eigenvalues and eigenfunctions
Materials properties
Liapunov functions
Stiffness
Derivatives
stiffness
eigenvectors
cross section
methodology
cross sections
material

Keywords

  • Axial vibration
  • Buckling
  • Material and geometric properties
  • Vibration confinement

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Condensed Matter Physics
  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Choura, S., El-Borgi, S., & Nayfeh, A. H. (2005). Axial vibration confinement in nonhomogenous rods. Shock and Vibration, 12(3), 177-195.

Axial vibration confinement in nonhomogenous rods. / Choura, S.; El-Borgi, Sami; Nayfeh, A. H.

In: Shock and Vibration, Vol. 12, No. 3, 2005, p. 177-195.

Research output: Contribution to journalArticle

Choura, S, El-Borgi, S & Nayfeh, AH 2005, 'Axial vibration confinement in nonhomogenous rods', Shock and Vibration, vol. 12, no. 3, pp. 177-195.
Choura, S. ; El-Borgi, Sami ; Nayfeh, A. H. / Axial vibration confinement in nonhomogenous rods. In: Shock and Vibration. 2005 ; Vol. 12, No. 3. pp. 177-195.
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