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Effects and applications associated with zero group velocity Lamb waves / submitted by Clemens Grünsteidl
AutorInnenGrünsteidl, Clemens
Beurteiler / BeurteilerinBauer, Siegfried ; Burgholzer, Peter
ErschienenLinz, February 2017
Umfangix, 76 Seiten : Illustrationen
HochschulschriftUniversität Linz, Dissertation, 2017
Zusammenfassung in deutscher Sprache
Bibl. ReferenzOeBB
Schlagwörter (DE)Lambwellen / Plattenwellen / Gruppengeschwindigkeit / negative Reflexion / Ultraschall / Laser / Interferometer
Schlagwörter (EN)Lambwaves / guided waves / laser ultrasonics / negative reflection
Schlagwörter (GND)Plattenwelle / Gruppengeschwindigkeit / Ultraschall / Laser / Interferometer
URNurn:nbn:at:at-ubl:1-13868 Persistent Identifier (URN)
 Das Werk ist gemäß den "Hinweisen für BenützerInnen" verfügbar
Effects and applications associated with zero group velocity Lamb waves [8.53 mb]
Zusammenfassung (Englisch)

Lamb waves are guided elastic waves in plates, which are mathematically described by the dispersion relation of their infinite numbered modes. This complex function f(k), relating frequency f and wavenumber k of the guided wave modes, is determined by the material properties of the plate and scales with its thickness. Many ordinary materials show local minima in their dispersion relation f(k) at values for |k|>0. At these points the group velocity c_G =2 pi df/dk and the related power flux of a Lamb mode along the plate vanishes. Thus, the energy of an acoustic source coupling into a zero group velocity (ZGV) Lamb wave is locally trapped and causes resonances, which appear as distinct, dominant peaks in the acoustic response spectrum of a plate. In the articles which are consolidated to my dissertation, me and my co-authors study the contact--free excitation and detection of these ZGV resonances, their mathematical description, the characterization of plates by measuring their location (f,k) and the propagation of Lamb waves close to the ZGV point. Investigating the thermo-elastic coupling of a pulsed laser into ZGV Lamb waves, we were able to experimentally confirm the laser spot diameter for optimum coupling calculated in previous work. Additionally, insight in the temporal decay behavior of the resonant mode was gained by studying the experimental data and results from a finite elements model. We further give an exact analytic approach to find the location (f,k) of ZGV points and state an inverse problem to directly determine elastic properties of a plate from the frequencies of two ZGV points. In two practical examples, its iterative solution is demonstrated with the experimentally found ZGV frequencies of an aluminum and a tungsten plate. Preliminary, we developed a method not only to measure the frequency, but also the wavenumber of acoustic wave modes. It is based on periodic excitation patterns instead of a focused laser spot and can be applied to determine the wavenumber of ZGV Lamb waves. By extending the inverse problem to include this additional information, the simultaneous determination of the elastic properties and the thickness of a plate is possible. Of fundamental physical interest are regions of negative group velocity in the dispersion relation of Lamb waves, concomitant to ZGV points. The wavefronts of these backward-waves move in opposite direction of the energy flux. If, upon reflection at a free edge of plate, these modes convert into forward propagating modes, negative reflection occurs. We present theoretical and experimental wavefields impressively showing this intriguing effect for a point-like source located close to a straight edge of a plate. Due to broad angle negative reflection, the reflected waves originating from one point, roughly focus again in another point. As part of this work, I have built and refined the laser based setups for excitation and detection of acoustic waves.

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