Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone

Nonlinear resonant ultrasound spectroscopy (NRUS) is a resonance-based technique exploiting the significant nonlinear behavior of damaged materials. In NRUS, the resonant frequency(ies) of an object is studied as a function of the excitation level. As the excitation level increases, the elastic nonlinearity is manifest by a shift in the resonance frequency. This study shows the feasibility of this technique for application to damage assessment in bone. Two samples of bovine cortical bone were subjected to progressive damage induced by application of mechanical cycling. Before cycling commenced, and at each step in the cycling process, NRUS was applied for damage assessment. For independent assessment of damage, high-energy x-ray computed tomography imaging was performed but was only useful in identifying the prominent cracks. As the integral quantity of damage increased, NRUS revealed a corresponding increase in the nonlinear response. The measured change in nonlinear response is much more sensitive than the change in linear modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work must be carried out for a better understanding of the physical nature of damaged bone and for the ultimate goal of the challenging in vivo implementation of the technique.     

Applying nonlinear resonant ultrasound spectroscopy to improving thermal damage assessment in concrete

Nonlinear resonant ultrasound spectroscopy (NRUS) consists of evaluating one or more resonant frequency peak shifts while increasing excitation amplitude. NRUS exhibits high sensitivity to global damage in a large group of materials. Most studies conducted to date are aimed at interrogating the mechanical damage influence on the nonlinear response, applying bending, or longitudinal modes. The sensitivity of NRUS using longitudinal modes and the comparison of the results with a classical linear method to monitor progressive thermal damage (isotropic) of concrete are studied in this paper. In addition, feasibility and sensitivity of applying shear modes for the NRUS method are explored.     

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。      

绝缘颗粒液体主体基质复合介质的非线性光学性质

利用Maxwell-Garnett近似，并结合谱表示方法，理论研究了具有一般非线性的绝缘颗粒，无规则浸入液体主体基质复合体系的非线性光学性质-在弱非线性条件下，数值研究了体系的有效线性介电函数和光学非线性随体积分数的变化，并发现体系的线性介电函数比光学非线性更依赖于绝缘颗粒组分的体积分数-在一般非线性条件下，研究体系的有效介电函数随入射光强度的依赖关系，还研究了s方向和p方向极化的总反射率的行为- 关键词： 复合介质 谱表示 非线性光学性质     

Local interaction simulation approach to modelling nonclassical,nonlinear elastic behavior in solids

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.     

Bone micro-damage assessment using non-linear resonant ultrasound spectroscopy (NRUS) techniques: a feasibility study

Non-linear resonant ultrasound spectroscopy (NRUS) is a technique exploiting the significant non-linear behavior of damaged materials, related to the presence of damage. This study shows for the first time the feasibility of this technique for damage assessment in bone. Two samples of bovine cortical bone were subjected to a progressive damage experiment. Damage accumulation was progressively induced in the samples by mechanical testing. For independent assessment of damage, X-ray CT imaging was performed at each damage step, but only helped in the detection of the prominent cracks. Synchrotron micro-CT imaging and histology using epifluorescence microscopy were performed in one of the two samples at the last damage step and allowed detection of micro-cracks for this step. As the quantity of damage accumulation increased, NRUS revealed a corresponding increase in the non-linear response. The measured change in non-linear response is much more sensitive than the change in elastic modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work has to be carried out for a better understanding of the physical nature of damaged bone, and for the ultimate goal of in vivo implementation of the technique where bone access will be a challenging problem.     

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.     

高灵敏度表面光学非线性测量法

提出了一种测量非透明材料表面光学非线性的新方法:挡板反射4F测量法。该方法在反射4F相位相干成像系统的基础上,在4F系统的像平面放置一个与系统入射面光阑相匹配的不透明挡板,通过测量不同情况下的反射率,实现对材料光学非线性的测量。详细介绍了该方法的基本原理,并通过数值模拟计算了入射角对测量灵敏度的影响。该方法具有单脉冲测量,可同时得到材料的非线性吸收与折射系数等特点。结果表明,在相同条件下挡板反射4F测量法的灵敏度比反射Z扫描方法高2个数量级。     

Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics

A dual frequency mixing technique has been developed for measuring velocity changes caused by material nonlinearity. The technique is based on the parametric interaction between two surface acoustic waves (SAWs): The low frequency pump SAW generated by a transducer and the high frequency probe SAW generated and detected using laser ultrasonics. The pump SAW stresses the material under the probe SAW. The stress (typically <5 MPa) is controlled by varying the timing between the pump and probe waves. The nonlinear interaction is measured as a phase modulation of the probe SAW and equated to a velocity change. The velocity-stress relationship is used as a measure of material nonlinearity. Experiments were conducted to observe the pump-probe interaction by changing the pump frequency and compare the nonlinear response of aluminum and fused silica. Experiments showed these two materials had opposite nonlinear responses, consistent with previously published data. The technique could be applied to life-time predictions of engineered components by measuring changes in nonlinear response caused by fatigue.     

Analysis of nonlinear oscillators using Volterra series in the frequency domain

The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett (1965) [1] proposed a time domain criterion to prove that the Volterra series converges within a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation. A common and severe nonlinear phenomenon called jump, a behavior associated with the Duffing oscillator and the multi-valued properties of the response solution, is investigated using the new frequency domain criterion of establishing the upper limits of the nonlinear oscillators, to predict the onset point of the jump, and the Volterra time and frequency domain analysis of this phenomenon are carried out based on graphical and numerical techniques.     

Measurement of the frequency response induced by electrostriction in optical fibers

Accurate measurements of the frequency response of the nonlinear refractive index induced by the combined effects of Kerr nonlinearity with electrostrictional excitation of acoustic waves in optical fibers are presented. A detailed experimental investigation of both standard (zero-dispersion wavelength,lambda(0) approximately 1.31microm) and dispersion-shifted (lambda(0)=1.55microm) single-mode fibers showed the presence of several resonant peaks induced by the electrostrictive nonlinearity in the fiber structure. This investigation has provided better insight into the frequency behavior of the electrostriction-induced acoustic waves in optical fibers.     

Ultrafast optical switching in Kerr nonlinear photonic crystals

Nonlinear photonic crystals made from polystyrene materials that have Kerr nonlinearity can exhibit ultrafast optical switching when the samples are pumped by ultrashort optical pulses with high intensity due to the change of the refractive index of polystyrene and subsequent shift of the band gap edge or defect state resonant frequency. Polystyrene has a large Kerr nonlinear susceptibility and almost instantaneous response to pump light, making it suitable for the realization of ultrafast optical switching with a response time as short as a few femtoseconds. In this paper, we review our experimental progress on the continual improvement of all-optical switching speed in two-dimensional and three-dimensional polystyrene nonlinear photonic crystals in the past years. Several relevant issues are discussed and analyzed, including different mechanisms for all-optical switching, preparation of nonlinear photonic crystal samples by means of microfabrication and self-assembly techniques, characterization of optical switching performance by means of femtosecond pump-probe technique, and different ways to lower the pump power of optical switching to facilitate practical applications in optical information processing. Finally, a brief summary and a perspective of future work are provided.     

A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media

Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear (NL) hysteretic effects in their elastic behaviour. These observations suggest the existence of a NL mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitly consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.     

New methods to solve the resonant nonlinear Schrödinger’s equation with time-dependent coefficients

In this study, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method (HSIVM) are applied to seek the exact solitary wave solutions for the resonant nonlinear Schrödinger equation with time-dependent coefficients. Using these methods, we investigate exact solutions for the nonlinear resonant Schrödinger equation with time-dependent coefficients two forms of nonlinearity, including power and dual-power law nonlinearity. Moreover, many new analytical exact solutions are obtained which are expressed by hyperbolic solutions, trigonometric solutions, and rational solutions. In addition, we obtained the bright soliton by HSIVM. These methods are powerful, efficient and those can be used as an alternative to establishing new solutions of different types of differential equations in mathematical physics and engineering.     

The study of the nonlinear absorption in the nonlinear-imaging technique with phase object

The nonlinear absorption can produce a nonlinear image very similar with the one created by the nonlinear refraction when using the nonlinear-imaging technique with phase object to measure the third-order nonlinearity of materials, but the principles of them are different. The formation of the nonlinear absorption image is explained, and the condition that the highest sensitivity of the nonlinear absorption measurement can be reached is deduced. For the materials with both nonlinear absorption and refraction, we find a proper phase shift of the phase object where the effect of the nonlinear refraction to the measured signal can be eliminated. The nonlinear absorption and refraction are numerically simulated when the phase shift of phase object to be π/2 that is normally used. The qualitative tendency of the signal variation is presented.     

Theoretical and experimental study of the nonlinear resonance vibration of cementitious materials with an application to damage characterization

This paper presents a theoretical and experimental study of the nonlinear flexural vibration of a cement-based material with distributed microcracks caused by an important deterioration mechanism, alkali-silica reaction (ASR). The general equation of motion is derived for the flexural vibration of a slender beam with the nonlinear hysteretic constitutive relationship for consolidated materials, and then an approximate formula for excitation-dependent resonance frequency is obtained. A downward shift of the resonance frequency is related to the nonlinearity parameters defined in the constitutive relationship. Vibration experiments are conducted on standard mortar bar samples undergoing progressive ASR damage. The absolute nonlinearity parameters are determined from these experimental results using the theoretical solution in order to investigate their dependence on the damage state of the material. With the progress of the ASR damage, the absolute value of the hysteresis nonlinearity parameter increases by as much as six times from the intact (undamaged) state in the sample with highly reactive aggregate; this is in contrast to a change of about 16% in the linear resonance frequency. It is demonstrated that the combined theoretical and experimental approach developed in this research can be used to quantitatively characterize ASR damage in mortar samples and other cement-based materials.     

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.     

Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system

We measure the Kerr-nonlinear index of refraction of a three-level Lambda-type atomic system inside an optical ring cavity. The Kerr nonlinearity is modified and greatly enhanced near atomic resonant conditions for both probe and coupling beams. The Kerr nonlinear coefficient n(2) changes sign when the coupling beam frequency detuning switches sign, which can lead to interesting applications in optical devices such as all-optical switches.     

Multiwave mixing of singular light beams in resonant media

A method for transforming the topological structure of a singular light beam under multiwave mixing in the media with resonant nonlinearity is justified theoretically. The effect of self-and cross-modulation of the light waves under condition of nonlinear variation of the refractive index on stability of the optical vortices appearing in the multiwave mixing is studied.