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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.
Among the various types of guided acoustic waves, acoustic wedge waves are non-diffractive and non-dispersive. Both properties make them susceptible to nonlinear effects. Investigations have recently been focused on effects of second-order nonlinearity in connection with anisotropy. The current status of these investigations is reviewed in the context of earlier work on nonlinear properties of two-dimensional guided acoustic waves, in particular surface waves. The role of weak dispersion, leading to solitary waves, is also discussed. For anti-symmetric flexural wedge waves propagating in isotropic media or in anisotropic media with reflection symmetry with respect to the wedge’s mid-plane, an evolution equation is derived that accounts for an effective third-order nonlinearity of acoustic wedge waves. For the kernel functions occurring in the nonlinear terms of this equation, expressions in terms of overlap integrals with Laguerre functions are provided, which allow for their quantitative numerical evaluation. First numerical results for the efficiency of third-harmonic generation of flexural wedge waves are presented.
The laser ultrasound (LU) technique has been used to determine dispersion curves for surface acoustic waves (SAW) propagating in AlScN/Al2O3 systems. Polar and non-polar Al0.77Sc0.23N thin films were prepared by magnetron sputter epitaxy on Al2O3 substrates and coated with a metal layer. SAW dispersion curves have been measured for various propagation directions on the surface. This is easily achieved in LU measurements since no additional surface structures need to be fabricated, which would be required if elastic properties are determined with the help of SAW resonators. Variation of the propagation direction allows for efficient use of the system’s anisotropy when extracting information on elastic properties. This helps to overcome the complexity caused by a large number of elastic constants in the film material. An analysis of the sensitivity of the SAW phase velocities (with respect to the elastic moduli and their dependence on SAW propagation direction) reveals that the non-polar AlScN films are particularly well suited for the extraction of elastic film properties. Good agreement is found between experiment and theoretical predictions, validating LU as a non-destructive and fast technique for the determination of elastic constants of piezoelectric thin films.
Laser ultrasound was used to determine dispersion curves of surface acoustic waves on a Si (001) surface covered by AlScN films with a scandium content between 0 and 41%. By including off-symmetry directions for wavevectors, all five independent elastic constants of the film were extracted from the measurements. Results for their dependence on the Sc content are presented and compared to corresponding data in the literature, obtained by alternative experimental methods or by ab-initio calculations.