Refine
Document Type
- Article (reviewed) (7) (remove)
Language
- English (7)
Has Fulltext
- no (7)
Is part of the Bibliography
- yes (7)
Keywords
- Surface acoustic waves (2)
- Elastische Welle (1)
- Finite element method (1)
- Guided waves (1)
- Keil (1)
- Laser (1)
- Lasertechnologie (1)
- Oberfläche (1)
- Optical phase matching (1)
- Silicon crystal (1)
Institute
Open Access
- Closed Access (7) (remove)
Surface acoustic waves are propagated toward the edge of an anisotropic elastic medium (a silicon crystal), which supports leaky waves with a high degree of localization at the tip of the edge. At an angle of incidence corresponding to phase matching with this leaky wedge wave, a sharp peak in the reflection coefficient of the surface wave was found. This anomalous reflection is associated with efficient excitation of the leaky wedge wave. In laser ultrasound experiments, surface acoustic wave pulses were excited and their reflection from the edge of the sample and their partial conversion into leaky wedge wave pulses was observed by optical probe-beam deflection. The reflection scenario and the pulse shapes of the surface and wedge-localized guided waves, including the evolution of the acoustic pulse traveling along the edge, have been confirmed in detail by numerical simulations.
Propagation of acoustic waves is considered in a system consisting of two stiff quarter-spaces connected by a planar soft layer. The two quarter-spaces and the layer form a half-space with a planar surface. In a numerical study, surface waves have been found and analyzed in this system with displacements that are localized not only at the surface, but also in the soft layer. In addition to the semi-analytical finite element method, an alternative approach based on an expansion of the displacement field in a double series of Laguerre functions and Legendre polynomials has been applied.
It is shown that a number of branches of the mode spectrum can be interpreted and remarkably well described by perturbation theory, where the zero-order modes are the wedge waves guided at a rectangular edge of the stiff quarter-spaces or waves guided at the edge of a soft plate with rigid surfaces.
For elastic moduli and densities corresponding to the material combination PMMA–silicone–PMMA, at least one of the branches in the dispersion relation of surface waves trapped in the soft layer exhibits a zero-group velocity point.
Potential applications of these 1D guided surface waves in non-destructive evaluation are discussed.
In numerical calculations, guided acoustic waves, localized in two spatial dimensions, have been shown to exist and their properties have been investigated in three different geometries, (i) a half-space consisting of two elastic media with a planar interface inclined to the common surface, (ii) a wedge made of two elastic media with a planar interface, and (iii) the free edge of an elastic layer between two quarter-spaces or two wedge-shaped pieces of a material with elastic properties and density differing from those of the intermediate layer.
For the special case of Poisson media forming systems (i) and (ii), the existence ranges of these 1D guided waves in parameter space have been determined and found to strongly depend on the inclination angle between surface and interface in case (i) and the wedge angle in case (ii). In a system of type (ii) made of two materials with strong acoustic mismatch and in systems of type (iii), leaky waves have been found with a high degree of spatial localization of the associated displacements, although the two materials constituting these structures are isotropic.
Both the fully guided and the leaky waves analyzed in this work could find applications in non-destructive evaluation of composite structures and should be accounted for in geophysical prospecting, for example.
A critical comparison is presented of the two computational approaches employed, namely a semi-analytical finite element scheme and a method based on an expansion of the displacement field in a double series of special functions.
For an elastic medium containing a homogeneous distribution of micro-cracks, an effective one-dimensional stress-strain relation has been determined with finite element simulations. In addition to flat micro-cracks, voids were considered that contain a Hertzian contact, which represents an example for micro-cracks with internal structure. The orientation of both types of micro-cracks was fully aligned or, for flat micro-cracks, totally random. For micro-cracks with Hertzian contacts, the case of random orientation was treated in an approximate way. The two types of defects were found to give rise to different degrees of non-analytic behavior of the effective stress-strain relation, which governs the nonlinear propagation of symmetric (S0) Lamb waves in the long-wavelength limit. The presence of flat micro-cracks causes even harmonics to grow linearly with propagation distance with amplitudes proportional to the amplitude of the fundamental wave, and gives rise to a static strain. The presence of the second type of defects leads to a linear growth of all harmonics with amplitudes proportional to the power 3/2 of the fundamental amplitude, and to a strain-dependent velocity shift. Simple expressions are given for the growth rates of higher harmonics of S0 Lamb waves in terms of the parameters occurring in the effective stress-strain relation. They have partly been determined quantitatively with the help of the FEM results for different micro-crack concentrations.
Laser pulses focused near the tip of an elastic wedge generate acoustic waves guided at its apex. The shapes of the acoustic wedge wave pulses depend on the energy and the profile of the exciting laser pulse and on the anisotropy of the elastic medium the wedge is made of. Expressions for the acoustic pulse shapes have been derived in terms of the modal displacement fields of wedge waves for laser excitation in the thermo-elastic regime and for excitation via a pressure pulse exerted on the surface. The physical quantity considered is the local inclination of a surface of the wedge, which is measured optically by laser-probe-beam deflection. Experimental results on pulse shapes in the thermo-elastic regime are presented and confirmed by numerical calculations. They pertain to an isotropic sharp-angle wedge with two wedge-wave branches and to a non-reciprocity phenomenon at rectangular silicon edges.
The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump–probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented.