Acoustic nonlinearity of cracks partially filled with liquid: cubic approximation.

The theoretical investigation of mechanisms of the acoustic nonlinearity (elastic and inelastic) of cracks partially filled with an ideal and viscous liquid and associated with the nonlinear dependence of the capillary and viscous pressure in the liquid on the distance between the crack surfaces and the velocity of the change of this distance is proposed. The nonlinear (in cubic approximation) equations of the state of these cracks is obtained, and its parameters are defined. It is shown that the presence of the viscous liquid may lead to the considerable increase of the acoustic nonlinearity of such cracks in comparison with cracks filled with the ideal liquid.     

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 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 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.     

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。      

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.     

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.     

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.     

Numerical models for the study of the nonlinear frequency mixing in two and three-dimensional resonant cavities filled with a bubbly liquid

The objective of this work is to develop versatile numerical models to study the nonlinear distortion of ultrasounds and the generation of low-ultrasonic frequency signals by nonlinear frequency mixing in two and three-dimensional resonators filled with bubbly liquids. The interaction of the acoustic field and the bubble vibrations is modeled through a coupled differential system formed by the multi-dimensional wave equation and a Rayleigh-Plesset equation. The numerical models we develop are based on multi-dimensional finite-volume techniques and a time discretization carried out by finite differences. Numerical experiments are performed for complex modes in many different cavities considering different kinds of boundary conditions and taking advantage of the dispersive character of the bubbly fluid to match specific resonances of the cavities. Results show the distribution of fundamental and harmonics for single frequency excitation and difference-frequency component for two-frequency excitation that are promoted by the strong nonlinearity of the bubbly medium. The numerous simulations analyzed suggest that the new numerical models developed and proposed in this paper are useful to understand the behavior of ultrasounds in bubbly liquids for sonochemical processes and applications of nonlinear frequency mixing.     

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。      

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.     

Baseline-free estimation of residual fatigue life using a third order acoustic nonlinear parameter

Prediction of crack growth and fatigue life estimation of metals using linear/nonlinear acousto-ultrasound methods is an ongoing issue. It is known that by measuring nonlinear parameters, the relative accumulated fatigue damage can be evaluated. However, there is still a need to measure two crack propagation states to assess the absolute residual fatigue life. A procedure based on the measurement of a third-order acoustic nonlinear parameter is presented to assess the residual fatigue life of a metallic component without the need of a baseline. The analytical evaluation of how the cubic nonlinear-parameter evolves during crack propagation is presented by combining the Paris law to the Nazarov-Sutin crack equation. Unlike other developed models, the proposed model assumes a crack surface topology with variable geometrical parameters. Measurements of the cubic nonlinearity parameter on AA2024-T351 specimens demonstrated high sensitivity to crack propagation and excellent agreement with the predicted theoretical behavior. The advantages of using the cubic nonlinearity parameter for fatigue cracks on metals are discussed by comparing the relevant results of a quadratic nonlinear parameter. Then the methodology to estimate crack size and residual fatigue life without the need of a baseline is presented, and advantages and limitations are discussed.     

Acoustic heating produced in the thermoviscous flow of a Bingham plastic

This study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic’s viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation governing acoustic heating, and to retain those belonging to the thermal mode. The nonlinear terms of the final equation are a result of interaction between sounds and the thermal mode. In the field of intense sound, the resulting nonlinear acoustic terms form a driving force for the heating. The final governing dynamic equation of the thermal mode is valid in a weakly nonlinear flow. It is instantaneous, and does not imply that sounds be periodic. The equations governing the dynamics of both sounds and the thermal mode depend on sign of the shear rate. An example of the propagation of a bipolar initially acoustic pulse and the evolution of the heating induced by it is illustrated and discussed.     

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.     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

A generalized Westervelt equation for nonlinear medical ultrasound

A model equation is derived for nonlinear medical ultrasound. Unlike the existing models, which use spatial coordinates, material coordinates are used and hence a model for a heterogeneous medium is able to be derived. The equation is a generalization of the Westervelt equation, and includes the nonlinearity, relaxation, and heterogeneity of soft tissue. The validity of the generalized Westervelt equation as a model equation for a Piola-Kirchoff acoustic pressure and as an equation for the acoustic pressure is discussed. In the second case it turns out that the model follows from two geometric approximations which are valid when the radius of curvature of the phase fronts is much larger than the particle displacements. The model is exact for plane waves and includes arbitrary nonlinearity in the stress-strain relation.     

鼓泡床中超声驻波的模拟及其对气泡的调制机理

采用计算流体动力学（CFD）的方法，数值生成了鼓泡床中一对声换能器以16kHz高频振动引发的超声场。数值计算是基于包括粘性影响的可压缩流体基本守恒方程，并耦合了水的状态方程。模拟结果表明，在本研究所用的几何布置和换能器与时间相关的速度入口边界条件下，反应器中形成了一个稳定的驻波声场；由于波的非线性以及水的粘性，压力波节点呈现出轻微的时间漂移性。模拟结果与前人的实验结果定性吻合。在模拟的声压分布的基础上，分析了驻波声场调制气泡的机理。如比较熟知，气泡在驻波声场作用下或者向压力波节点运动或者向压力波腹点运动，取决于气泡尺寸与共振尺寸的关系。     

Influence of resonator shape on nonlinear acoustic field in a thermoacoustic engine

The influence of the resonator shape on nonlinear acoustic field in a thermoacoustic engine is studied.The resonator of themoacoustic engine is boundary driving by a piston at one end,and the other end of it is rigid closed.A one-dimensional wave equation that accounts for gas dynamic nonlinearities and viscous dissipation in the resonator is established based on the governing equations of viscous hydromechanics.The nonlinear wave equation is solved using approximate Galerkin method.The nonlinear acoustic field in four different types of shaped resonators including hyperbolical,exponential,conical and sinusoidal are obtained and compared with that of a cylindrical resonator.It is found that the amplitude and waveform of the pressure are strongly affected by the resonator shape,the driving amplitude and the oscillation frequency of the piston.Waveform distortion,resonance frequency shift and hysteresis are observed,when the piston oscillation amplitude is large enough.The advantages of shaped resonator for thermoacoustic engine lie in inhibition of higher order harmonics and improvement of pressure ratio,etc.