Dispersion and attenuation of surface shear acoustic waves with horizontal polarization on the free statistically rough surface of the hexagonal crystal

Expressions for dispersion of the phase velocity and inverse damping depth of surface acoustic waves with shear horizontal polarization are derived in an analytical form within perturbation theory using the modified mean-field method for the Z-cut hexagonal crystal with a free statically rough surface. Both two-and one-dimensionally rough surfaces are considered. The one-dimensionally rough surface is considered as a special case of the two-dimensionally rough surface. It is shown that shear surface waves with horizontal polarization cannot exist on the flat surface of the Z-cut hexagonal crystal. The derived expressions are studied analytically and numerically in the entire frequency range accessible in perturbation theory. The long-wavelength limit (most interesting from the experimental point of view) is considered, where the wavelength is much longer than the roughness correlation radius. The conditions for the existence of SH-polarized waves are determined for both roughness types. It is shown that dispersion and attenuation of SH polarized waves are qualitatively similar in character to those we considered previously for an isotropic medium.     

Influence of a structurally damaged surface layer of the hexagonal crystal on the dispersion and attenuation of Rayleigh surface acoustic waves

Analytical expressions for the dispersion of the phase velocity and the inverse attenuation length of Rayleigh waves are derived with allowance made for a thin (as compared to the length of the surface wave) isotropic damaged surface layer that is contiguous with vacuum and located on the surface of a hexagonal crystal with the sixfold axis perpendicular to the surface. It is demonstrated that, in the limit of long wavelengths (as compared to the characteristic inhomogeneity size), which is of greatest interest for experimenters, the change in the dispersion of the phase velocity of Rayleigh waves is proportional to the second power of the frequency, whereas the inverse attenuation length of Rayleigh waves is proportional to the fifth power of the frequency. The inverse attenuation length of the Rayleigh wave is calculated numerically. The calculation method previously proposed by one of the authors (Kosachev, 1998) is generalized to the case of an isotropic damaged layer on an anisotropic (hexagonal) substrate.     

Dispersion and attenuation of Rayleigh waves at a one-dimensional random roughness of the free surface of a hexagonal crystal

Analytical expressions are derived for dispersion and attenuation of Rayleigh waves propagating along the statistically rough free surface of a hexagonal crystal (Z cut). The roughness under consideration is one-dimensional (the profile function of the roughness depends on one coordinate) and has the form of hollows of a random lattice. The results obtained earlier in the solution of an analogous problem for a two-dimensional roughness are used in the one-dimensional case. The relationships derived for the dispersion and attenuation of Rayleigh waves are treated analytically and numerically over the entire range of frequencies acceptable in the framework of the perturbation theory. It is shown that the dispersion and attenuation of Rayleigh waves are qualitatively similar to those observed in an isotropic medium.     

Dispersion and attenuation of surface acoustic waves of shear horizontal polarization on a free surface of a hexagonal crystal with a structurally damaged isotropic surface layer

The phase velocity dispersion and the inverse attenuation length of surface acoustic waves of shear horizontal polarization propagating along a free flat (smooth) surface of a hexagonal crystal (Z cut) in the presence of a thin (compared to the wavelength) structurally damaged surface layer are found in the analytical form. It is shown that, in the long-wavelength limit (the wavelength is large compared to the characteristic size of layer inhomogeneities), which is of the greatest interest to experimenters, the change in the phase velocity dispersion and the change in the inverse attenuation length are proportional to the third and sixth powers of the wave frequency, respectively. The inverse attenuation length is numerically calculated.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Scattering of bulk acoustic waves with different polarizations on a statistically rough free surface of a solid at oblique incidence

In the first Born approximation of the perturbation theory by a Green's function method developed by Maradudin, Mills [7] and Kosachev, Lokhov, Chukov [8,9] the problem of scattering bulk acoustic waves with different polarizations at oblique incidence on a statistically rough free boundary of an isotropic solid was solved. When the correlation function of the surface roughness is of a Gaussian form, the expressions for the transformation energy factor of the incident wave in the scattered volume and surface Rayleigh waves with respect to polarization, frequency and grazing angle of the incident wave as well as the roughness parameters and the Poisson coefficient of the medium were obtained. These results are helpful in accounting for the experiments on residual losses [15–17].     

Analysis of coherent surface wave dispersion and attenuation for non-destructive testing of concrete

Rayleigh waves measurements are used to characterise cover concrete and mortar in the frequency range 60–180 kHz. At these frequencies, the wavelength is comparable to the size of the aggregates, and waves propagate in a multiple scattering regime. Acquired signals are then difficult to interpret due to an important incoherent part. The method proposed here is the study of the coherent waves, obtained by averaging signals over several configurations of disorder. Coherent waves give information on an equivalent homogeneous medium. To acquire a large amount of measurements with accuracy, an optimised piezoelectric source is used with a laser interferometer for reception. Adapted signal processing technique are presented to evaluate the coherent phase and group velocities and also the coherent attenuation parameter. The sensitivity of these three parameters with the properties of concrete is discussed, as well as the necessity to use coherent waves to obtain accurate results.     

Scattering of a spherical wave by a statistically irregular dielectric surface

The scattering of a spherical wave by a static irregular dielectric surface, separating two subspaces with dielectric constant close to the permittivity of free space, is investigated by the Kirchhoff method. The irregularities of the surface — large-scale with small angles of inclination, and their heights are distributed according to a normal law. Self-shadowing and the set of spots associated with scattering on such a surface are taken into account. The polarization matrix of second moments of the components of the scattered field is calculated. The dependence of the matrix elements on the statistical parameters of a randomly irregular surface are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 7–10, May, 1974.     

Effect of the structurally damaged surface layer of an isotropic solid on Rayleigh wave dispersion and damping

The effect of the structurally damaged isotropic surface layer on the free surface of an isotropic solid on the Rayleigh wave propagation has been considered. The phase velocity dispersion and inverse Rayleigh wave decay length in the second order of vanishing with respect to the ratio of the structurally damaged layer thickness to the wavelength have been obtained in an analytical form. For the dispersion and the inverse wave decay length, the long-wave limit has been studied when the wavelength is much larger than the characteristic size of layer inhomogeneity. The inverse decay length has been calculated numerically.     

Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.     

Experimental study of wave dispersion and attenuation in concrete

Results from an experimental study concerning wave propagation in cementitious materials are presented in this paper. Narrow band pulses at several frequencies were introduced into specimens of cement paste, mortar and concrete allowing direct measurement of longitudinal wave velocities and amplitude for each frequency. It is shown that aggregate content play an important role in wave propagation increasing considerably the wave velocity, while the aggregate size seems to control the attenuation observed. Slight velocity variations observed with frequency are discussed in relation to the degree of inhomogeneity of the materials.     

声表面波在压电晶体表面上的聚焦特性

研究了压电晶体表面上圆弧形叉指换能器产生的声表面波的聚焦现象。用作者提出的压电晶体表面激发的严格矢量场理论来计算会聚的表面波声场,取代了比较流行的源于光学的标量角谱理论。理论分析表明介质的各向异性对声束的会聚特性有很大的影响,如焦长和焦点附近声场的对称性。在实验中可以用光学暗场法来观察声表面波场的会聚。尽管各向异性介质或各向异性压电晶体上表面波声场的会聚都非常复杂,实验的结果和理论分析比较一致。