Acoustic nonlinearity of cracks partially filled with a viscous liquid: A quadratic approximation

A mechanism that accounts for the acoustic nonlinearity of cracks partially filled with a viscous liquid is proposed. The mechanism is related to the nonlinear dependences of the capillary and viscous pressures in liquid on the distance between the crack surfaces and on the rate of change of this distance. The nonlinear equation of state is obtained for this type of cracks, and the parameters of this equation are determined. It is shown that the presence of a viscous liquid can lead to a considerable increase in the acoustic nonlinearity of such cracks, as compared to the cracks filled with an ideal liquid.     

Nonlinear wave processes in media containing cracks partially filled with a viscous liquid

A nonlinear (in the cubic approximation) relaxation equation of state is derived for a rod containing cracks partially filled with an incompressible viscous liquid. The nonlinear effects of the self-action and interaction of low-and high-frequency longitudinal elastic waves propagating in such a rod are studied for the cases of identical and size-varied cracks. Linear and nonlinear acoustic parameters characterizing the self-action and interaction of elastic waves in a cracked rod are determined.     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

Nonlinear frequency mixing in a resonant cavity: Numerical simulations in a bubbly liquid

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared. The results show highly efficient generation of the difference frequency at high excitation amplitude. The large acoustic nonlinearity of the bubbly liquid that is responsible for the strong difference-frequency resonance also induces significant enhancement of the parametric frequency mixing effect to generate second harmonic of the difference frequency.     

Nonlinearity of solids with micro- and nanodefects and characteristic features of its macroscopic manifestations

The meaning of the experimentally measured nonlinear parameters of a medium is discussed. The difference in meaning between the local nonlinearity, which is measured in the vicinity of a single defect and depends on the size of the region of averaging, and the effective volume nonlinearity of the medium containing numerous defects is emphasized. The local nonlinearity arising at the tip of a crack is calculated; this non-linearity decreases with an increase in the region of second harmonic generation. The volume nonlinearity is calculated for a solid containing spherical cavities. The volume nonlinearity is also calculated for a medium containing infinitely thin cracks in the form of circular disks, which assume the shape of ellipsoids in the course of the crack opening. The nonlinear acoustic parameter is calculated with the use of the exact classical results of the theory of cracks.     

Modeling nonlinearities of ultrasonic waves for fatigue damage characterization: Theory,simulation, and experimental validation

A dedicated modeling technique for comprehending nonlinear characteristics of ultrasonic waves traversing in a fatigued medium was developed, based on a retrofitted constitutive relation of the medium by considering the nonlinearities originated from material, fatigue damage, as well as the “breathing” motion of fatigue cracks. Piezoelectric wafers, for exciting and acquiring ultrasonic waves, were integrated in the model. The extracted nonlinearities were calibrated by virtue of an acoustic nonlinearity parameter. The modeling technique was validated experimentally, and the results showed satisfactory consistency in between, both revealing: the developed modeling approach is able to faithfully simulate fatigue crack-incurred nonlinearities manifested in ultrasonic waves; a cumulative growth of the acoustic nonlinearity parameter with increasing wave propagation distance exists; such a parameter acquired via a sensing path is nonlinearly related to the offset distance from the fatigue crack to that sensing path; and neither the incidence angle of the probing wave nor the length of the sensing path impacts on the parameter significantly. This study has yielded a quantitative characterization strategy for fatigue cracks using embeddable piezoelectric sensor networks, facilitating deployment of structural health monitoring which is capable of identifying small-scale damage at an embryo stage and surveilling its growth continuously.     

Acoustic wave dispersion in a cylindrical elastic tube filled with a viscous liquid

This paper deals with the study of the velocity and the attenuation of an acoustic wave propagating inside a cylindrical elastic tube filled with a viscous liquid. A theory describing the propagation of the axisymmetrical modes in such waveguides is presented, with special attention given to the absorption produced by the viscous mechanisms in the liquid. One of these mechanisms is related to the momentum transfer between the compression and rarefaction regions of a propagating wave. The other viscous mechanism is due to the momentum transport inside the viscous boundary layer, close to the tube wall. Numerical calculations were carried out to investigate the influence of different parameters (frequency, tube radii, viscosity coefficient) on the propagation of acoustic waves.     

All-optical probing of the nonlinear acoustics of a crack

Experiments with an all-optical method for the study of the nonlinear acoustics of cracks in solids are reported. Nonlinear acoustic waves are initiated by the absorption of radiation from a pair of laser beams intensity modulated at two different frequencies. The detection of acoustic waves at mixed frequencies, absent in the frequency spectrum of the heating lasers, by optical interferometry or deflectometry provides unambiguous evidence of the elastic nonlinearity of the crack. The high contrast in crack imaging achieved by remote optical monitoring of the nonlinear acoustic processes is due to the strong dependence of the efficiency of optoacoustic conversion on the state of the crack. The highest acoustic nonlinearity is observed in the transitional state of the crack, which is intermediate between the open and the closed ones.     

声波在有裂纹的固体中的非经典非线性传播

固体材料的无损检测是一个非常重要的课题,带裂纹的固体材料显示非经典非线性声学现象,本文对此现象进行了实验和理论研究。从实验上一维观察到此现象,发现奇次谐波振幅与基波振幅呈平方关系,与理论预计基本吻合;理论上从二维的角度数值模拟了声波在有损耗的带裂纹的固体中的声传播,并讨论了经典非线性和非经典非线性对声传播的影响,发现裂纹的贡献主要体现在非经典非线性上。分析了样品中裂纹的宽度和位置与非线性声参数的关系,在靠近样品中心的两个对称区域以及距离声源较近点,非线性声参数对样品的破损较为敏感,而在中央和距声源最远端敏感性较低;随着裂纹宽度的扩大,非线性声参数也开始变大,但在破损区域蔓延到棒边缘之前,有下降的趋势。      

Acoustic nonlinearity of water-like materials with partially liquid-filled capillaries

A theoretical study of elastic nonlinearity is carried out for a porous water-like material containing a set of parallel cylindrical cavities (capillaries) partially filled with an ideal incompressible liquid.     

Nonlinear acoustic spectroscopy of local defects in geomaterials

General approaches to solving the problem of nonlinear acoustic spectroscopy of defects in geomaterials are considered. Expressions that relate the nonlinear response (scattering at combination frequencies) to the position, orientation, and nonlinear characteristics of narrow cracks are obtained. The expressions describe a broad class of nonlinear interactions at a crack. The nonlinearity caused by the contact of uneven rough edges of a crack is analyzed in detail. The results of the analysis are compared with the results obtained earlier from considering micromechanical models and with experimental data. The satisfactory agreement between the theoretical and experimental values of Landau’s moduli suggests that the mechanism of contact nonlinearity may manifest itself in the process of fracture of polycrystalline rock, when narrow cracks with uneven edges are formed. Numerical examples demonstrate the possibility of determining the orientation and position of a narrow crack. The procedure of solving the problem of crack localization is illustrated by the example of a crack in a thin rod. The importance of taking into account the phase data in the determination of the crack coordinate is pointed out.     

非线性声波方程二次谐波高阶近似解及实验验证

非线性声波方程的传统二次谐波二阶近似解不够精确,对测量材料的非线性系数造成较大误差。利用摄动法展开非线性声波方程得到一系列非齐次偏微分方程,根据低阶解的性质拟定高阶特解的形式,通过符号计算求出高次谐波特解,对所有二次谐波成分求和最终获得二次谐波的高阶近似解。在水中开展非线性声学实验验证高阶近似解,结果表明:二次谐波相对幅度随传播距离和输入信号均呈现先增加后减小的趋势,高阶近似解即使在传播距离不太短和输入信号不太弱的宽泛条件下也能更好地吻合实验结果。得到的高阶近似解不仅弥补了现有二次谐波幅度理论公式的不足,进行非线性声学实验时还可扩展测量范围,充分利用实验数据也能提高非线性系数的测量精度。      

In situ estimation of crack concentration in hard rock

Results of a 2004 field experiment aimed at determining the quadratic nonlinearity parameter in granite that forms the shore of the Ladoga lake are presented. The measurements were based on the observation of the nonlinear interaction between monochromatic waves excited by two hydroacoustic radiators of 1 kW each positioned near the shore. The initial level of nonlinear distortions was much lower than the level of the received difference-frequency signal. The quadratic nonlinearity parameter proved to be higher than that reported in the majority of publications. An assumption was put forward that the high nonlinearity of granite is caused by the high concentration of cracks in it. Pieces of rock were taken from the measurement site, and rectangular samples were prepared from them. The samples were studied by the acoustic spectroscopy method in laboratory conditions. As a result, estimates of crack concentration were obtained, which proved to be consistent with the field measurements of the quadratic nonlinearity parameter. Thus, the possibility of estimating the crack concentration in situ from the measurements of the quadratic nonlinearity parameter was demonstrated.     

Impulsive fracture of silicon by elastic surface pulses with shocks

During nonlinear evolution of surface acoustic waves (SAWs) stress increases with propagation, and may cause fracture of brittle materials. This effect was used to evaluate the strength of crystalline silicon with respect to impulsive load in the nanosecond time scale without using seed cracks. Short SAW pulses propagating in the [11(macro)2] direction on the Si(111) plane induce fracture at significantly lower SAW amplitudes than the mirror symmetric wave propagating in the [112(macro)] direction. This effect is explained by the differences in elastic nonlinearity of the two propagation directions.     

Nonlinear increase in bubbles radii caused by sound in a bubbly liquid

The nonlinear interaction of acoustic and entropy modes in a bubbly liquid is considered. The reasons for interaction are both nonlinearity and dispersion. In the field of intense sound, a decrease in the mixture density is predicted. That corresponds to the well-established growth of bubbles volumes due to rectified diffusion. The nonlinear interaction of modes as a reason for a bubble to grow due to sound, is discovered. The example considers variation in the mixture density and bubbles radii caused by acoustic soliton.     

Nonlinear analysis of a wave motion on the surface of a jet moving in a dielectric medium placed in a longitudinal electric field

The possibility of degenerate internal nonlinear resonance interaction between capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid is demonstrated. The jet moves in an ideal incompressible dielectric medium collinearly with an external uniform electrostatic field. It is shown, in particular, that six different resonance situations take place for axisymmetric waves in which primary waves and waves due to the nonlinearity of the equations of hydrodynamics exchange energy.     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

Nonlinear acoustic effects in a resonator with saturation of hysteretic loss

Nonlinear wave processes in an acoustic rod resonator with hysteretic nonlinearity under harmonic excitation are studied. The characteristics of longitudinal nonlinear modes of the resonator with hard and soft boundaries (amplitude-dependent loss, shifts of resonance frequencies, and amplitudes of the second and third harmonics) are determined. The comparison of the theoretical and experimental dependences of nonlinear acoustic effects in a resonator that is made of annealed polycrystalline copper is used to determine the parameters of the hysteretic nonlinearity.     

Acoustic cavitation mechanism: a nonlinear model

During acoustic cavitation process, bubbles appear when acoustic pressure reaches a threshold value in the liquid. The ultrasonic field is then submitted to the action of the bubbles. In this paper we develop a model to analyze the cavitation phenomenon in one-dimensional standing waves, based on the nonlinear code SNOW-BL. Bubbles are produced where the minimum rarefaction pressure peak exceeds the cavitation threshold. We show that cavitation bubbles appear at high amplitude and drastically affect (dissipation, dispersion, and nonlinearity) the ultrasonic field. This paper constitutes the first work that associates the nonlinear ultrasonic field to a bubble generation process.     

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.