Numerical simulation of ultrasonic transmission through curved interface

The direct boundary integral equation formalism is used to model reflected and transmitted wave fields due to a bounded ultrasonic beam incident upon an arbitrarily curved interface separating a fluid and a solid media. The numerical procedure involves application of point collocation with quadratic isoparametric approximation that reduce the integral equations to a discrete set of linear algebraic equations. Numerical results are provided for plane, concave and convex interfaces for incident beam profiles which are Gaussian or approximately rectangular. The case of surface wave excitation on a plane interface is considered and features of their numerical solution are discussed. Constraints on the various parameters of the numerical model and their effects on the accuracy of the solution are investigated in detail.     

Reflection of plane waves at the boundary of a pre-stressed elastic half-space subject to biaxial stretch and simple shear

This paper is concerned with the effect of finite pure homogeneous biaxial stretch together with simple shear deformation on the reflection from a plane boundary of elastic waves propagating in a half-space of incompressible isotropic elastic material. This generalizes the previous work in which, separately, pure homogeneous strain and simple shear were considered. For a special class of constitutive law, it is shown that an incident plane harmonic wave propagating in the considered plane gives rise to a surface wave in addition to a reflected wave for every angle of incidence. The amplitude of the surface wave may vanish at certain discrete angles depending on the state of stress, biaxial stretch and simple shear deformation and then specialized to recover results obtained previously. The amplitude of the reflected wave is independent of the pre-stress but does depend upon the magnitude of deformation under consideration. The dependence of the reflected and surface wave behavior on the angle of incidence, amount of shear strain, biaxial stretch and the state of stress is illustrated graphically.     

Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating an isotropic and a biaxial medium.

Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.     

Anomalous propagation of elastic waves through a boundary between liquid and magnetoacoustic material

We consider a longitudinal acoustic wave incident onto a plane boundary between a liquid and a magnetoacoustic medium representing an antiferromagnetic material with anisotropy of the easy plane type, occurring in the vicinity of an orientational phase transition with respect to magnetic field. The directions of propagation and the amplitudes of reflected and transmitted longitudinal and transverse waves are determined. The possibility of an effective field control for the refraction angle and the wave type transformation is demonstrated. Beginning with a certain critical angle of incidence, the longitudinal and, eventually, the transverse waves in the magnetic medium become inhomogeneous and slide along the interface. If the magnetic material is sufficiently close to the phase transition point, the waves can be reirradiated into the liquid medium.     

Wave propagation in a restricted class of orthotropic inhomogeneous half-planes

This work presents closed-form solutions for free-field motions in a certain type of orthotropic, continuously inhomogeneous half-planes that include both incident and reflected waves from the traction-free horizontal surface. A state of plane strain holds and both pressure and vertically polarized shear waves are considered. The methodology is restricted to media with orthotropic material characteristics that vary quadratically with respect to the depth coordinate. The method of solution is a hybrid approach based on the plane wave decomposition technique, augmented by appropriate functional transformation relations for the displacement vector. The existence of a unique analytical solution as superposition of incident P- or SV-waves and the corresponding reflected P- and SV-waves is proved under certain restrictions on the incident wave direction. Finally, a numerical study reveals the influence of material inhomogeneity and orthotropy on the displacement free-field motion.     

Phases of the SAW reflection and transmission coefficients for short reflectors on 128 degree LiNbO3

We study numerically the phase of surface acoustic waves reflected by or transmitted through short reflectors comprising only 1-3 aluminium electrodes on 128 degree YX-cut lithium niobate (LiNbO3). The electrodes have a finite thickness, and they are either open-circuited or grounded. The center-to-center distance between adjacent electrodes d corresponds roughly either to half of the characteristic wavelength d proportional to lambda0/2 or to d proportional to lambda0, for the reflectors operating at the fundamental and second harmonic modes, respectively. We use software based on the finite-element and boundary-element methods (FEM/BEM) for numerical experiments with a tailored test structure having 3 interdigital transducers (IDTs), simulating experimental conditions with an incident wave and reflected and transmitted surface acoustic wave (SAW). Using artificial enhancement of time resolution in conjunction with the fast Fourier transform (FFT) and time-gating, calculation of the Y-parameters in a relatively wide frequency range allows us to determine the phase of the reflection and transmission coefficients.     

Boundary element solution of 3-D wave scatter problems in a poroelastic medium

This study details the development of boundary integral equations suitable for treating problems involving the scatter of a plane harmonic wave by an inclusion embedded in an infinite poroelastic medium. The pore pressure-solid displacement form of the harmonic equations of motion are developed from the form of the equations originally presented by Biot. Fundamental solutions and a generalized reciprocal work relation are developed, and these are used to formulate a solution representation in terms of an integral over the inclusion surface. The corresponding boundary integral equations are developed in a form that is integrable in the usual sense, eliminating the need to evaluate Cauchy principal value integrals. These boundary integral equations are discretized and implemented into a boundary element computer program. The so-called forbidden frequency problem which causes computational difficulties in boundary integral treatments of wave scatter in elastic and acoustic media is shown to be absent in the poroelastic case. Numerical results obtained from the boundary element program are compared with analytical results for some test problems, and the program appears to produce accurate results at moderate frequencies.     

利用波动法研究曲梁结构中的波形转换和能量传递

基于Flugge理论,建立了薄壁均质常曲率曲梁面内运动的6阶微分控制方程,得到了曲梁的频散特性曲线和6种波的轴向位移和径向位移的比值,推导了位移和内力响应的表达式以及物理域和波数域的变换矩阵。利用波的传递和反射矩阵对曲梁和半无限长直梁耦合时的能量传递系数和反射系数进行了求解分析。对于半无限长直梁中给定的拉伸波或弯曲波入射,得到了和频率,曲率半径和伸展角度相关的各种波传递和反射的能量系数表达式。数值结果表明,纵波和弯曲波在经过曲梁结构之后发生了波形转换,并研究了能量传递和反射系数随频率,伸展角度,曲梁曲率半径和截面尺寸比的变化。结果表明,无限长直梁和曲梁耦合系统中,低频时,经过曲梁反射和传递后的弯曲波和纵波会相互转化;高频时弯曲波和纵波都能够没有散射地通过曲梁而进行传播。为改善高频时曲梁中的能量衰减效果,研究了在曲梁结构中插入单个、多个中间支撑或阻振质量块时的能量传递和反射系数。结果表明,阻振质量块能够很好地阻止高频时曲梁中能量的传递,对于周期分布的多个阻振质量块,能量传递系数随频率的变化存在周期结构的阻带特征。这些研究结果为曲梁结构的设计提供定性的理论基础。     

Influence of total reflection on the imaging quality of optical systems

In the case of total reflection at a boundary surface between two different optical media, the ray reflected at the boundary is spatially shifted with respect to the point where the incident ray intersects the boundary. The light penetrates into the second medium, and the evanescent electromagnetic wave propagates along the boundary. The described effect is called the Goos-H?nchen effect. Our work describes the influence of the Goos-H?nchen effect on the imaging properties of planar optical systems, and a differential equation of a wave-front meridian that corresponds to a reflected bundle of rays is derived. It is shown that the wave front can be described by the d'Alambert differential equation. This equation makes it possible to determine the coordinates of individual points on the wave-front meridian. The influence of total reflection on the value of the Strehl definition of the reflected ray bundle, is also investigated.     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

基于两向设计地震动的二维自由场构建

针对在设计地震动基础上构建平面半空间自由场的问题,在综合考虑水平向与竖直向设计地震动基础上获得平面半空间自由场,实现了将设计地震动与以任意角度组合入射的P波、SV波构成的自由场相联系。首先在已有成果的基础上,研究了以任意角度入射情况下P波及其反射波、SV波及其反射波对水平向和竖直向设计地震动的贡献;然后在假设入射P波、SV波与两向设计地震动具有相同频率组成的基础上,获得了以特定角度组合入射条件下P波、SV波的频谱和相位信息;进而通过傅里叶逆变换获得入射P波、SV波的时间序列;最后依据P波、SV波及其反射波在平面半空间的传播情况获得自由场条件下平面半空间内任意点的水平向和竖直向地震动。该文所采用的波场构建方法可实现对包含任意频谱和相位信息的两向设计地震动所对应的平面半空间自由场的构建,所获得的斜入射P波和SV波也具有各自的频谱和相位信息。最终得到的平面半空间自由场任意点水平向和竖直向地震动时间序列具有非一致性;根据入射P波、SV波结合地基边界条件确定的空间点地震动时间序列可用于结构的非一致地震动输入。     

基于PVDF薄膜的智能材料回声控制实现

提出了用高分子压电材料——PVDF薄膜作为激励声源，将其内嵌于基体材料聚氨酯橡胶中制成具有特殊功能的消声材料。通过声时延的方法，用布置在消声样件前方的两传声器检测出平面入射声波和反射声波，利用压电材料PVDF薄膜的逆压电性能，对其施加具有一定幅值和相位的电压，实现样件材料的声阻抗和介质声阻抗的匹配，以使得反射声波达到最小或零，从而实现回声控制的目的。最后对不同频率的入射声波进行了基于声阻抗管的回声控制实验测试并对结果进行了分析。     

The laws of plane defect wave propagation across the interface between two viscoplastic media

Relations determining the laws of reflection and refraction of a plane wave in the defect field at an interface between two viscoplastic media are obtained based on the dynamic equations of the continuum theory of defects. The reflection and transmission coefficients relating the amplitudes of reflected and transmitted waves to the incident wave amplitude are determined. The obtained relations are applied to a particular case of media with weakly decaying waves.     

On the effects of reflected waves in transient shear wave elastography

In recent years, novel quantitative techniques have been developed to provide noninvasive and quantitative stiffness images based on shear wave propagation. Using radiation force and ultrafast ultrasound imaging, the supersonic shear imaging technique allows one to remotely generate and follow a transient plane shear wave propagating in vivo in real time. The tissue shear modulus, i.e., its stiffness, can then be estimated from the shear wave local velocity. However, because the local shear wave velocity is estimated using a time-of- flight approach, reflected shear waves can cause artifacts in the estimated shear velocity because the incident and reflected waves propagate in opposite directions. Such effects have been reported in the literature as a potential drawback of elastography techniques based on shear wave speed, particularly in the case of high stiffness contrasts, such as in atherosclerotic plaque or stiff lesions. In this letter, we present our implementation of a simple directional filter, previously used for magnetic resonance elastography, which separates the forward- and backward-propagating waves to solve this problem. Such a directional filter could be applied to many elastography techniques based on the local estimation of shear wave speed propagation, such as acoustic radiation force imaging (ARFI), shearwave dispersion ultrasound vibrometry (SDUV), needle-based elastography, harmonic motion imaging, or crawling waves when the local propagation direction is known and high-resolution spatial and temporal data are acquired.     

Achromatic 90° polarization rotating prisms

Half wave plates are often used to rotate the plane of polarization by 90° at one wavelength. To rotate the plane of polarization over a range of wavelengths, Fresnel rhombs may be used. Fresnel rhombs, however, exhibit significant deviation from precisely 180° retardation over any broad wavelength range. This note describes two prism (or mirror) designs which rotate the incident polarization exactly 90° at all wavelengths. In one case the incident beam direction is deviated by 90°, while in the other case the incident beam is transmitted undeviated.     

Transverse-electric/transverse-magnetic polarization converter using 1D finite biaxial photonic crystal

We show that by using a one-dimensional anisotropic photonic structure, it is possible to realize optical wave polarization conversion by reflection and transmission processes. Thus a single incident S(P) polarized plane wave can produce a single reflected P(S) polarized wave and a single transmitted P(S) polarized wave. This polarization conversion property can be fulfilled with a simple finite superlattice (SL) constituted of anisotropic dielectric materials. We discuss the appropriate choices of the material and geometrical properties to realize such structures. The transmission and reflection coefficients are calculated in the framework of the Green's function method. The amplitude and the polarization characteristics of reflected and transmitted waves are determined as functions of frequency, wave vector k(parallel) (parallel to the interface), and the orientations of the principal axes of the layers constituting the SL. Specific applications of these results are given for a SL consisting of alternating biaxial anisotropic layers NaNO(2)/SbSI sandwiched between two identical semi-infinite isotropic media.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

A note on energy flux in micropolar elastic waves

The expressions for the time average power per unit area, the kinetic energy per unit volume, strain energy per unit volume and velocity of energy flux are derived for the case of a plane time harmonic micropolar elastic waves and it has been shown that the time-average energy density is equally divided between the time-averages of the kinetic and strain energy densities. The energy ratios of reflected micropolar elastic waves with the angle of emergence of incident longitudinal displacement wave have been shown graphically.     

Dynamic stress concentration studies by boundary integrals and Laplace transform

The dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined. The material may be linear elastic or viscoelastic, while the dynamic load consists of plane compressional waves of harmonic or general transient nature. The method consists of applying the Laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method. The stress field can then be obtaind by a numerical inversion of the trasformed solution. The correspondence principle is invoked for the case of viscoelastic material behavious. The method is simplified for the case of harmonic waves where no numerical inversion is involved.     

Wave reflection in a rotating pyroelectric half-plane

This paper describes the rotation effects on the wave reflection in a pyroelectric half-plane using an inhomogeneous wave approach. The rotation in the governing pyroelectric equation is characterized by considering the Coriolis and centrifugal accelerations. A scenario is modeled where a quasi-transverse wave is incident on the free boundary surface, resulting in reflected waves like temperature wave, quasi-transverse wave, quasi-longitudinal wave, and surface wave. Rotation’s effects on the reflection angle, velocity, attenuation, and energy coefficients of the reflected wave are presented.