Performance evaluation of fiber array for NDE application

This paper evaluates the performance of an optical fiber phased array as a source of ultrasonic generation for nondestructive applications. The results of the shear and longitudinal wave directivity patterns generated with this technique are presented. The signal enhancements produced by increasing the number of fibers in the array are presented for both shear and longitudinal waves. The receiving transducers were two piezoelectric transducers.     

Shear modulus imaging with 2-D transient elastography

In previous work, we have shown that time-resolved 2-D transient elastography is a promising technique for characterizing the elasticity of soft tissues. It involves the measurement of the displacements induced by the propagation of low frequency (LF) pulsed shear waves in biological tissues. In this paper, we present a novel apparatus that contains a LF vibrating device surrounding a linear array of 128 ultrasonic transducers that performs ultrafast ultrasonic imaging (up to 10,000 frames/s) and that is able to follow in real time the propagation of a LF shear wave in the human body. The vibrating device is made of two rods, fixed to electromagnetic vibrators, that produce in the ultrasonic image area a large amplitude shear wave. The geometry has been chosen both to enhance the sensitivity and to create a quasi linear shear wave front in the imaging plane. An inversion algorithm is used to recover the shear modulus map from the spatio-temporal data, and the first experimental results obtained from tissue-equivalent materials are presented.     

激光致声技术的研究

从热弹与烧蚀机制两个方面，讨论了激光超声表面波的产生。通过对点光源激励声表面波的机理进行分析，出线光源激励的表达式。进行了表面波同线光源能量、方向角、位置、长度关系的实验研究。实验结果验证了激光超声表面波理论模型的合理性，证实了线光源产生的表面波具有信号强、方向性好等优点。     

单台阶同心圆盘辐射声场的指向性计算

作为向空气中辐射的声辐射器,弯振阶梯薄盘或矩形板在工业上有很多应用。由于计算的复杂性,以前的文献对阶梯圆盘的声场指向性未作研究。利用点声源组合的方法（Rayleigh积分）,计算了边界自由的弯振阶梯圆盘辐射声场的指向性,与弯曲振动的圆盘相比,阶梯圆盘的声场指向性得到了明显改善,理论计算结果与Gallego的实际测试图案相吻合。计算为这类辐射器的高效应用、优化设计提供了理论依据。     

Evaluation of Fatigue Crack Orientation Using Non-collinear Shear Wave Mixing Method

In this paper, a non-collinear shear wave mixing technique is proposed for evaluation of fatigue crack orientation. Numerical analysis of the nonlinear interaction of two shear waves with crack is performed using two-dimensional finite-element simulations. The simulation results show that the nonlinear interaction of the two shears waves with cracks leads to the generation of transmitted and reflected sum-frequency longitudinal waves (SFLW), moreover the propagation direction of reflected SFLW is correlated with the orientation of crack, which can be used for crack orientation evaluation. Non-collinear wave-mixing experiments were conducted on specimens with fatigue crack. The experimental results show that the directivity of the generated SFLW agrees well with the simulation results, and non-collinear shear wave mixing has potential use in fatigue crack orientation evaluation.     

The role of viscosity in the impulse diffraction field of elastic waves induced by the acoustic radiation force

Several ultrasound-based techniques for the estimation of soft tissue elasticity are currently being investigated. Most of them study the medium response to dynamic excitations. Such responses are usually modeled in a purely elastic medium using a Green's function solution of the motion equation. However, elasticity by itself is not necessarily a discriminant parameter for malignancy diagnosis. Modeling viscous properties of tissues could also be of great interest for tumor characterization. We report in this paper an explicit derivation of the Green's function in a viscous and elastic medium taking into account shear, bulk, and coupling waves. From this theoretical calculation, 3D simulations of mechanical waves in viscoelastic soft tissues are presented. The relevance of the viscoelastic Green's function is validated by comparing simulations with experimental data. The experiments were conducted using the supersonic shear imaging (SSI) technique which dynamically and remotely excites tissues using acoustic radiation force. We show that transient shear waves generated with SSI are modeled very precisely by the Green's function formalism. The combined influences of out-of-plane diffraction, beam shape, and shear viscosity on the shape of transient waves are carefully studied as they represent a major issue in ultrasound-based viscoelasticity imaging techniques.     

多极声源在裸眼井外的纵横波辐射特性

声波远探测方法已逐渐成为石油测井的一门重要应用技术,声源向井外地层中的辐射特性是远探测声场的主控因数。推导了单极、偶极和四极子声源的远场位移渐近解与辐射指向性公式,模拟分析了低频和常规测井频率下多极子声源在井外地层中的辐射图样,优选出不同声源辐射到地层中的优势波类型,并对比了不同频率下优势波指向性的变化规律。结果表明:单极辐射P波和偶极辐射SH横波在各自的辐射声场中占据了主导地位,它们对应的最佳激发频段分别在10 k Hz和4 k Hz左右,而在四极子声源的辐射声场中,P波和SH横波的指向性相近,均优于SV横波,且两者在7 k Hz左右达到最佳,为多极子声波远探测技术的应用提供了理论支持。     

Narrowband shear wave generation by a Finite-Amplitude radiation force: The fundamental component

A highly localized source of low-frequency shear waves can be created by the modulated radiation force resulting from two intersecting quasi-continuous-wave ultrasound beams of slightly different frequencies. In contrast to most other radiation force-based methods, these shear waves can be narrowband. Consequently, different frequency-dependent effects will not significantly affect their spectrum as they propagate within a viscoelastic medium, thereby enabling the viscoelastic shear properties of the medium to be determined at any given modulation frequency. This can be achieved by tracking the shear wave phase delay and change in amplitude over a specific distance. In this paper we explore the properties of short duration (dynamic) low-frequency shear wave propagation and study how the shear displacement field depends on the excitation conditions. Our investigations make use of the approximate Green's functions for viscoelastic media, and the evolution of such waves is studied in the spatiotemporal domain from a theoretical perspective. Although nonlinearities are included in our confocal source model, just the properties of the fundamental shear component are examined in this paper. We examine how the shear wave propagation is affected by the shear viscosity, the coupling wave, the spatial distribution of the force, the shear speed, and the duration of the modulated wave. A method is proposed for estimating the shear viscosity of a viscoelastic medium. In addition, it is shown how the Voigt model paremeters can be extracted from the frequency-dependent speed and attenuation.     

Sol-gel transition in agar-gelatin mixtures studied with transient elastography

Using the shear wave propagation in solids, the transient elastography technique has been developed to assess the elastic properties of soft tissues. Here, a new approach of transient elastography allows assessing the viscoelastic properties of soft tissues. In this paper, the method is used to follow-up the sol-gel transition of an agar-gelatin mixture noninvasively. The shear wave velocity and shear wave attenuation through the mixture were continuously monitored in the audible range of frequencies (from 50 Hz to 200 Hz). The observed changes in velocities and attenuations as a function of frequency confirmed the validity of the Voigt's model to describe the gel at its stable mechanical state. By a simple inverse problem approach, based on the one-dimensional (1-D) Helmholtz equation, the elasticity and the viscosity of such a mixture were recovered as a function of time. The results obtained are in good agreement with the literature and theoretical predictions. Overall, they demonstrate the high sensitivity of the transient elastography measurements to the rheological parameter changes in agar-gelatin mixtures during gelation.     

Scattering of antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface

Summary We present analytical solutions for the scattering of an antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface. We first consider the simple case in which the imperfection is homogeneous along the interface. Two typical imperfect interfaces are addressed: 1) mechanically compliant and dielectrically weakly conducting interface, and 2) mechanically compliant and dielectrically highly conducting interface. The expressions for the directivity pattern and scattering cross-section of the scattered shear waves are derived. We then investigate the more difficult problem in which the imperfection is circumferentially inhomogeneous along the interface. A concise expression for an inhomogeneously compliant and weakly conducting interface is derived by means of matrix notation. Numerical examples are presented to demonstrate the effect of the imperfection and the circumferential inhomogeneity of the interface on the directivity patterns and scattering cross-sections of the scattered shear wave. The circumferentially inhomogeneous interface is also utilized to model the interface where an arbitrary number of cracks exist. Results show that when every part of the interface is rather compliant, large low-frequency peaks of the scattered cross-sections, which correspond to the resonance scattering, can be observed no matter if the interface is homogeneous or inhomogeneous. The appearance of large low-frequency peaks can be well explained by estimating the natural frequency of the corresponding reduced mass-spring system where the cylinder is assumed as a rigid body. Peaks of the scattered cross-sections spanning from low frequencies to high frequencies can be observed for a cylinder with a partially debonded interface.     

Propagation of shear waves generated by a modulated finite amplitude radiation force in a viscoelastic medium

An effective way to generate localized narrow-band low-frequency shear waves within tissue noninvasively, is by the modulated radiation force, resulting from the interference of two confocal quasi-CW ultrasound beams of slightly different frequencies. By using approximate viscoelastic Green's functions, investigations of the properties of the propagated shear-field component at the fundamental modulation frequency were previously reported by our group. However, high-amplitude source excitations may be needed to increase the signal-to-noise-ratio for shear-wave detection in tissue. This paper reports a study of the generation and propagation of dynamic radiation force components at harmonics of the modulation frequency for conditions that generally correspond to diagnostic safety standards. We describe the propagation characteristics of the resulting harmonic shear waves and discuss how they depend on the parameters of nonlinearity, focusing gain, and absorption. For conditions of high viscosity (believed to be characteristic of soft tissue) and higher modulation frequencies, the approximate shear wave Green's function is inappropriate. A more exact viscoelastic Green's function is derived in k-space, and using this, it is shown that the lowpass and dispersive effects, associated with a Voigt model of tissue, are more accurately represented. Finally, it is shown how the viscoelastic properties of the propagating medium can be estimated, based on several spectral components of the shear wave spectrum.     

医用线列阵声场计算方法

用指向性函数分别描述了医用线列阵单频波和宽带波声场。讨论了应用电子聚焦处理、幅度加权变迹处理和孔径变迹处理的方法来改善波束特性；论述了在实际中应用较多的宽带波声场的计算。通过分析表明，宽带波持续时间愈长，宽带波声场就愈接近于单频波声场。     

Ultrasonic Beam Models for Angle Beam Surface Wave Transducers

ABSTRACT

Explicit three-dimensional (3D) point source and multi-Gaussian beam models are obtained for the Rayleigh waves generated by a surface wave angle beam transducer using an angular plane wave spectrum approach. Simulations show that the multi-Gaussian surface wave beam model agrees well with the point source model while being computationally more efficient. The theoretical predictions obtained with the models are also compared to the experimental measurement results where good agreement with the models is found for both on-axis and off-axis field comparisons.     

A flexible piezoelectric transducer design for efficient generation and reception of ultrasonic Lamb waves

This paper describes the development of a flexible piezoelectric transducer for the generation and detection of ultrasonic symmetrical Lamb waves in plate-like structures. This piezoplatelet transducer structure comprises an array of miniature piezoceramic plates embedded within a soft setting polymer filler material, combining the efficiency of the active piezoceramic phase with a degree of flexibility, which is a function of the platelet/polymer dimensions. For many condition-monitoring applications, the generation of ultrasonic Lamb waves is often appropriate, and this was achieved by incorporating interdigital design techniques via the transducer electrode pattern. The performance of the piezoplatelet transducer structure was evaluated using a combination of linear systems and finite-element modeling, substantiated by experimental results. Importantly, the transducer is shown to operate as an ensemble of platelets, each operating in the thickness mode and well decoupled from neighboring piezoelectric elements. Using this transducer configuration, an unimodal s1 Lamb wave, at 1.45 MHz, has been generated and detected in a 3-mm thick steel plate. Furthermore, a propagation distance of almost 1 m was recorded for s0 Lamb wave generation/detection in a fiber-reinforced composite plate.     

Supersonic shear imaging: a new technique for soft tissue elasticity mapping

Supersonic shear imaging (SSI) is a new ultrasound-based technique for real-time visualization of soft tissue viscoelastic properties. Using ultrasonic focused beams, it is possible to remotely generate mechanical vibration sources radiating low-frequency, shear waves inside tissues. Relying on this concept, SSI proposes to create such a source and make it move at a supersonic speed. In analogy with the "sonic boom" created by a supersonic aircraft, the resulting shear waves will interfere constructively along a Mach cone, creating two intense plane shear waves. These waves propagate through the medium and are progressively distorted by tissue heterogeneities. An ultrafast scanner prototype is able to both generate this supersonic source and image (5000 frames/s) the propagation of the resulting shear waves. Using inversion algorithms, the shear elasticity of medium can be mapped quantitatively from this propagation movie. The SSI enables tissue elasticity mapping in less than 20 ms, even in strongly viscous medium like breast. Modalities such as shear compounding are implementable by tilting shear waves in different directions and improving the elasticity estimation. Results validating SSI in heterogeneous phantoms are presented. The first in vivo investigations made on healthy volunteers emphasize the potential clinical applicability of SSI for breast cancer detection.     

Plastic deformation behind strong shock waves

The dislocation produced plastic deformation that must occur behind the front of strong shock waves is analysed in this paper. (A strong shock has a driving stress that is large compared with the bulk elastic modulus). Because the front of strong shock waves must be exceedingly narrow, there is a problem of how the effective shear stress, which is probably of the order of the theoretical shear strength at the immediate front itself, is relaxed in the region behind the shock front. Our analysis (Weertman and Follansbee, 1983)) of moderate strength shock waves is used for the relaxing region behind a strong shock wave front. It is concluded that a strong shock wave front has the following dislocation structure: The shock front, of atomic dimensions, consists of a Smith dislocation interface of dislocations that keep up with the front by moving at transonic or supersonic velocities. Immediately behind the Smith interface is a region of moving dislocations that do not keep up with the shock front. In this region normal dislocation motion and multiplication takes place. Within this region of normal plastic deformation the shock pressure rises by an amount that is quite small compared with the shock pressure itself.     

相控线阵声源在套管井中的应用

在常规的单极子套管井测井中,由于过套管测量,即使在I、II界面均胶结好的状况下,测量的地层波信息也比较弱。利用相控线阵声源的声束偏转和能量聚焦技术,可大大提高声源的辐射强度和信噪比。采用FEM有限元软件建立了套管井和相控声源的二维模型,计算了点声源和相控线阵声源在套管井中的声压波形。计算结果发现当控制相控线阵阵元间延迟时间使其辐射主声束偏转角满足地层纵波发生临界折射时,可以明显增强地层波幅度,即使在I界面或II界面胶结不好时也可观测到地层波,因此利用相控线阵声源的强穿透性可以帮助我们在套管井胶结不好的情况下探测地层。     

Elastic stress transmission in cellular systems—Analysis of wave propagation

A closely packed array of thin-walled rings constitutes an idealisation of a cellular structure. Elastic waves propagating through such structures must do so via the ring (cell) walls. A theoretical investigation into the propagation of elastic stresses in thin-walled circular rings is undertaken to examine the nature of wave transmission. Three modes of motion, corresponding to shear, extensional and flexural waves, are established and their respective velocities defined by a cubic characteristic equation. The results show that all three waves are dispersive. By neglecting extension of the centroidal axis and rotary inertia, explicit approximate solutions can be obtained for flexural waves. Employment of Love's approach for extensional waves [Love AEH. A treatise on the mathematical theory of elasticity, 4th ed. New York: Dover Publications; 1944. p. 452–3] enables approximate solutions for shear waves to be derived. The three resulting approximate solutions exhibit good agreement with the exact solutions of the characteristic equation over a wide range of wavelengths. The effects of material property, ring wall thickness and ring diameter on the three wave modes are discussed, and the results point to flexural waves as the dominant means of elastic energy transmission in such cellular structures. Wave velocities corresponding to different frequency components determined from experimental results are compared with theoretical predictions of group velocity for flexural waves and good correlation between experimental data and theory affirms this conclusion.     

Some results on finite amplitude elastic waves propagating in rotating media

Summary. Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity provides such a framework for incompressible solids. Second: how can finite amplitude exact solutions be generated? It is seen that for some finite amplitude transverse waves in rotating incompressible elastic solids with general shear response the solutions are obtained by reduction of the equations of motion to a system of ordinary differential equations equivalent to the system governing the central motion problem of classical mechanics. In the special case of circularly-polarized harmonic progressive waves, the dispersion equation is solved in closed form for a variety of shear responses, including nonlinear models for rubberlike and soft biological tissues. A fruitful analogy with the motion of a nonlinear string is pointed out.     

Vortex array generation by interference of spherical waves

Interferometric methods of vortex generation involve the interference of three or more plane waves. We show that spherical wave interference can produce vortex lattices similar to the one produced in the three-beam interference of plane waves. Three spherical waves of the same curvature are made to interfere in a shear interferometer introduced in a Mach-Zehnder configuration.