Fourier analysis of wave turbulence in a thin elastic plate

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of...

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Bibliographic Details
Published inThe European physical journal. B, Condensed matter physics Vol. 76; no. 4; pp. 537 - 545
Main Author Mordant, N.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.08.2010
EDP Sciences
Springer
Subjects
Analysis
Chaotic Dynamics
Complex Systems
Condensed Matter Physics
Exact sciences and technology
Fluid- and Aerodynamics
Fundamental areas of phenomenology (including applications)
Nonlinear Sciences
Physics
Physics and Astronomy
Solid mechanics
Solid State Physics
Statistical and Nonlinear Physics
Structural and continuum mechanics
Turbulence
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Dispersion Relation
Video Projector
Linear Dispersion Relation
Time Spectrum
Wave Turbulence
Finite size effect
Fourier transformation
Turbulence
Turbulent flow
Vibration
Dispersion relation
Thin plate
Fourier analysis
Modeling
Surface metrology
Wave dispersion
Continuous wave
Line width
Continuous spectrum
High speed
Non linear effect
Energy absorption
Kolmogorov equation
Isotropic material
Profilometry
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Summary:The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2010-00197-y