Some recently obtained results in classical vibration and acoustics: Coexistence of traveling and standing waves in a one-dimensional non-dispersive continuum

Antoine Blanchard, Yongxiong Xiao, D. Michael McFarland, Alexander F. Vakakis, Lawrence Bergman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The problem of free vibration of a linear uniform axial bar, fixed at one end and connected to ground at the other end through a linear viscous damper has been carefully studied by several researchers. It's known that, for a fixed set of bar parameters and the special case of the damping coefficient λ equal to EA / c (c being the speed of sound in the continuum), no eigenvalues exist. Thus, energy imparted to the bar via harmonic motion of the fixed support will propagate through the bar and be fully dissipated in the damper, in effect making the bar appear to be semi-infinite. I will show some recent results by the present authors in which this phenomenon has been exploited in several other nondispersive media, the taut string and the circular acoustic duct, incorporating viscoelastic supports or absorbers to produce responses to harmonic motion at one or both boundaries that exhibit complete separation of traveling and standing waves, in effect localizing the vibration over a portion of the domain.

Original languageEnglish (US)
Title of host publicationA Tribute Conference Honoring Daniel Inman
EditorsPablo A. Tarazaga, Donald J. Leo
PublisherSPIE
ISBN (Electronic)9781510608290
DOIs
StatePublished - Jan 1 2017
EventA Tribute Conference Honoring Daniel Inman 2017 - Portland, United States
Duration: Mar 29 2017 → …

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume10172
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Other

OtherA Tribute Conference Honoring Daniel Inman 2017
CountryUnited States
CityPortland
Period3/29/17 → …

Keywords

  • mode complexity
  • nondispersive medium
  • one-dimensional continua
  • separation of standing and traveling waves

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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