Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

<正>The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated.The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves,pseudo-Rayleigh waves,flexural waves,and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients.The corresponding acoustic waveforms illustrate their properties in time domain.The results are also compared with those based on generalized Biot's theory.The results show that the influence of non-Newtonian effect on acoustic guided wave,especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.     

A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation

A 2.5-dimensional method in frequency wave-number domain is developed to investigate the mode waves in a deviated borehole penetrating a transversely isotropic formation. The phase velocity dispersion characteristics of the fast and slow flexural mode waves excited by a dipole source are computed accurately at various deviation angles for both hard and soft formations. The sensitivities of the flexural mode waves to all elastic constants in a transversely isotropic formation are calculated. Numerical results show that, for a soft formation, the fast flexural mode wave is dominated by c66 at high deviation angles and low frequencies, while the slow flexural mode wave is dominated by c44 at the same conditions. Waveforms in time domain are also presented to support the conclusions.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.     

Homogenization of Three-Dimensional Periodic Solid-Solid Elastic Composites

We develop an approach to homogenize three-dimensional periodic solid-solid elastic composites with cubic lattice at low frequencies, by using plane wave expansion and perturbation theory with respect to the long wavelength limit. Based on the fact that the two shear waves propagating along lattice axis are degenerated, we derive formulae for effective velocities parallel and normal to the lattice axis, from which three independent effective elastic moduli are calculated, respectively. Theoretical results, which take into account the multiple scattering and the structure of the periodic medium, are in good agreement with the previous isotropic theory at high-symmetry directions.     

Thickness-shear modes and magnetoelastic waves in a longitudinally magnetized ferromagnetic plate

Magnetoelastic (ME) waves and thickness-shear modes in the ferromagnetic plate are studied. Coupled vibrations of magnetization and shear elastic deformations excited simultaneously by a variable magnetic field propagate in two mutually perpendicular directions: parallel and normal to a surface. For parameters characteristic of isotropic ferromagnet with the sample magnetization and Zeeman field parallel to the surface, resonant frequencies of shear modes are computed and their dispersion law is examined. It is shown that the dependence of dimensional resonances frequencies on wave number k_z of ME wave propagating along saturating field direction occurs. The possibility of excitation of ME waves with different k_z explains multimode character of thickness ME resonances.     

沿均匀无限介质中固体杆传播的导波特性研究

针对均匀无限固体介质包围的无限长固体杆,研究了沿固体杆传播的导波的频散和激发特性。在理论分析的基础上,用二分法快速求取了导波所有模式的频散曲线,在4种介质参数下,对斯东利模式和简正模式进行了深入的分析和总结;研究了固体杆中导波的激发强度特性,分别在对称点源、轴向力源和径向力源激励下,研究了导波诸模式的激发机理及频谱特性,分析了不同频段导波的主导模式,研究了主导模式的频响特性及位移径向分布关系。      

Propagation properties of elastic waves in semi-infinite phononic crystals and related waveguides

The transmission and reflection coefficients of two-dimensional semi-infinite solid-solid phononic crystal systems and fluid-fluid phononic waveguide structures have been investigated. The numerical results show that the transmission spectra for longitudinally and transversally polarized incident waves are different, and the spectra of the transmission and reflection coefficients of the semi-infinite system agree well with the band structure. The numerical results show that when a guided wave incident, localized modes are excited, and different polarities have different coupling efficiencies with the incident guided wave. At the same time, far from the cutoff frequency, the guided wave couples out of semi-infinite waveguide highly efficiently.     

Electroseismic waves excited by vertical magnetic dipole in borenole

Acoustic and electromagnetic fields are coupled in a fluid saturated porous medium due to seismoelectric effect. Seismoelectric well logging method has been proposed to detect deep target formation utilizing such effect. Because of uncoupling of SH waves with P-SV waves, a simple and forthright way to get shear waves information is possible, especially for soft or slow formation whose shear wave velocity is lower than the velocity of borehole fluid. We consider the wave fields excited by a vertical magnetic dipole (VMD) source. Two methods are used to simulate, one is the coupled method based on Pride model and the other is the uncoupled method. For two methods, the frequency wavenumber domain representations of the acoustic field and associated seismoelectric field are formulated. The full waveforms of acoustic waves and electromagnetic wave induced SH waves excited by VMD source in the time domain propagation in borehole are simulated and analyzed.     

Rayleigh wave dispersion and attenuation on a statistically rough free surface of a hexagonal crystal

Dispersion and attenuation of Rayleigh surface acoustic waves on a statistically rough free surface of a Z-cut hexagonal crystal were analytically studied using a modified mean-field method within the perturbation theory. Numerical calculations were carried out in the frequency range accessible for the perturbation theory using expressions for the real and imaginary parts of the complex frequency shift of Rayleigh waves caused by a slight surface roughness. The Rayleigh wave dispersion and attenuation in the Z-cut hexagonal crystal were shown to coincide qualitatively with those in an isotropic medium, differing only quantitatively. In the long-wavelength limit λ?a, where a is the lateral roughness correlation length, explicit analytical expressions for the relative change in the phase velocity and the inverse damping depth of Rayleigh waves were derived and used in numerical calculations.     

Stoneley wave generation by an external seismic point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation: Basic relationships

The method of integral transformations is used to obtain a long-wave solution to the problem of tube wave excitation by an external point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation. The external field that occurs in the formation gives rise to waves in the borehole fluid. The waves generated in the borehole include the lowest mode of the Stoneley wave (tube wave), which is the borehole eigenmode, and the qP-and qSV-waves. It is shown that the Stoneley wave is determined by the contributions of two poles in the complex plane of horizontal slowness. According to the asymptotic solution, the Stoneley wave can be described by one of three different waveforms depending on the relationship between the elastic parameters of the surrounding anisotropic formation and the borehole fluid. An analysis of the results of calculations shows that the shape and polarity of the Stoneley wave strongly depend on the sign of the nonellipticity parameter of the elastic medium, which offers a possibility of estimating the anisotropy of the borehole environment from observations of the waveform of the Stoneley wave.     

偶极子声波测井在套管井中的声场特征*

偶极子声波测井在套管井中的应用越来越多,本文重点研究了套管井不同胶结状况下偶极子声源在套管井中激发的声场特征,通过解析方法分析了水泥环第一界面和第二界面不同胶结状况下井孔模式波的频散和衰减。计算结果表明,在水泥环第一界面或第二界面胶结差时井孔声场中可观测地层弯曲波和套管弯曲波;与胶结良好时相比,地层弯曲波的频散曲线向低频偏移,水泥环第二界面胶结差时偏移较大;套管弯曲波对水泥界面存在的流体环厚度很敏感,随着流体环厚度的增加套管弯曲波的相速度逐渐增大,激发幅度也明显增强,这一特征为利用套管弯曲波的相速度估算流体环厚度提供了可能。本文的计算结果为利用套管井中越来越多的偶极子声波测井资料评价水泥胶结质量奠定了理论基础。     

Ultrasonic guided wave focusing by a generalized phased array

Ultrasonic guided wave focusing by a generalized phased array is studied based on dispersion curves in a multi-layered medium. The different phase of the guided waves with different frequency is added on the excitation signal on each element of the transducer array for focusing. This can be realized by designing a proper excitation pulse based on the dispersion curves of the guided waves for each of the transducer array elements. The numerical simulation results show that the guided waves with different modes, different frequency components, and from different elements of the transducer array can all be focused at the target and focusing is achieved.     

Shear-horizontal transverse-electric seismoelectric waves in cylindrical double layer porous media

The shear-horizontal(SH) waves excited by the shear source in a borehole are easy to analyze due to the simple waveform. The borehole-side structures make the formation properties discontinuous. We consider a cylindrical double layer structure and study the borehole shear-horizontal and transverse-electric(SH-TE) seismoelectric waves. We first derive the expressions of the basic field quantities, and simulate the acoustic field and electric field using the real axis integral method. Compared with the wave fields of an infinitely homogeneous porous medium outside the borehole, the cylindrical layered structure makes the multi-mode cylindrical Love waves and their accompanying electric fields excited.Next, in order to study the interface response law of the inducing electric fields, we use the secant integral method to calculate the interface converted electromagnetic waves and analyze the causes of each component. It is found that an interface response occurs each time the SH wave impinges the interface in the layered porous medium. The results show that the SH-TE mode has a potential application for borehole-side interface detection in geophysical logs.     

Propagation characteristics of guided waves in a rod surrounded by an infinite solid medium

The dispersion and excitation characteristics of the guided waves in a rod surrounded by an infinite solid medium (cladding) are investigated. First, the bisection technique is employed to find all the roots of the dispersion function on the basis of theoretical analysis and to obtain the complex phase and group velocity dispersion curves of the guided modes. Second, according to their different dispersion characteristics, the guided modes are divided into two categories: normal modes and Stoneley modes. And it is concluded that the normal modes merely exist in the “hard cladding” model in which the cladding’s shear velocity is larger than the rod’s; while the Stoneley modes in cylindrical interface are highly dispersive and merely exist in the model whose acoustical parameters satisfied the existence condition of the Stoneley waves. Third, the seldom discussed issue, the excitation mechanisms of the guided waves, excited by three source models: symmetric point source, axial and radial force sources, are simulated respectively. Attention is paid on the dominant mode which has better excitation sensitivity and the suitable excitation frequency range. Moreover, the propagation characteristics of the Stoneley modes, ignored in previous references, are analyzed and compared with those of the normal modes.     

分层固体板中导波的激发与频散特性

针对无限大弹性分层固体板,研究了结构中导波的频散和激发特性。首先使用传递矩阵法推导分层板模型中导波的频散方程,然后用二分法求取导波各模式的频散曲线,进而分析结构中导波的频散特性。结果表明:在速度递增或递减的分层板中,基阶模式和高阶模式的高频极限分别等于低速层的瑞利波速和横波波速。对于含低速夹层的分层板,所有模式的高频极限都等于低速层的横波速度。在导波激发特性方面,研究了在具有一定宽度的法向力源作用下的分层板中导波各模式在结构中的法向位移谱。发现在速度递增的分层板结构中基阶模式是主导模式,而对于速度递减和含低速夹层模型,主导模式在不同的频段范围内对应不同的导波模式。      

Self-consistent renormalized phonons in metallic and nonmetallic solids

The interaction of charged particle beam with non-linear “cubic” type media has been studied; the dielectric permeability of such media depends on the square strength of the electric field produced by the beam-excited wave. The processes of the Cherenkov excitation of the medium by a modulated definite current are investigated as well as the polarization of longitudinal oscillations of the medium excited by the current. The equations are obtained to determine the dependence of fields excited by the current on the amplitude of the exciting current. It is found that under certain circumstances (near the radiation cut-off) the conditions of Cherenkov radiation may be violated due to non-linearities of the medium and the particle radiation loss vanish. The amplification of longitudinal waves in an arbitrary isotropic medium with “cubic” non-linearity by a monoenergetic particle beam is studied when the frequencies of amplified oscillations are close to the resonance frequencies of the medium.     

Elastic waves excited by a plane source on the surface of a multilayered medium

Elastic waves excited by a plane piezoelectric source with an arbitrary shape on the surface of a multilayered medium have been studied for the first time in this paper. On the basis of Abzo-zena [Geophys. J. R. Astron. Soc. 58, 91-105 (1979)] and Menke [Geophys. J. R. Astron. Soc. 59, 315-323 (1979)], the propagator matrix for the elastic wave field in multilayered medium is extended from two- to three-dimensional (3D) space. 3D elastic wave field is investigated and the displacement-stress response for the boundary conditions is obtained. The propagation of elastic wave in multilayered media is analyzed in 3D space in the frequency domain. The P-SV and SH modes corresponding to the poles are studied. The excitation and propagation of the modes are analyzed further. It is found that the propagation velocities of the P-SV and SH modes do not depend on the propagation azimuth theta in the plane parallel to the free surface of the multilayered medium while the displacement amplitudes are strongly dependent on the azimuth theta. The directional distribution functions of the modes are independent of the medium parameters and the modes and dependent on the shape and excitation fashion of the source. Finally, as an example, the displacement fields of the P-SV and SH modes excited by a rectangle source are analyzed. The displacement representation and numerical results of the directivity distribution functions for the P-SV and SH modes are obtained.     

Measurement of the dispersion relation of guided non-axisymmetric waves in filament-wound cylindrical structures

To determine the dispersion relation, guided waves are excited in specimens over a broad frequency range. The surface displacements are measured over time and space. The recorded data are analysed using a quasi-three-dimensional spectrum estimation algorithm. In the time domain a fast Fourier transform is used to extract the frequencies. To obtain the wave numbers, in space a two-dimensional matrix-pencil approach is applied to the data set. Using a suitable constitutive model (transversely isotropic or orthotropic) dispersion curves are calculated. Good agreement was found between the experimental and the numerically calculated dispersion relations after adjusting the material parameters. Since the dispersion relation of a structure depends on the mechanical material properties frequency-dependent material parameters can be extracted from the above-mentioned relation between frequency and wave number.     

Magneto-optical effects in crystals at the normal incidence

We consider the interaction of a polarized electromagnetic wave in a magnetically ordered crystal plate surrounded by an isotropic ambient at the normal incidence. The crystalline medium of the plate is specified by the general non-symmetric permittivity tensor. The results are expressed in terms of the transmission and reflection matrices which relate the electric fields of the incident wave to those of transmitted and reflected waves. Their applications are illustrated by examples of an isotropic plate magnetized normal to the interface, a cubic crystal magnetized parallel to the interface and an orthorhombic crystal magnetized along the axis normal to the interface. The effect of the reflection from the interfaces and the interference effect are included. The paper treats the reflection at an interface between an isotropic ambient and an absorbing magnetic crystal at small non-zero angles of incidence. The general reflection matrix is applied to the determination of the magneto-optical effects quadratic in magnetization.