岩石等非线性介观弹性固体材料的谐波特性的超声研究

岩石、混凝土等非线性介观弹性固体材料显示出与经典的非线性声学不同的非经典非线性声学现象，比如滞后现象、离散记忆等。本文实验研究了超声波在岩石材料中产生的基波、二次、三次谐波随声源幅度的依赖关系，研究了岩石的超声衰减，与金属材料的进行了对比；并且将浸水后的混凝土与浸水前的混凝土的超声谐波特性进行了对比，对此实验现象作出了定性的解释。此研究有利于岩石等非线性介观弹性固体材料的无损检测的研究。     

表面张力对Rayleigh-Taylor不稳定性谐波的影响

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability (RTI) for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third harmonics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.     

Dependence of the driving current on the harmonic behavior of giant magneto-impedance voltage of Co-based amorphous wires

The frequency and the amplitude of the driving AC current dependence on the harmonic behavior of the giant magneto-impedance (GMI) voltage of Co-rich amorphous wire have been studied. Single-peak, two-peak and three-peak behavior in the GMI characteristics was studied with the change of amplitude and frequency of the AC current. GMI ratio was calculated from the first harmonic signals which were initially increased and then decreased monotonically with the increase of frequency (f) and the amplitude (I_AC) of the driving current. The response of the GMI voltage was found non-linear with the generation of higher harmonics at higher amplitude of the driving current. The second and third harmonic signals were also evaluated and their dependence on the driving current amplitude and frequency were presented in the paper. The experimental results were analyzed using single domain rotational model. The voltage harmonics were calculated through Fourier transform of the time derivative of the estimated circular magnetization of the sample.     

Multiplication of the drive signal frequency in a relativistic microwave amplifier with a rod slow-wave structure

A theory is developed for the one-dimensional nonlinear multimode simulation of a Cerenkov maser of special configuration (antenna-amplifier [1, 2]) where a tubular relativistic electron beam propagates along a circular waveguide with a dielectric rod. The operating mode is the fundamental azimuthally asymmetric HE ₁₁ mode. Harmonics at the input signal frequency can be amplified because they fall into the amplification bands for higher modes. At certain parameters, the output power at the second or third harmonic may considerably exceed that of the amplified signal at the fundamental frequency. The powers of output harmonics can be efficiently controlled by varying the point of electron beam extraction from the interaction region, as well as by varying the input frequency or by switching the polarization of the input signal from linear to circular.     

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.     

Spatial distribution of the nonlinear acoustic parameters in a thin polycrystalline plate of alloy with defects

By the results of experimental measurements of the Lamb wave’s amplitude at the fundamental frequency and its second and third harmonics, the spatial distributions of the quadratic and cubic nonlinear acoustic parameters in a thin circular plate of D16 polycrystalline aluminum alloy with defects were calculated. The correlation between these distributions and defect positions in the plate was determined.     

Effective nonlinear AC response to graded cylindrical composites

The perturbation method is used to study the effective nonlinear response of graded cylindrical composites with power-law gradient inclusions under a sinusoidal alternating current (AC) external field of finite frequency ω. In dilute limit, the local potentials and the formulae of effective nonlinear AC responses are derived at the fundamental frequency and the third harmonics. Furthermore, the general effective nonlinear responses are given and compared with the effective nonlinear AC responses of fundamental frequency and the third harmonics, and the relationships between the nonlinear effective AC response and the general effective nonlinear response are also determined.     

Weak Nonlinearity of Ablative Rayleigh--Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh-Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh-Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.     

Cumulative solutions of nonlinear longitudinal vibration in isotropic solid bars

Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regarded as the first-order correction to the linear wave equation. To solve the equation, the biggest challenge is that the secular terms exist not only in the fundamental wave equation but also in the harmonic wave equation （unlike the Duffing oscillator, where they exist only in the fundamental wave equation）. In order to overcome this difficulty and to obtain a steady periodic solution by the perturbation technique, the following procedures are taken： （i） for the fundamental wave equation, the secular term is eliminated and therefore a frequency response equation is obtained; （ii） for the harmonics, the cumulative solutions are sought by the Lagrange variation parameter method. It is shown by the results obtained that the second- and higher-order harmonic waves exist in a vibrating bar, of which the amplitude increases linearly with the distance from the source when its length is much more than the wavelength; the shift of the resonant peak and the amplitudes of the harmonic waves depend closely on nonlinear coefficients; there are similarities to a certain extent among the amplitudes of the odd- （or even-） order harmonics, based on which the nonlinear coefficients can be determined by varying the strain and measuring the amplitudes of the harmonic waves in different locations.     

Harmonic generation in superconducting Bi(Pb)SrCaCuO thick films

We present a detailed study of harmonic generation in Bi(Pb)SrCaCuO superconducting thick film prepared by screen printing technique. A comparative study of amplitude of harmonics of two films of different J_c have been carried out. The variation of amplitudes of the harmonics are studied as a function of magnitude of ac and dc field. The temperature dependence of amplitude of third harmonic (V³) is studied with increasing amplitude as well as frequency of ac field. These results are analyzed in the frame work of critical state model. V₃ -T curve also indicates the presence of two phases in Bi(Pb)SrCaCuO film.     

Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging

A time-domain numerical code (the so-called Texas code) that solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been extended from an axis-symmetric coordinate system to a three-dimensional (3D) Cartesian coordinate system. The code accounts for diffraction (in the parabolic approximation), nonlinearity and absorption and dispersion associated with thermoviscous and relaxation processes. The 3D time domain code was shown to be in agreement with benchmark solutions for circular and rectangular sources, focused and unfocused beams, and linear and nonlinear propagation. The 3D code was used to model the nonlinear propagation of diagnostic ultrasound pulses through tissue. The prediction of the second-harmonic field was sensitive to the choice of frequency-dependent absorption: a frequency squared f2 dependence produced a second-harmonic field which peaked closer to the transducer and had a lower amplitude than that computed for an f1.1 dependence. In comparing spatial maps of the harmonics we found that the second harmonic had dramatically reduced amplitude in the near field and also lower amplitude side lobes in the focal region than the fundamental. These findings were consistent for both uniform and apodized sources and could be contributing factors in the improved imaging reported with clinical scanners using tissue harmonic imaging.     

Comparison of fundamental, second harmonic, and superharmonic imaging: a simulation study

In medical ultrasound, fundamental imaging (FI) uses the reflected echoes from the same spectral band as that of the emitted pulse. The transmission frequency determines the trade-off between penetration depth and spatial resolution. Tissue harmonic imaging (THI) employs the second harmonic of the emitted frequency band to construct images. Recently, superharmonic imaging (SHI) has been introduced, which uses the third to the fifth (super) harmonics. The harmonic level is determined by two competing phenomena: nonlinear propagation and frequency dependent attenuation. Thus, the transmission frequency yielding the optimal trade-off between the spatial resolution and the penetration depth differs for THI and SHI. This paper quantitatively compares the concepts of fundamental, second harmonic, and superharmonic echocardiography at their optimal transmission frequencies. Forward propagation is modeled using a 3D-KZK implementation and the iterative nonlinear contrast source (INCS) method. Backpropagation is assumed to be linear. Results show that the fundamental lateral beamwidth is the narrowest at focus, while the superharmonic one is narrower outside the focus. The lateral superharmonic roll-off exceeds the fundamental and second harmonic roll-off. Also, the axial resolution of SHI exceeds that of FI and THI. The far-field pulse-echo superharmonic pressure is lower than that of the fundamental and second harmonic. SHI appears suited for echocardiography and is expected to improve its image quality at the cost of a slight reduction in depth-of-field.     

Improved contrast to tissue ratio at higher harmonics

The challenge in ultrasound contrast imaging is a better discrimination between the perfused tissue and the contrast bubbles, which is usually expressed by contrast to tissue ratio (CTR). Imaging based on the second harmonic frequency showed a higher CTR than imaging at the fundamental frequency. However, because of nonlinear propagation of ultrasound waves, harmonic frequencies are generated. These harmonic frequencies will be linearly reflected by the tissue and therefore limit the CTR at the second harmonic frequency. In order to reduce the scattering of tissue at harmonic frequencies and by that increase the CTR, nonlinear distortion has to be reduced. We demonstrate in this study that the CTR increases with the harmonic number. The increase is substantial when transmitting at lower frequencies. To take advantage of the higher harmonics (third, fourth, fifth and the ultraharmonics and termed here super harmonics), we have developed a new phased array transducer with a wide frequency band. In-vitro measurements using the new probe show an increase of 40 dB of the CTR for super harmonic components over the conventional second harmonic system. The increase in CTR is in agreement with the calculations using existing models for the response of encapsulated bubbles and known theory of nonlinear propagation.     

Experimental and theoretical study of harmonic generation at contacting interface

The second harmonic generation behavior of a contacting interface has been evaluated experimentally and discussed theoretically in the light of a nonlinear interface model. Two aluminum blocks were mated together to constitute a contact interface and subjected to normal compressive loading. A 5 MHz longitudinal toneburst wave was sent to the interface in the normal direction and the transmitted wave was recorded, from which the fundamental and the second harmonic components were extracted. A nonlinearity parameter was obtained as the ratio of the second harmonic amplitude to the squared fundamental amplitude. From the measured contact pressure dependence of the transmitted fundamental amplitude, the linear and the second-order interfacial stiffness parameters were identified, which enabled the evaluation of the nonlinearity parameter based on the theoretical model. The theoretical contact pressure dependence of the nonlinearity parameter was found to be in good qualitative agreement with the experimental results.     

Nonlinear response and avalanche behavior in metallic glasses

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd₄₀Ni₄₀P₂₀ metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke’s Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.     

Localization and source level estimates of black drum (Pogonias cromis) calls

A four hydrophone linear array was used to localize calling black drum and estimate source levels and signal propagation. A total of 1025 source level estimates averaged 165 dB(RMS) relative (re:) 1 μPa (standard deviation (SD)=1.0). The authors suggest that the diverticulated morphology of the black drum swimbladder increase the bladder's surface area, thus contributing to sound amplitude. Call energy was greatest in the fundamental frequency (94 Hz) followed by the second (188 Hz) and third harmonics (282 Hz). A square root model best described propagation of the entire call, and separately the fundamental frequency and second harmonic. A logarithmic model best described propagation of the third harmonic which was the only component to satisfy the cut-off frequency equation. Peak auditory sensitivity was 300 Hz at a 94 dB re: 1 μPa threshold based on auditory evoked potential measurements of a single black drum. Based on mean RMS source level, signal propagation, background levels, and hearing sensitivity, the communication range of black drum was estimated at 33-108 m and was limited by background levels not auditory sensitivity. This estimate assumed the source and receiver were at approximately 0.5 m above the bottom. Consecutive calls of an individual fish localized over 59 min demonstrated a mean calling period of 3.6 s (SD=0.48), mean swimming speed of 0.5 body lengths/s, and a total distance swam of 1035 m.     

失谐驻波管及其极高纯净驻波场性质的研究

由直径不同的两级直圆管连接而成的两级突变截面驻波管具有失谐性,即高阶共振频率不是一阶共振频率的整数倍. 两级突变截面驻波管的失谐性质能够很好地抑制一阶共振频率激励下的大振幅非线性驻波畸变产生的高次谐波,从而获得大振幅纯净驻波场. 通过对两级突变截面驻波管失谐性质的研究,采用大功率扬声器正接等措施,利用两级突变截面驻波管的失谐性质在一阶共振频率激励下获得了184 dB的极高纯净驻波场,并对二至五阶共振频率激励下的声场进行了相应的实验研究. 在二阶、四阶共振频率激励下分别获得了180和166 dB波形比较规整的大振幅非线性驻波,并在三阶、五阶共振频率激励下观察到了谐波饱和现象和锯齿波. 关键词： 失谐驻波管 大振幅驻波 畸变 饱和