Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads

Dynamic acoustoelastic testing is applied to weakly pre-loaded unconsolidated water-saturated glass beads. The gravitational acceleration produces, on the probed beads, a static stress of order 130 Pa, thus the granular medium is close to the jamming transition. A low-frequency (LF) acoustic wave gently disturbs the medium, inducing successively slight expansion and compaction of the granular packing expected to modulate the number of contacts between beads. Ultrasound (US) pulses are emitted simultaneously to dynamically detect the induced modification of the granular skeleton. US propagation velocity and attenuation both increase when the LF pressure increases. The quadratic nonlinear elastic parameter β, related to the pressure dependence of US propagation velocity, was measured in the range 60-530 if water-saturated glass beads are considered as an effective medium. A dynamic modification of US scattering induced by beads is proposed to modulate US attenuation. Complex hysteretic behaviors and tension-compression asymmetry are also observed and analyzed by time-domain and spectral analyses. Furthermore acoustic nonlinearities are measured in cases of quasi-static and dynamic variations of the LF wave amplitude, providing quantitatively similar acoustic nonlinearities but qualitatively different.     

垂直载荷下湿玻璃珠样品的声速和衰减测量及非线性声学响应

为了分析垂直载荷下颗粒物质的声速、声衰减系数、谐波非线性等特性,本工作采用飞行时间法测量了不同含水量下声速随压强的变化规律,并利用傅里叶变换法分析了干、湿玻璃珠样品的声衰减和非线性声学特性。结果表明:干、湿玻璃珠样品中的声速、声衰减系数以及谐波非线性均随压强呈幂律变化;湿颗粒样品中随着液体含量增多,声速逐渐增加,超声波透过湿颗粒样品时的能量耗散和非线性逐渐减小。分析原因表明,压强和孔隙流体改变了颗粒之间的接触分布,使得颗粒体系的声速、声衰减以及谐波非线性等特性都随之发生变化。     

Wave anisotropy of shear viscosity and elasticity

The paper presents the theory of shear wave propagation in a “soft solid” material possessing anisotropy of elastic and dissipative properties. The theory is developed mainly for understanding the nature of the low-frequency acoustic characteristics of skeletal muscles, which carry important diagnostic information on the functional state of muscles and their pathologies. It is shown that the shear elasticity of muscles is determined by two independent moduli. The dissipative properties are determined by the fourth-rank viscosity tensor, which also has two independent components. The propagation velocity and attenuation of shear waves in muscle depend on the relative orientation of three vectors: the wave vector, the polarization vector, and the direction of muscle fiber. For one of the many experiments where attention was distinctly focused on the vector character of the wave process, it was possible to make a comparison with the theory, estimate the elasticity moduli, and obtain agreement with the angular dependence of the wave propagation velocity predicted by the theory.     

Acoustic field excited by a pulsed laser line source in a cylinder

The excitation and propagation of the acoustic waves in an elastic cylinder are studied by laser ultrasonics both theoretically and experimentally. The theoretical analysis of the two-dimensional acoustic field excited by a pulsed laser line source impacting on the generatrix of an elastic cylinder is presented. The dispersive properties for both cylindrical Rayleigh wave and the higher modes--whispering gallery (WG) modes are analyzed in detail. The numerical transient displacement waveforms for a detecting point located another terminal of the cylinder diameter opposite the source are calculated. The experimental excitation and detection of the acoustic waves in an aluminum cylinder are carried out on a laser ultrasonic system, which mainly consists of a Q-switched Nd:YAG laser and a laser interferometer. The wave components of bulk waves and surface waves (cylindrical Rayleigh waves and WG modes) are analyzed by comparing the numerical and experimental waveforms. The results are in good agreement.     

Increase in the efficiency of the shear wave generation in gelatin due to the nonlinear absorption of a focused ultrasonic beam

Experimental results and theoretical estimates are presented to demonstrate the prospects of using the acoustic nonlinearity of a gel-like medium for increasing the efficiency of the shear wave generation in it by a pulsed ultrasonic beam. The experiment is based on the propagation of a focused beam of longitudinal acoustic waves at a frequency of 1.1 MHz in a gelatin sample and on the detection of shear waves by the optical method [1]. It is demonstrated that the amplitude of the shear wave excited by a nonlinear acoustic pulse can be increased by an order of magnitude owing to the formation of shock fronts in the profile of this pulse.     

Analysis of the space-time dynamics of acoustic fields on the surface of a solid

The space-time dynamics of an acoustic field produced by a piezoelectric transducer in a pulsed mode is studied. The detection of acoustic fields is achieved using a Doppler laser interferometer. It is shown that, for a pictorial representation of the dynamics of a pulsed process, it is convenient to use the patterns of instantaneous spatial field distributions within the scanning area, the observation of which at successive instants makes it possible to trace the acoustic field variations on a time scale considerably smaller than the period of the ultrasonic wave. Experimental data demonstrating the process of phase propagation along the sample boundary as a function of time are presented. They are in good agreement with theoretical results obtained by using various methods of acoustic field calculation and different scalar potential distributions over the transducer surface. It is shown that the velocity of phase propagation along the sample boundary, which is mainly determined by the wave front curvature of the elastic wave incident on the sample surface, can considerably exceed the wave velocity in the unbounded medium.     

Propagation of weak ultrasonic pulses in an intense low-frequency wave field in a granite resonator

Results of an experimental study of nonlinear attenuation and carrier frequency phase delay of weak ultrasonic pulses under the effect of an intense low-frequency wave in a bar resonator made from Karelian granite are presented. The effects observed in the experiment are analytically described in terms of the phenomenological equation of state containing hysteretic and dissipative nonlinearities. A frequency dependence of nonlinearity is revealed, and the effective values of nonlinear parameters of granite are estimated for the frequency range from 150 kHz to 1 MHz.     

Longitudinal and lateral low frequency head wave analysis in soft media

This article studies the influence of the head wave in the lateral and longitudinal components of the displacements generated by the radiation of low-frequency elastic waves in an isotropic and homogeneous soft solid. Low-frequency shear waves are used to characterize elastic properties of soft tissues. In this context, it is useful to have a detailed study of the low-frequency wave field in this kind of material. A soft medium is characterized by the fact that the head wave is found in the source's axis. Even though its amplitude is small compared with the shear wave, it is possible to be observed experimentally by recording consecutive ultrasonic A-lines while the low-frequency wave propagates inside the medium. A standard one-dimensional speckle tracking technique is employed to measure the displacements. Experimental results were interpreted through the exact Green's function solution to the half-space problem. According to the theoretical and experimental analysis, the head wave and surface related terms in general contribute to the displacements in the low-frequency range. This article thoroughly analyzes and experimentally shows the contribution of the head wave for the lateral component, which is not fully addressed by the literature.     

The acoustoelastic effect on Rayleigh waves in elastic--plastic deformed layered rocks

On the basis of the acoustoelastic theory for elastic--plastic materials, the influence of statically deformed states including both the elastic and plastic deformations induced by applied uniaxial stresses on the Rayleigh wave in layered rocks is investigated by using a transfer matrix method. The acoustoelastic effects of elastic--plastic strains in rocks caused by static deformations, are discussed in detail. The Rayleigh-type and Sezawa modes exhibit similar trends in acoustoelastic effect: the acoustoelastic effect increasing rapidly with the frequency-thickness product and the phase velocity change approaching a constant value for thick layer and high frequency limit. Elastic--plastic deformations in the Castlegate layered rock obviously modify the phase velocity of the Rayleigh wave and the cutoff points for the Sezawa modes. The investigation may be useful for seismic exploration, geotechnical engineering and ultrasonic detection.     

Anisotropy of the phonon-phason dynamics and the pinning effect in icosahedral AlPdMn quasicrystals

A minimal model of the phonon-phason dynamics in icosahedral quasicrystals with inclusion of the pinning effect is suggested. Resonant attenuation of low-frequency acoustic waves in the temperature range corresponding to thermal activation of phasons is considered. In the long-wave length limit, the velocity of acoustic phonons is isotropic; however, the phonon-phason coupling causes anisotropy of the velocity and of the attenuation of acoustic waves with small wave vectors. These effects manifest themselves most strongly at an acoustic wave frequency close to the inverse relaxation time of phasons with the same wave vector. The pinning effect can cause a significant decrease in the anisotropy of the velocity and of attenuation of acoustic waves.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Laser detection of elastic waves diffraction by the crack’s edge

Diffraction effects and features of acoustic wave propagation in elastic media with the surface-breaking microcrack were investigated in detail for the pulse probing signals. The crack’s plane was oriented along the direction of longitudinal ultrasonic wave incidence in such a way that the detection of the crack with such an unfavorable spatial location was difficult by means of traditional acoustic techniques. Using laser Doppler interferometer a set of instantaneous pictures of acoustic field on the specimen’s surface, corresponding to the different moments of time was obtained. This allowed us to investigate and visualize the diffraction effects of acoustic field in dynamics. Using numerical modeling of diffraction processes of acoustic waves on the crack’s edge and top for pulse signals the origin of V-like structures on the snapshots of acoustic fields was explained and analyzed.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

Elastic constants determination by direct measurement of the beat wavelength between A0 and S0 Lamb modes with pulsed TV holography

A whole-field optical technique of high sensitivity, namely pulsed TV holography with phase evaluation by the Spatial Fourier Transform Method, is applied to the acquisition of instantaneous displacement fields of ultrasonic Lamb waves in aluminium plates a few millimetres thick. Two Lamb modes, the A0 and S0 ones, are simultaneously generated in the plate, producing a clear beating. Several values of the beat wavelength, corresponding to different excitation frequencies, are obtained by direct measurement of the distance between nodes in the wave field. The obtained values are fitted to the theoretical Rayleigh–Lamb frequency spectrum in order to determine the elastic constants of the plate material. We conclude that it is necessary to know the value of another parameter to univocally solve the problem, and so the bulk longitudinal wave velocity is measured by the pulse-echo method. Then the Poisson's ratio is obtained and, from these two parameters, the Young's modulus can also be determined.     

Acoustic nonlinearity parameter tomography for biological tissues via parametric array from a circular piston source--theoretical analysis and computer simulations

The acoustic nonlinearity parameter B/A describes the nonlinear features of a medium and may become a novel parameter for ultrasonic tissue characterization. This paper presents a theoretical analysis for acoustic nonlinear parameter tomography via a parametric array. As two primary waves of different frequencies are radiated simultaneously from a circular piston source, a secondary wave at the difference frequency is generated due to the nonlinear interaction of the primary waves. The axial and radial distributions of sound pressure amplitude for the generated difference frequency wave in the near field are calculated by a superposition of Gaussian beams. The calculated results indicated that the difference frequency component of the parametric array grows linearly with distance from the piston source. It therefore provides a better source to do the acoustic nonlinearity parameter tomography because the fundamental and second harmonic signals both have a near field that goes through many oscillations due to diffraction. By using a finite-amplitude insert substitution method and a filtered convolution algorithm, a computer simulation for B/A tomography from the calculated sound pressure of the difference frequency wave is studied. For biological tissues, the sound attenuation is considered and compensated in the image reconstruction. Nonlinear parameter computed tomography (CT) images for several biological sample models are obtained with quite good quality in this study.     

Profiles of initially sinusoidal waves propagating in nonlinear microinhomogeneous materials

The asymptotic analytical theory predicting acoustic wave profiles in microinhomogeneous materials with hysteretic quadratic nonlinearity and attenuation proportional to an even power of frequency is developed. The theory predicts that the influence on the nonlinear wave of the Rayleigh scattering of acoustic waves, which is proportional to the forth power of frequency, results in the net diminishing of wave attenuation. This is due to the suppression (diminishing) by scattering of the nonlinear hysteretic losses which is more important than direct increase in linear losses added by scattering.