Scattering of acoustic waves by elastic and viscoelastic obstacles immersed in a fluid

A scattering or T-matrix approach is presented for studying the scattering of acoustic waves by elastic and viscoelastic obstacles immersed in a fluid. A Kelvin-Voigt model is used to obtain the complex elastic moduli of the viscoelastic solid. The T-matris formulation is somewhat complicated because the wave equations and fields are quite different in the solid and fluid regions and are coupled by continuity conditions at the interface. We have obtained fairly extensive numerical results for prolate and oblate spheroids for a variety of scattering geometries. The backscattering, bistatic, absorption and extinction cross-section are presented as a function of the frequency of the incident wave.     

Wave dispersion in randomly layered materials

Wave scattering in materials composed of two kinds of alternating layers with different elastic properties and randomly distributed thicknesses has been modeled. The general form of the dispersion equation is derived for the unbounded layered medium. It defines two basic macroscopic characteristics of the scattered wave: phase velocity and attenuation, which are explicit functions of wave frequency and microscopic parameters of the system: acoustic properties of the layers and stochastic characteristics of their thickness distributions. The analytical expressions are derived for three special cases: for long waves; for a periodic medium composed of layers with constant thicknesses and for random medium with uniform distribution of layer thicknesses. Special attention is paid to the analysis of the frequency dependence of the wave parameters. It was shown that the predictions of the model for long waves and for periodic medium are compatible with the results obtained in the literature.Moreover, comparison of theoretical results for frequency dependent wave parameters with numerical simulations of pulse transmission through the slab of the randomly layered medium shows good qualitative and quantitative agreement in wide frequency range.     

A novel method for investigation of acoustic and elastic wave phenomena using numerical experiments

The emergence of new types of composite materials, the depletion of existing hydrocarbon deposits, and the increase in the speed of trains require the development of new research methods based on wave scattering. Therefore, it is necessary to determine the laws of wave scattering in inhomogeneous media. We propose a method that combines the advantages of a numerical simulation with an analytical study of the boundary value problem of elastic and acoustic wave equations. In this letter we present the results of the study using the proposed method: the formation of a response from a shear wave in an acoustic medium and the formation of shear waves when a vertically incident longitudinal wave is scattered by a vertical gas-filled fracture. We have obtained a number of analytical expressions characterising the scattering of these wave types.     

Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack

Nonlinear scattering of ultrasonic waves by closed cracks subject to contact acoustic nonlinearity (CAN) is determined using a 2D Finite Element (FE) coupled with an analytical approach. The FE model, which includes unilateral contact with Coulomb friction to account for contact between crack faces, provides the near-field solution for the interaction between in-plane elastic waves and a crack of different orientations. The numerical solution is then analytically extended in the far-field based on a frequency domain near-to-far field transformation technique, yielding directivity patterns for all linear and nonlinear components of the scattered waves. The proposed method is demonstrated by application to two nonlinear acoustic problems in the case of tone-burst excitations: first, the scattering of higher harmonics resulting from the interaction with a closed crack of various orientations, and second, the scattering of the longitudinal wave resulting from the nonlinear interaction between two shear waves and a closed crack. The analysis of the directivity patterns enables us to identify the characteristics of the nonlinear scattering from a closed crack, which provides essential understanding in order to optimize and apply nonlinear acoustic NDT methods.     

Boundary element modeling for defect characterization potential in a wave guide

Wave scattering analysis implemented by boundary element methods (BEM) and the normal mode expansion technique is used to study the sizing potential of two-dimensional shaped defects in a wave guide. Surface breaking half-elliptical shaped defects of three opening lengths (0.3, 6.35 and 12.7 mm) and through-wall depths of 10–90% on a 10 mm thick steel plate were considered. The reflection and transmission coefficients of both Lamb and shear horizontal (SH) waves over a frequency range 0.05–2 MHz were studied. A powerfully practical result was obtained whereby the numerical results for the S₀ mode Lamb wave and n₀ mode SH wave at low frequencies showed a monotonic increase in signal amplitude with an increase in the defect through-wall depth. At high frequency (usually above the cut-off frequency of the A₁ mode for Lamb waves and the n₁ mode for SH waves, respectively), the monotonic trend does not hold in general due to the energy redistribution to the higher order wave modes. Guided waves impinging onto an internal stringer-like an inclusion were also studied. Both the Lamb and SH waves were shown to be insensitive to the stringer internal inclusions at low frequency. Experiments with piezoelectric Lamb wave transducers and non-contact SH wave electro-magnetic acoustic transducers (EMAT) verified some of the theoretical results.     

Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer

The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato (Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13(2), 125–147 (1983)). The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. (Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6(4), 241–249 (2003)). The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.     

Scattering of an incident wave from an interface separating two fluids

We consider the scattering of an incident pulse from an interface separating two fluids. The interface can be either an elastic membrane or a two-fluid interface with surface tension. By considering the limit where the ratio of acoustic wavelength to the surface wavelength is small, we systematically derived a boundary condition relating the scattered wave and the surface deformation. This condition is local and can be used to derive a partial differential equation for the deformation of the interface. This equation includes the contribution of the acoustic waves induced by the motion of the interface and once it is solved it can be used to determine the scattered field. At leading order in our analysis we find the plane wave approximation. The addition of the next order terms results in an on surface condition equivalent to that of Kriegsmann and Scandrett. We present numerical calculations to show that our results are in good agreement with the exact numerical solution as well as that of Kriegsmann and Scandrett. Physical situations where the conditions of our analysis are valid are presented.     

Linearized inverse scattering for elastic parameters in a half-space with reflection data

ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｌｔｉｐａｒａｍｅｔｅｒｉｎｖｅｒｓｅｓｃａｔｔｅｒｉｎｇｆｏｒｅｌａｓｔｉｃｍｅｄｉｕｍｉｓａｆｏｕｎｄａｔｉｏｎａｌｐｒｏｂｌｅｍｉｎｓｅｉｓｍｏｌｏｇｙａｎｄｎｏｎｄｅｓｔｒｕｃｔｉｖｅｔｅｓｔｉｎｇ .ＷｉｔｈｉｎｔｈｅＢｏｒｎａｐｐｒｏｘｉｍａｔｉｏｎ ,ｔｈｉｓｐｒｏｂｌｅｍｈａｓｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｂｙｓｅｖｅｒａｌａｕｔｈｏｒｓ.Ｂｌａｃｋｌｅｄｇｅｅｔａｌ.[1]ｈａｖｅｅｘｔｅｎｄｅｄｔｈｅＸ＿ｒａｙｔｏｍｏｇｒａｐｈｙｓｃｈｅｍｅｔｏｔｈｅｄ…     

Self-demodulation acoustic signatures for nonlinear propagation in glass beadsSignatures acoustiques de l'auto-démodulation basse fréquence lors de la propagation non linéaire dans des billes de verres

The present Note describes some experimental work related to the nonlinear propagation of acoustic waves in granular media such as unconsolidated glass beads. The studied nonlinear effect is a self-demodulation process performed with the operation of the so-called parametric transmitting antenna. The pump (or carrier) wave is generated by a high power ultrasonic broad-band transducer (100 kHz central frequency) which is LF (low frequency, i.e., a few kHz) amplitude modulated. As the attenuation of acoustic waves increases with frequency, only the LF demodulated wave can be transmitted. A parametric study is performed where the HF central frequency is monitored between 60 and 300 kHz. The LF demodulation profile versus the HF frequency is modified, its shape being temporally derived almost twice. A numerical analysis of the order of temporal derivation is done in the Fourier domain, its value varying from 1.25 to 2.7. Qualitative agreement with current theoretical models is described, and an advanced theoretical analysis by the same authors [Phys. Rev. E 66 (2002) 041303], taking into account absorption, nonlinearity, dispersion and scattering, is briefly discussed. To cite this article: V. Tournat et al., C. R. Mecanique 331 (2003).     

The low frequency scatter of SH waves by a rough interface in an elastic plate

The study of the reflection and transmission of low frequency SH waves incident upon a rough interface in an elastic plate is undertaken by employing a theory of acoustic wave scattering from rough surfaces originally due to Biot and subsequently generalised to the case of elastic media. In this theory the interface is replaced by a distribution of voids/asperities whose individual size is small compared to the excitation wavelength. We plot the absolute values of the reflection and transmission coefficients versus frequency when a single symmetric SH plate mode is used as the input excitation. The different types of inclusions are used to simulate the rough surface are the hollow, fluid filled and aluminum spheres. Lastly, the loss of energy due to scattering is also estimated for the different inclusion distributions considered.     

弯曲波在含非圆孔洞无限压电薄板中的散射

基于线性压电动力学理论,采用波函数展开法、保角映射以及复变函数,对含非圆孔洞无限大压电薄板弹性波的散射及动应力集中问题进行了分析,给出了其动弯矩集中系数(DMCF)的解析表达式.为说明问题,以PZT-4为例,讨论了外加电场、椭圆孔长短半轴比、椭圆孔倾角以及入射波频率对含圆孔和椭圆孔无限大压电薄板弹性波散射的影响,并分别...     

The multi-parameter inversion of elastic wave in half-space

The multi-parameter inverse scattering problem of elastic wave equation with single frequency is investigated within Born approximation. By use of a wideband measuring scheme in which both transmitters and receivers scan over the half-space surface, the formula of the scattering field of elastic wave is derived. Four types of mode conversion of elastic wave (P→P,P→S,S→P,S→S) are separated from the scattering field. These components contain sufficient information for us to reconstruct the configurations of the density and Lamé parameters of the medium. The inverse formulas have the form of filtered back-propagation as in the acoustic diffraction tomography. Computer simulations are also obtained. Supported by Foundation of Ph.D Program of the State Education Commission of China.     

Attenuation of shock waves propagating over arrayed baffle plates

The paper reports results of shock tube experiments of the attenuation of shock waves propagating over arrayed baffle plates, which is motivated to simulate shock wave attenuation created accidentally at the acoustic delay line in synchrotron radiation factory upon the rupture of a metal membrane separating the acceleration ring at high vacuum and atmospheric test chambers. Experiments were carried out, by using double exposure holographic interferometry with double path arrangement, in a 100 mm×180 mm shock tube equipped with a test section of 180 mm×1100 mm view field. Two baffle plate arrangements were tested: Oblique and staggered baffle plates; and vertical symmetric ones. Pressures were measured along the shock tube sidewall at individual compartments for shock Mach numbers ranging from 1.2 to 3.0 in air. The results were compared with a numerical simulation. The rate of shock attenuation over these baffle plates was compared for vertical and oblique baffle plates. Shock wave attenuation is more pronounced in the oblique baffle plate arrangements than in the vertical ones. PACS 47.40.Nm; 42.40.Kw Communicated by C. Needham     

Scattering of elastic waves by a periodic array of cracks in 3-D space

The problem of scattering of normal incident time harmonic plane elastic waves by a co-planar periodic array of cracks in 3-D space is investigated. The scattered waves consist of a superposition of an infinite number of wave modes [M, N]^T and [M, N]^L,M. N=0, 1, 2, , but only a finite number of them are propagating wave modes. The numerical calculation has been made for rectangular cracks and P wave incidence. The reflection coefficient of [O, O] order,R ₀ ³ , has been studied in detail for various wave numbers and parameters of the geometry for the problem. The reliability of the numerical calculation has been checked by an application of the balance of rates of energies. For an elongated rectangular crack,R ₀ ³ in the corresponding 2-D problem in [2] is recovered. The dynamic stress intensity factors around the crack edge have been obtained. The results as the wave number goes to zero have been compared with those in the correspoding static case. Good agreement is observed.     

Exploiting the limiting amplitude principle to numerically solve scattering problems

A numerical method for solving reduced wave equations is presented. The technique is basically a relaxation scheme which exploits the limiting amplitude principle. A modified radiation condition at ‘infinity’ is also given. The method is tested on two model problems: the scattering of plane shallow water waves off shoals and the scattering of plane acoustic waves off a sound-soft cylinder imbedded between two homogeneous but different half spaces. The numerical solutions exhibit correct refractive and diffractive effects at moderate frequencies.     

不均匀磁电弹板中的厚度扭曲波的传播

压电-压磁复合材料或结构的许多应用是与弹性波的传播密切相关的,这要求人们首先从理论的角度弄清楚弹性波的传播规律。本文研究由多个不均匀磁电弹介质组成的薄板厚度扭曲波的传播性质,从磁电弹全耦合场三维方程出发得到了其精确解,根据所得到的解分析了波的传播特征,这些结果对于理解和设计谐振器、滤波器以及声波元件提供了有价值的理论基础。     

Transient analysis of a three-dimensional plate by the ray grouping technique

The propagation of transient waves in an elastic plate excited by an arbitrary loading is investigated. Exact three-dimensional transform solutions are derived for a plate suddenly loaded on one of its bounding surfaces, with the inversion effected by Cagniard's technique. The solution is based on three canonical problems for finding the n-th reflected waves from only the information on the (n − 1)-th reflected waves. The technique automatically groups rays which arrive simultaneously at one point, thus simplifying the computations needed by the ray tracing technique. A nonaxially symmetric sample loading is selected for demonstrating the technique, and numerical results are presented. The Ray Grouping Technique can be extended to the layered medium case.     

缺陷岩体中弹性波传播的多次散射效应分析

弹性波在岩体中传播时与岩体缺陷相互作用形成复杂的传播图案。为研究缺陷对弹性波多次散射作用的影响,建立了双椭圆缺陷模型,基于Green函数基本解,采用边界积分的计算方法,得到了反映缺陷界面条件的刚度矩阵,分析了弹性波在双椭圆缺陷间的多次散射效应。结果表明：与单椭圆缺陷模型相比,双缺陷的相互作用使得弹性波频散和衰减效应增强,定量给出了缺陷的影响区域,从而明确了多次散射效应的尺度界限。进一步探讨了弹性波传播的多尺度效应,结果表明频散的Rayleigh峰、Mie峰和衰减的峰值频率同椭圆长轴和入射波波长两个尺度密切相关,存在明确的定量关系。相应的数值模拟结果表明,弹性波和缺陷相互作用在缺陷界面上诱发界面波,该界面波也存在频率相关性,影响了弹性波宏观传播的频散和衰减特征。     

Scattering coefficient reconstruction in plates using focused acoustic beams

A method has been developed and proven using highly focused acoustic beams that allows for the rapid reconstruction of scattering coefficients of a thin anisotropic plate immersed in liquid. In a single bistatic coordinate scan, nearly the entire range of wave number within the spatial and temporal frequency bandwidth of the transducer can be reconstructed. This paper also reports the development of a multiple-source complex transducer point model that includes all extrinsic factors and permits prediction of the wave number-frequency (k–f) domain result obtained from a scan of focused transducers in a pitch-catch reflection or transmission arrangement. Extensive experiments have been performed to test the method and the model and to demonstrate transducer beam effects on the k–f domain results, leading to a very efficient method for mapping major portions of the guided wave dispersion spectrum in thin-plate media. As a demonstration of the technique, an estimate of material elastic properties in an isotropic and a transversely-isotropic plate is reported, making only minimal use of the highly redundant dispersion data. Acoustic velocities inferred from these experiments show a disparity of less than 3% from contact acoustic estimates of the same parameters in either plate.     

Self-switching of displacement waves in elastic nonlinearly deformed materialsSelf-commutation d'ondes de déplacement dans les milieux élastiques non-linéaires

The problem of self-switching plane waves in elastic nonlinearly deformed materials is formulated. Reduced and evolution equations, which describe the interaction of two waves the power pumping wave and the faint signal wave are obtained. For the case of wave numbers matching the pumping and signal waves, a procedure of finding the exact solution of evolution equations is described. The solution is expressed by elliptic Jacobi functions. The existence of the power wave self-switching is shown and commented. To cite this article: J. Rushchitsky, C. R. Mecanique 330 (2002) 175–180.