Parametric scattering of high-frequency elastic waves by a small spherical cavity oscillating under the action of a Rayleigh wave

Scattering of high-frequency transverse and longitudinal plane waves incident on a spherical cavity located at a small depth under the surface of a half-space is considered. The cavity oscillates as a whole in the field of a low-frequency Rayleigh surface wave, the oscillation vectors of the longitudinal, transverse, and surface waves being coplanar. The cavity radius is assumed to be small compared to the wavelengths of the sounding wave and the pumping surface wave. The scattered compression and shear waves at the combination frequencies ω±Ω are calculated in the dipole approximation. Expressions obtained describe the qualitative behavior of the combination-frequency signal levels produced at the outputs of horizontally and vertically oriented geophones moving over the free surface of the elastic half-space.     

Scattering of obliquely incident shear waves from a cylindrical cavity

Prior work has proposed the use of ultrasonic angle-beam shear wave techniques to detect cracks of varying angular location around fastener sites by generating and detecting creeping waves. To better understand the nature of the scattering problem and quantify the role of creeping waves in fastener site inspections, a 3D analytical model was developed for the propagation and scattering of an obliquely incident plane shear wave from a cylindrical cavity with arbitrary shear wave polarization. The generation and decay of the spiral creeping waves was found to be dependent on both the angle of incidence and polarization of the plane shear wave. A difference between the angle of displacement in 3D and the direction of propagation for the spiral creeping wave was observed and attributed to differences in the curvature of the cavity surface for the tangential and vertical (z) directions. Using the model, practical insight was presented on measuring the displacement response in the far-field from the hole. Both analytical and experimental results highlighted the value of the diffracted and leaky spiral creeping wave signals for nondestructive evaluation of a crack located on the cavity. Last, array and signal processing methods are discussed to improve the resolution of the weaker creeping wave signals in the presence of noise.     

The multiple scattering of non-homogeneous shear waves from two cavities in functionally graded materials

The propagation and multiple scattering of non-homogeneous shear waves resulting from two cavities embedded in exponential functional graded materials (FGMs) were investigated, and the dynamic stress around the two cavities derived. The non-homogeneous scattering fields of shear waves around the cavities are analytically expressed by using the wave function expansion method. The interaction of non-homogeneous scattering fields between the two cavities is described accurately. The dynamic stresses around the cavities under different geometrical and physical parameters are graphically illustrated and analyzed. Analysis shows that the non-homogeneous properties of FGMs exhibit a significant effect on the dynamic stress around the cavities. The effect of the non-homogeneous properties of FGMs on the dynamic stress is also dependent on the gradation direction, the distance between the two cavities, the relative position of the two cavities and the incident frequency of waves. A comparison with other existing studies in the literature is also presented.     

Damping rates of waves in a switched magnetoplasma medium:longitudinal propagation

The interaction of a circularly polarized electromagnetic wave with a switched-on magnetoplasma medium is considered. A static magnetic field in the direction of propagation is assumed to be present, resulting in longitudinal propagation. The incident wave splits into three waves whose frequencies are different from that of the incident wave. It is shown that these waves ultimately damp out if the plasma is even slightly lossy. The damping of the waves is interpreted in terms of their attenuation with distance and decay with time as they propagate in the lossy plasma. The attenuation-length and decay-time constants of the waves are obtained, and their dependence on the incident-wave frequency and the gyrofrequency is examined. Optimum parameters for an experiment to detect these waves are suggested     

General solution of a system of equations for acoustic wave propagation in a partially ionized gas in an external electric field

In this paper a system of equations describing the propagation of acoustic waves in multicomponent partially ionized plasma in an external electric field is solved generally, when these waves are generated by an external neutral sound wave in plasma. The equations are solved by means of Laplace transformation. It has been found that a sound wave generates a group of waves with different frequencies and wave vectors. For the sake of comparison, the solution without an external field and the linear solution in the form of waves having the same frequencies as the frequency of the excitation wave are given.     

The anisotropy of elastic waves in a tellurium crystal

For acoustic waves propagating in an acoustooptic tellurium crystal, the dependence of their polarization on the propagation direction with respect to the crystal axes is discussed. The characteristic features of waves propagating in the crystal are considered; these features manifest themselves in an excess of the phase velocity of shear acoustic modes over the velocity of longitudinal modes. The change in the wave type from quasi-longitudinal to quasi-transverse as a result of the variation in the propagation direction of ultrasound is investigated. It is shown that such a behavior of bulk acoustic waves is caused by the specific relation between the elastic moduli, which differs from the corresponding relations observed in other acoustooptic materials.     

Potential surface waves at the boundary of a metal with a magnetoactive plasma at finite pressure

The propagation of surface-type potential waves along the interfacial boundary of a plasma with an ideally conducting metal in an external magnetic field perpendicular to the boundary is examined. It is shown that a necessary condition for the existence of these waves in the system is a finite gas kinetic pressure. Dispersion relations for these waves and expressions for the penetration depth of the wave fields into the plasma are obtained, and they are studied numerically for various plasma parameters. The frequency region for propagation of these waves is found. It is also shown that in a nonzero external magnetic field a system of this kind has a range of frequencies in which the wave is a generalized surface wave. Zh. Tekh. Fiz. 69, 30–33 (November 1999)     

Interaction of a shear wave with a moving domain wall in a ferromagnetic crystal with allowance for the external magnetic field

The boundary-value problem of the magnetoelastic wave interaction with a moving domain wall in a ferromagnetic crystal is solved in the nonexchange magnetostatic approximation with allowance for the external magnetic field. It is shown that the difference introduced by magnetic field between the ferromagnetic resonance frequencies of the domains does not cause any noticeably departure of the refraction characteristics of reflected and transmitted waves from those observed at zero frequency mismatch. By contrast, the magnitudes of the transmission and reflection coefficients strongly depend on the external magnetic field and on the mobility of the domain wall. The dependence of the magnitude of the reflection coefficient on the external magnetic field at a fixed angle of shear wave incidence is found to possess two ferromagnetic resonance peaks. The positions and heights of the peaks may vary depending on the mobility of the domain wall.     

Shear magnetoelastic modes in a ferromagnetic cylinder

Features of the mode spectrum of shear magnetoelastic waves circulating along the boundary of a ferromagnetic cylinder are discussed in the nonexchange magnetostatic approximation. Depending on the level of the spin-phonon coupling in the crystal and on the frequency, the lowest order normal mode may be either fast or slow relative to the bulk shear wave in an infinite crystal. It is shown that, unlike the lowest order mode, the higher order modes, which primarily depend on the curvature of the boundary, demonstrate a weak nonreciprocity of propagation in directions with opposite azimuths. Conditions for the slow propagation of the lowest order mode, when it is identified with a surface magnetoelastic wave, are only possible sufficiently far away from the cutoff frequency of the mode spectrum in ferromagnetic cylinders with a strong spin-phonon coupling and a small curvature of the boundary.     

Nonlinear propagation of ultra-low-frequency electromagnetic modes in a magnetized dusty plasma

A theoretical investigation has been made of nonlinear propagation of ultra-low-frequency electromagnetic waves in a magnetized two fluid (negatively charged dust and positively charged ion fluids) dusty plasma. These are modified Alfvén waves for small value of and are modified magnetosonic waves for large , where is the angle between the directions of the external magnetic field and the wave propagation. A nonlinear evolution equation for the wave magnetic field, which is known as Korteweg de Vries (K-dV) equation and which admits a stationary solitary wave solution, is derived by the reductive perturbation method. The effects of external magnetic field and dust characteristics on the amplitude and the width of these solitary structures are examined. The implications of these results to some space and astrophysical plasma systems, especially to planetary ring-systems, are briefly mentioned. Received 8 July 1999 and Received in final form 11 October 1999     

Dynamo-optical effects in a plasma

The propagation of electromagnetic waves in a nonuniformally moving cold electron plasma with no external magnetic field and collisions is considered. The motion is assumed to be stationary. It is shown that in the case of smooth variation of the parameters of the medium the trajectories of the rays in the zero approximation of geometric-optics are determined by the concentration distribution, while the motion leads to rotation of the polarization plane in the wave. For plane-stratified flow with a constant velocity gradient an exact solution of the equations is determined which constitutes the superposition of two independent waves that are elliptically polarized in opposite directions. The refraction law of these waves is found, and the corresponding reflection and penetration coefficients are calculated in the case of a layer having a finite thickness.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 2, pp. 183–190, February, 1972.     

Computational and experimental investigation of the fields generated by a 1-3 piezocomposite transducer

Large-scale three-dimensional numerical simulations using the finite-difference time domain technique are used to compute the continuous wave fields associated with a composite transducer. The interior of the transducer is made of a periodic array of square rods. This lattice causes elastic wave Bragg diffraction similar to electrons in a periodic lattice. A low frequency mode shape is assumed for the rods. This prescribed motion includes longitudinal and transverse components. It is shown that the transverse motion in the rod gives rise to shear waves causing standing waves (lateral resonances) in the polymer regions. This is also confirmed by experimental results presented here and other independent analytical and experimental work. The full-scale numerical simulation is performed on a large parallel supercomputer and permits modeling of not only the composite transducer but the radiated pressure from near to far field. In addition, cover plates and edge effects are included, unlike analytical treatments. Although only mechanical effects are included, the wave propagation approach captures many essential features.     

QCM based sensor for detecting volumetric properties of liquids

We introduce a microacoustic sensor, which combines the quartz crystal microbalance, a liquid-filled cavity and an intermediate artificial layer with effective acoustic properties. Each of the three components fulfils a specific task. The quartz vibrates in its thickness shear mode and acts as source and detector of shear waves, which penetrate the intermediate artificial layer and excite a resonance in the liquid-filled cavity. Both the piezoelectric transducer and the liquid-filled cavity are high-Q resonators with well-adjusted resonance frequencies very close to each other. The intermediate artificial layer couples the two resonators in a distinct manner via control of the propagation of acoustic waves between the quartz crystal and the liquid-filled cavity layer. The origin of the sensor signal is a change of the resonance frequency of the liquid-filled cavity caused by variations of acoustic properties of the liquid analyte inside the cavity, first of all speed of sound. This resonance appears as second resonance peak in the admittance spectrum of the quartz crystal.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

DISCRETE HUYGENS' MODELLING APPROACH TO WAVE PROPAGATIONS IN A HOMOGENEOUS ELASTIC FIELD

The application of the discrete Huygens' modelling has been discussed for acoustic wave propagation problems, in which the scalar wave field problems have been focused. The present paper extends the application of the modelling to the elastic wave propagation in a homogeneous elastic medium in which two types of waves, the longitudinal wave and the shear wave, are independent except at the boundary. Each wave can be treated like a scalar wave until the two waves reach the boundary where they couple so as to satisfy the displacement or stress boundary condition. We propose the approach confining ourselves to the two-dimensional field. Some examples are demonstrated, whose solutions are compared with the vectorial wave modelling and finite difference modelling solutions whenever they are available.     

圆柱空腔上裂纹的爬波检测方法

通过牛顿迭代法求解了固体内部圆柱空腔上爬波的频散方程,分析了爬波的频散和衰减特性。利用动态光弹法显示了爬波的直观图像和圆柱空腔附近各散射波的空间关系。根据爬波具有的频散、衰减以及辐射横波特征,设计了斜入射脉冲回波实验装置,测量了特定位置处裂纹反射爬波辐射出的横波信号,其与柱面反射波的时差和理论预测一致。进一步实验研究发现,爬波回波幅度与特定位置的裂纹长度具有近似单调的对应关系,在裂纹长度较大时,回波幅度趋于稳定。以上工作为圆柱空腔上裂纹的爬波定量检测提供了物理基础和实现方法。      

Measurement of sound-pressure distribution in replicas of the oral cavity.

The spatial distributions of sound pressure in artificial oral cavities were measured to examine the characteristics of wave propagation in the vocal tract. The measurement was performed with plaster replicas of the oral cavity, and pure tones were used as the driving signals to obtain both amplitude and phase distributions at varied frequencies. Plane-wave propagation, which has been widely assumed for speech production models, was examined from the measured spatial distributions of sound pressure. Trajectories of media particles and vectorial maps of acoustic intensity, which can be computed from the measured pressure distributions, were also presented to visualize the acoustic field in the oral cavity. The results showed that at certain frequencies there existed points where sound pressure was absolutely zero, with the phase spatially circulating around them. Up to about 4 kHz, except at these certain frequencies, the wave front was almost one-dimensional, though an amplitude gradient was seen in the vertical direction.     

Polarization of elastic waves in tellurium single crystal

We study special cases of elastic bulk wave propagation in a crystal of tellurium, in which the phase velocity of shear waves can exceed those of longitudinal waves. The impact of the piezoelectric effect on the phase velocity and polarization of waves is discussed.