Diagnostics of elastic properties of a planar interface between two rough media using surface acoustic waves

The results of experimental studies on the nonlinear elastic properties of a planar interface between two media are presented—an optically polished glass substrate and flat samples with different degrees of roughness. The nonlinear elastic properties of the interfaces between two media were investigated by the spectral method using surface acoustic waves (SAWs). The effect of external pressure applied to the interface on the efficiency of the generation of the second SAW harmonic was studied. Using the measured amplitudes of the first and second harmonics of the SAW that passes along the interface, the second-order nonlinear acoustic parameter was calculated as a function of the external pressure applied to the sample at a fixed amplitude of a probing wave. It was revealed that the nonlinear parameter of the SAW is a nonmonotonic function of the pressure at the boundary. The results were analyzed on the basis of an elastic contact nonlinearity, and it is concluded that these results can be used in nondestructive testing for roughness and waviness of surfaces of flat solids.     

Wave processes in microinhomogeneous elastic media with hysteretic nonlinearity and relaxation

The nonlinear propagation of an initially harmonic acoustic wave in a microinhomogeneous medium containing defects with quadratic hysteretic nonlinearity and relaxation is studied by the perturbation method. The frequency dependences of the effective nonlinearity parameters are determined for the self-action of the quasi-harmonic acoustic wave and the higher harmonic generation processes.     

Pulse propagation in an elastic medium with quadratic nonlinearity (L)

This letter examines the propagation of an acoustic pulse in an elastic medium with weak quadratic nonlinearity. Both a displacement pulse and a stress pulse of arbitrary shapes are used to generate the wave motion in the solid. By obtaining the explicit solutions for arbitrary pulse shapes, it is shown that for a sinusoidal tone-burst, in addition to a second order harmonic field, a radiation induced static strain field is also generated. These results help clarify some confusion in the recent literature regarding the shape of the propagating static displacement pulse.     

Generation of higher acoustic harmonics at a flat rough interface between two solids

The results of experimental studies of the influence of a static pressure applied to a flat rough interface between two solids on its nonlinear elastic properties are presented. The studies were performed by the spectral method on the basis of an analysis of the efficiency of generation of higher acoustic harmonics, which arise upon the reflection of a longitudinal elastic wave of finite amplitude from the boundary and the passage through it. A nonmonotonic dependence of the amplitudes of acoustic harmonics on the value of the external reversible static pressure applied to the interface was revealed: pronounced amplitude maxima for the amplitudes of the second and third harmonics were observed with a decrease in the external static pressure. It was also found that the amplitudes of the second, third, and fourth acoustic harmonics increase with a decrease in the external static pressure (in comparison with their values at the same pressure values during its increase). The experimentally determined power dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic significantly differed from the classical indices for these harmonics. The influence of the external pressure on the values of the nonlinear second- and third-order elastic parameters was analyzed. The experimental results were analyzed on the basis of nonclassical acoustic nonlinearity.     

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 elastodynamics in micro-inhomogeneous solids observed by head-wave based dynamic acoustoelastic testing

Dynamic acoustoelastic testing provides a more complete insight into the acoustic nonlinearity exhibited by micro-inhomogeneous media like granular and cracked materials. This method consists of measuring time of flight and energy modulations of pulsed ultrasonic waves induced by a low-frequency standing wave. Here pulsed ultrasonic head waves were employed to assess elastic and dissipative nonlinearities in a region near the surface of a solid. Synchronization of the ultrasound pulse sequence with the low-frequency excitation provided instantaneous variations in the elastic modulus and the attenuation as functions of the instantaneous low-frequency strain. Weak quadratic elastic nonlinearity and no dissipative nonlinearity were detected in duralumin. In limestone, distinction between tensile and compressive behaviors revealed an asymmetry in the acoustic nonlinearity and hysteresis in both the elastic modulus and the attenuation variations. Measured nonlinear acoustical parameters are in good agreement with values obtained by different techniques. Reversible acoustically induced conditioning modified the acoustic nonlinearity both quantitatively and qualitatively. It reduced tension-compression asymmetry, suggesting a nonequilibrium modification of the sources of acoustic nonlinearity. Additionally to the metrology of the acoustic nonlinearity, head wave based dynamic acoustoelastic testing may be a useful tool to monitor changes in the microstructure or the accumulation of damage in solids.     

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。      

Nonlinear response to ultrasound of encapsulated microbubbles

The acoustic backscatter of encapsulated gas-filled microbubbles immersed in a weak compressible liquid and irradiated by ultrasound fields of moderate to high pressure amplitudes is investigated theoretically. The problem is formulated by considering, for the viscoelastic shell of finite thickness, an isotropic hyperelastic neo-Hookean model for the elastic contribution in addition to a Newtonian viscous component. First and second harmonic scattering cross-sections have been evaluated and the quantitative influence of the driving pressure amplitude on the harmonic resonance frequencies for different initial equilibrium bubble sizes and for different encapsulating physical properties has been determined. Conditions for optimal second harmonic imaging have been also investigated and some regions in the parameters space where the second harmonic intensity is dominant over the fundamental have been identified. Results have been obtained for albumin, lipid and polymer encapsulating shells, respectively.     

非线性声参量成像及其在医学诊断中应用

本文介绍了我们对于反射模式非线性参量B／A的成像技术的研究结果，包括：(1)基于二次谐波的非线性参量层析成像(2)基于参量阵差频波的非线性参量层析成像(3)非线性参量的等深度C-扫成像。利用这三种成像方法对多种生物组织，特别对正常和病变的生物组织进行非线性参量成像。结果表明，非线性声参量成像可以比线性声参量更容易地判别生物组织的病理状态，从而展示了它在医学超声诊断中的应用前景。     

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.     

Differential growth and instability in elastic shells

Differential growth in elastic materials can produce stress either through incompatibility of growth or by interaction with the surrounding medium. In many situations, this stress can be sufficient to induce shape instability in the growing medium. To gain better insight in growth-induced instabilities, the growth of an elastic shell loaded with hydrostatic pressure or embedded in an elastic medium is studied. The residual stress arising from the incompatibility of growth and the contact stress arising from the interaction with the surrounding medium are computed with respect to growth and geometric parameters and critical values for instability are obtained. Depending on these parameters, different modes of instability can be obtained.     

Study of acoustic nonlinearity parameter imaging methods in reflection mode for biological tissues

Three novel methods for acoustic nonlinearity parameter B/A imaging in reflection mode are developed in this paper. They are: (1) the acoustic nonlinearity parameter B/A tomography by detecting reflective second harmonic wave, (2) the B/A tomography in reflection mode via the measurement of the difference frequency wave generated by a parametric array, and (3) the C-scan imaging of B/A via the measurement of the echo second-harmonic signal. A theoretical analysis and the experimental imaging of normal and pathological biological tissues by using these methods are also present and discussed. Results show that using the acoustic nonlinearity parameter imaging we can more easily distinguish the diseased tissue from the normal one than using the linear acoustic parameters.     

The equation of state of a microinhomogeneous medium and the frequency dependence of its elastic nonlinearity

In the framework of a rheological model, a nonlinear dynamic equation of state of a microinhomogeneous medium containing nonlinear viscoelastic inclusions is derived. The frequency dependences of the effective nonlinear parameters are determined for the difference frequency and second harmonic generation processes in the case of a quadratic elastic nonlinearity. It is shown that the frequency dependence of the nonlinear elasticity of the medium is governed by the linear relaxation response of the inclusions at the primary excitation frequency, as well as by the relaxation of the inclusions at the nonlinear generation frequencies.     

Time reversed elastic nonlinearity diagnostic applied to mock osseointegration monitoring applying two experimental models

This study broadens vibration-like techniques developed for osseointegration monitoring to the nonlinear field. The time reversed elastic nonlinearity diagnostic is applied to two mock models. The first one consists of tightening a dental implant at different torques in a mock cortical bone; the second one allows one to follow glue curing at the interface between a dental implant and a mock jaw. Energy is focused near the implant interface using the time reversal technique. Two nonlinear procedures termed pulse inversion and the scaling subtraction method, already used successfully in other fields such as contrast agents and material characterization, are employed. These two procedures are compared for both models. The results suggest that nonlinear elasticity can provide new information regarding the interface, complementary to the linear wave velocity and attenuation. The curing experiment exhibits an overall low nonlinear level due to the fact that the glue significantly damps elastic nonlinearity at the interface. In contrast, the torque experiment shows strong nonlinearities at the focus time. Consequently, a parallel analysis of these models, both only partially reflecting a real case, enables one to envisage future in vivo experiments.     

Propagation of longitudinal elastic waves in a fluid-saturated porous medium with spherical inclusions

The Frenkel-Biot theory is used to study the propagation of a longitudinal harmonic wave of the first kind in an isotropic porous matrix with inclusions contrasting in elastic properties and hydrodynamic permeability. The generation of elastic waves of the second kind at the boundaries of inclusions is taken into account. The effective wave number of the longitudinal wave is calculated using the equations of multiple scattering theory. The characteristic size of inhomogeneities is assumed to be much greater than the size of pores. The parameters of the model used for calculations correspond to sandstone with centimeter-scale inhomogeneities. The presence of such inhomogeneities is typical of sedimentary rocks. Calculations show that, in the frequency range of acoustic logging, the effective attenuation factor of the longitudinal wave may noticeably exceed the attenuation factors of longitudinal waves of the first kind in both matrix and inclusions. From the results obtained, it follows that, when studying the propagation of elastic waves in fluid-saturated porous media, it is necessary to take into account the hydrodynamic effects associated with the filtration overflows that arise at the boundaries of inhomogeneities.     

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method (EMM) is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd (Gaunaurd GC and \"{U}berall H, {\em J. Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximation by comparing the dynamic (i.e. frequency-dependent) effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail. The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave. Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system's resonance induced by the existence of bubbles.     

Nonlinear elasticity in structurally inhomogeneous materials: An experimental study

Experimental results on the propagation of longitudinal and torsional elastic waves in polycrystalline copper under elastoplastic strain are reported. The strain in the interval of 0–0.06 was created by applying heavy tensile loads to the samples. The Young and shear moduli, Poisson ratio, and nonlinear acoustic parameters of longitudinal and torsional elastic waves were measured as functions of the static strain. The nonlinear acoustic parameters were found to behave anomalously in loading-unloading cycles in the plastic strain region. The experimental results are discussed. The nonlinear properties of structurally inhomogeneous materials are explained in terms of the clapping nonlinearity and hysteretic nonlinearity mechanisms.     

Testing for inhomogeneity of the nonlinear parameter in an acoustic medium by ultrasonic phase conjugation

The principle of applying a selective phase conjugation of the second harmonic of a focused ultrasonic wave to diagnosing inhomogeneity of the nonlinear parameter in an acoustic medium is considered. A solution to the three-dimensional problem of harmonic generation by phase-conjugated waves in a nonlinear medium with a localized isoechogenous inclusion is obtained. The signal amplitudes detected by a transmitting-receiving transducer at the second and forth harmonics of a probe wave are calculated for varying position of the inclusion relative to the focus.