Wave propagation along the boundary between a saturated porous medium and a liquid

The frequency dependences of the velocity and attenuation of waves propagating along the boundary between a saturated porous medium and a liquid are investigated. It is shown that, depending on the parameters of the saturated porous medium and the boundary conditions, the propagation of one, two, or three surface waves is possible, each of them being either a true mode or a pseudomode. The results of the study agree well with other investigations carried out in the high-frequency approximation.     

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.     

On wave propagation in a random micropolar thermoelastic medium,second moments,and associated Green’s tensor

The couple stress theory developed by Eringen comprises granular materials as also composite fibrous materials. As such, micropolar materials present an inclusive model of composite materials. This article endeavors to study aspects of wave propagation in a random weakly thermal micropolar elastic medium. The smooth perturbation technique has been employed. The classical thermoelasticity has been used. Six different types of waves have been observed to propagate in the random interacting medium. Dispersion equations have been derived. The effects due to random variations of micropolar elastic and thermal parameters have been observed. Change of phase speed occurs on account of randomness. Attenuation coefficients for high-frequency waves have been computed. Second moment properties have been discussed with application to wave propagation in the random micropolar elastic medium. 36 + 1 components of the associated Green’s tensor have been computed. Integrals involving correlation functions have been transformed to radial forms. A special type of correlation function has been used to approximately measure effects of random variations of parameters.     

Reference-wave solutions for the high-frequency fields in inhomogeneous-background random media

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is therefore desirable to have a solution for the high-frequency field propagating along an isolated ray trajectory. A new reference wave is applied to obtain an analytic solution of the parabolic wave equation that describes propagation along the ray trajectory of the deterministic-background medium. The methodology is based on defining a paired-field measure as a product of an unknown field propagating in a disturbed medium and the complex-conjugate component propagating in a medium without random fluctuations. When a solution of the equation for the paired-field measure is obtained, the solution of the deterministic component can be extracted from the paired solution to determine the solution of the unknown field in an explicit form.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Time reversing solitary waves

We present new results for the time reversal of nonlinear pulses traveling in a random medium, in particular for solitary waves. We consider long water waves propagating in the presence of a spatially random depth. Both hyperbolic and dispersive regimes are considered. We demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear (shallow water) conservation law is regularized leading to a viscous shock profile. This enables time-reversal experiments beyond the critical time for shock formation. Furthermore, we present numerical experiments for the time-reversed refocusing of solitary waves in a regime where theory is not yet available. Solitary wave refocusing simulations are performed with a new Boussinesq model, both in transmission and in reflection.     

被孔隙介质约束的弹性杆中的导波*

为了研究导波在被孔隙介质约束的弹性杆结构中的传播规律,分析孔隙参数对导波传播特性的影响,本文建立了无限大孔隙介质包裹圆柱体的理论模型,利用孔隙介质弹性波动理论,分析了导波的频散曲线,以及圆柱半径和孔隙参数对于导波传播特性的影响。结果表明,在该结构中传播的纵向导波存在频散特性。内部圆柱半径的改变影响波导结构,从而影响导波传播。外部孔隙介质的渗透率对于导波频散的影响较小,孔隙度的改变影响孔隙介质体波波速,从而影响导波频散曲线的截止频率。同时,导波存在较小的衰减,且衰减随孔隙度增大而增大。这些结果对于后续开展无限大介质包裹弹性杆结构的超声无损评价提供了一定的理论参考。     

The nonreciprocal effect under low- and high-frequency collinear acousto-optic interactions

The nonreciprocal effect under collinear acousto-optic interaction in the low- and high-frequency regimes is studied theoretically. The magnitudes of nonreciprocity determined from the ultrasonic frequency and from the wavelength of light are shown to be quantitatively identical. An expression that governs the magnitude of the nonreciprocity and that is valid for both low- and high-frequency regimes of the collinear acousto-optic interaction is obtained. The shape and width of the frequency characteristic of the collinear acousto-optic interaction calculated in the low diffraction efficiency approximation are shown to be the same in the low- and high-frequency regimes. The dependence of the frequency bandwidth of the collinear acousto-optic interaction on the ultrasonic-wave attenuation and diffraction efficiency is obtained. The magnitude of the nonreciprocal effect in some of the crystals used in acousto-optics is estimated numerically. The nonreciprocity of the collinear interaction is shown to be substantially stronger in the high-frequency regime relative to the low-frequency regime. Sapphire is proved to be an optimal material for experimental realization of the nonreciprocal effect in the high-frequency regime.     

Tempered relaxation with clustering patterns

This work is motivated by the relaxation data for materials which exhibit a change of the relationship between the fractional power-law exponents when different relaxation peaks in their dielectric susceptibility are observed. Within the proposed framework we derive a frequency-domain relaxation function fitting the whole range of the two-power-law dielectric spectroscopy data with independent low- and high-frequency fractional exponents γ and −α, respectively. We show that this effect results from a contribution of different processes. For high frequencies it is determined by random stops and movement of relaxing components, and the low-frequency slope is caused by clustering in their temporal changes.     

Ray theory for a locally layered random medium

We consider acoustic pulse propagation in inhomogeneous media over relatively long propagation distances. Our main objective is to characterize the spreading of the travelling pulse due to microscale variations in the medium parameters. The pulse is generated by a point source and the medium is modelled by a smooth three-dimensional background that is modulated by stratified random fluctuations. We refer to such media as locally layered .

We show that, when the pulse is observed relative to its random arrival time, it stabilizes to a shape determined by the slowly varying background convolved with a Gaussian. The width of the Gaussian and the random travel time are determined by the medium parameters along the ray connecting the source and the point of observation. The ray is determined by high-frequency asymptotics (geometrical optics). If we observe the pulse in a deterministic frame moving with the effective slowness , it does not stabilize and its mean is broader because of the random component of the travel time. The analysis of this phenomenon involves the asymptotic solution of partial differential equations with randomly varying coefficients and is based on a new representation of the field in terms of generalized plane waves that travel in opposite directions relative to the layering.     

Properties of the zeroth-, first-, and higher-order approximations of attributes of elastic waves in weakly anisotropic media

Use of the perturbation theory in the study of attributes of elastic waves propagating in weakly anisotropic media leads to approximate but transparent and simple formulas, which have many applications in forward and inverse wave modeling. We present and study such formulas. We show that all studied attributes depend on elements of a matrix linearly dependent on parameters of a medium. We study this dependence with the goal to understand which parameters of the medium, and in which combinations, affect individual wave attributes. Alternative auxiliar vector bases, in which the matrix can be specified, are proposed and studied. The vector bases offer alternative specifications of polarization vectors of qS waves. One of the important observations is that the higher-order (n > or = 2) perturbation formulas for qS waves are obtained separately for qS1 and qS2 waves. We also study effects of the use of the perturbation theory on the accuracy of the determination of the acoustical axes in weakly anisotropic media. We show that longitudinal directions in the first-order approximation are identical with actual ones. In singular directions, however, the first-order formulas provide directions, which may deviate from the exact ones, or they may even indicate false singular directions. Again, the above-mentioned matrix depending linearly on the parameters of the medium plays a central role in this study.     

Rayleigh wave propagation along the boundary of a non-Newtonian fluid-saturated porous medium

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.     

Optimal Acoustic Attenuation of Weakly Compressible Media Permeated with Air Bubbles

Based on fuzzy logic （FL） and genetic algorithm （GA）, we present an optimization method to obtain the optimal acoustic attenuation of a longitudinal acoustic wave propagating in a weakly compressible medium permeated with air bubbles. In the optimization, the parameters of the size distribution of bubbles in the medium are optimized for providing uniformly high acoustic attenuation in the frequency band of interest. Compared with other traditional optimization methods, the unique advantage of the present method is that it can locate the global optimum quickly and effectively in need of knowing the mathematical model precisely. As illustrated by a numerical simulation, the method is effective and essential in enhancing the acoustic attenuation of such a medium in an optimal manner. The bubbly medium with optimized structural parameters can effectively attenuate longitudinal waves at intermediate frequencies with an acoustic attenuation approximating a constant value of lO（dB/cm）. Such bubbly media with optimal acoustic attenuations may be applied to design acoustic absorbent by controlling broader attenuation band and higher efficiency.     

Wave processes in media with hysteretic nonlinearity: Part 2

Nonlinear processes caused by the propagation of low-frequency and high-frequency acoustic pulses in an unbounded medium and the propagation of continuous waves in a ring resonator are theoretically studied on the basis of two hysteretic equations of state for media with imperfect elasticity. The profiles and parameters of pulses, the resonance curve and the Q factor of the resonator, and the ratio of the nonlinear resonance frequency shift to the nonlinear damping decrement are determined. For nonlinear wave processes in such media, the distinctive features that allow one to choose an appropriate hysteretic equation of state for analytically describing the experimental data are revealed.     

Reference-wave solutions for high-frequency fields propagating in random media

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. According to the ray approach, the field at the observer can be synthesized from a variety of field species arriving along multiple ray trajectories resulting from refraction and scattering from boundaries and from scattering centers embedded in the random medium. For computations of the statistical measures, it is desirable therefore to possess a solution for the high-frequency field propagating along an isolated ray trajectory. For this reason, a new reference-wave method was developed to provide an analytic solution of the parabolic-wave equation.     

Singular value distribution of the propagation matrix in random scattering media

The distribution of singular values of the propagation operator in a random medium is investigated, in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of 64 programmable transducers placed in front of a random scattering medium. The impulse responses between each pair of transducers are measured and form the response matrix. The evolution of its singular values with time and frequency is computed by means of a short-time Fourier analysis. The mean distribution of singular values exhibits a very different behaviour in the single and multiple scattering regimes. The results are compared with random matrix theory. Once the experimental matrix coefficients are renormalized, experimental results and theoretical predictions are found to be in a very good agreement. Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. Finally, the possibility of detecting a target embedded in a random scattering medium based on the statistical properties of the strongest singular value is discussed.     

Dispersion relations of waves in a rod embedded in an elastic medium

The dispersion relations of waves propagating in a system consisting of an elastic rod of radius a embedded in a linear elastic medium are investigated, and phase speeds of waves of wavelength λ which propagate under steady state conditions are determined. The dispersive behaviour is found to be dependent on several non-dimensional parameters defined by the geometric ratio $\text{a}\text{λ}$, as well as on non-dimensional ratios of the rod-medium properties. It is shown that the resulting waves which can propagate under steady state conditions are surface waves which decay with the radial distance and which permit no radiation damping of energy. It is further shown that such waves can propagate freely only if the propagation speed of longitudinal waves in the corresponding free rod is less than that of shear waves propagating in the medium. Results are presented by means of dispersion curves and surfaces. From a study of the analytical results obtained, lower and upper bounds on the phase speeds are established.     

Measuring high-frequency wave propagation in railroad tracks by joint time-frequency analysis

The behavior of high-frequency elastic waves propagating in railroad tracks is relevant to the field of rail noise generation and long-range rail inspection. While a large amount of theoretical and numerical work exists to predict transient vibrations propagating in rails, obtaining experimental data has been particularly challenging due to the multimode and dispersive behavior of the waves.In this work a joint time-frequency analysis based on the Gabor wavelet transform is employed for characterizing longitudinal, lateral and vertical vibrational modes propagating in rails in the 1000- range. The Gabor transform optimizes the time-frequency resolution of the measurements and theoretically requires a single excitation point and a single measurement point. These features make the analysis well-suited for the study of wave propagation in rails.The theory of the wavelet transform is reviewed in the context of dispersive measurements. Accelerometer data were taken from a section of rail subject to impulse dynamic testing in the laboratory. The group (energy) velocity dispersion curves and the frequency-dependent attenuation of the waves were successfully extracted from the wavelet scalograms of the accelerometer signals.