Application of chaotic cavity transducer in nonlinear elastic detection

The conjunction of "Chaotic Cavity Transducer(CCT)" focusing with Nonlinear Elastic Wave Spectroscopy(NEWS)methods has been discussed in the detection of the localization of micro-damage.CCT focusing is a combination process of CCT with the techniques of acoustic Time Reversal(TR)or Inverse Filter(IF),which can improve the ability of localization. In order to improve the quality of focalization,in the experimental process the chirped excitation source signal and inverse filtering techniques have been used.A focusing process in a non-reverberant composite plate sample and an image of a crack in a steel sample demonstrate the focalization ability and high efficiency of imaging of the combination of CCT with NEWS,and proves that CCT can efficiently overcome the problems of "phantom" image and increasement of the strain at the boundary of medium.     

混沌腔体换能器在非线性弹性检测中的应用

介绍了混沌腔体换能器(Chaotic Cavity Transducer:CCT)聚焦与非线性弹性波谱(Nonlinear Elastic Wave Spectroscopy:NEWS)法的结合在材料微观缺陷检测中的应用。CCT聚焦是CCT与声学时间反转(Time Reversal:TR)技术或反向滤波(Inverse Filter:IF)技术相结合的过程,此过程能够有效提高聚焦检测的能力。为了提高聚焦的质量,实验过程中采用了线性调频激发信号源及反向滤波技术。非混响的合成平板介质材料的聚焦过程及钢介质材料裂纹的成像检测结果证实了CCT与NEWS的结合在非线性聚焦及成像过程的高效性,及CCT在应用过程中克服幻影成像问题及边界应变增加问题的有效性。      

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.     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

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.     

金属材料疲劳损伤检测的非线性声学方法*

金属材料的疲劳损伤有前期、后期两个阶段,前期疲劳损伤主要来源于位错,而随着疲劳程度的不断加深,位错密度也不断的增加,这将导致疲劳后期微裂纹的产生。这两个阶段产生声学非线性效应的机理不同,分别用位错模型、微裂纹模型对其产生非线性效应的机理进行了阐述,并对不同阶段的疲劳试样进行了相关实验研究。实验结果表明:对于材料早期疲劳损伤,随着疲劳程度的增加,其接收声波信号中的非线性谐波成分越来越显著,并且随着激励电压的增加,非线性效应更加明显,因此可用接收信号中的谐波激发情况来评估材料的早期疲劳损伤程度。而对于材料疲劳后期出现微裂纹后,其产生的非线性与早期疲劳损伤相比,谐波成分更加丰富,并且随激励电压的增加谐波幅度增加明显,可据此来判断材料中的疲劳损伤阶段。     

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.     

Nonlinear light propagation in the defect band of one-dimensional defective structures

In this paper we numerically investigate the nonlinear propagation of defect state in one-dimensional structures with defects. We investigate the nonlinear transmission spectra and the bistable response for defective structures with different index gradients. The results show that positive Kerr nonlinearity can suppress the Wannier-Stark localization. And the nonlinear response of defect states band exhibits an optical switch behavior, which may be applied to all-optical devices. And the gap solitons from these defect states are presented.     

Defect solitons supported by the interface between simple lattices and superlattices

We study surface defect solitons (SDSs) at an interface between superlattices and simple lattices with focusing saturable nonlinearity. The properties of the SDSs formed in such kinds of mixed structures are obviously different from those in single superlattices or single ordinary lattices. Research results show that surface solitons with a zero defect or a positive defect are stable in the semi-infinite gap and cannot exist in the first gap. For the case of a negative defect, the stable region of surface solitons will be narrower in the semi-infinite gap with the increase of the defect depth. Surface gap solitons (SGSs) can stably exist in the first gap for a deeper negative defect depth.     

三阶非线性聚合物光波导研究

以三阶克尔型非线性波导为例,利用雅可比椭圆函数的特性,定义了一种新颖的雅可比椭圆余切振幅函数,以此建立了类似线性的在非线性条件下的色散关系,使形式简化、物理意义清晰。并利用这一关系分析了该情况下的模式特性和场特性。     

Surface defect solitons at interfaces between dual-frequency and simple lattices

We reveal theoretically the existence and stability of surface defect solitons (SDSs) at interfaces between dual-frequency and simple lattices with focusing saturable nonlinearity. Solitons with some unique properties exist in such composite structures with the change of defect intensity. For zero defect or positive defect, the surface solitons exist at the semi-infinite gap and cannot exist in the first gap, and solitons are stable at lower power but unstable at high power. For the case of negative defect, the surface solitons exist not only in the semi-infinite gap, but also in the first gap. With increasing the defect depth, the stable region of surface solitons becomes narrower in the semi-infinite gap, these solitons are stable within a moderate power region in the first gap within unstable solitons in the entire semi-infinite gap.     

Acoustic Solit on in One-Dimensional Ferromagnetic Systems

The local nonlinear excitation caused by the magnon-phonon interactions as an anisotropic source of nonlinearity is studied. The nonlinear equation for the Schrodinger probability amplitude of spin motion is given, and its soliton solutions are obtained in a weak coupling approximation. The existence conditions are discussed. It is shown that the soliton excitation energy can be less than a one-magnon state and a gap appears in the energy spectrum. The effect of the magnon-rnagnon interactions on the local acouitic soliton excitation is also discussed.     

Nonlinear fluorescence through intermolecular energy transfer and resolution increase in fluorescence microscopy

We investigate a novel concept to efficiently generate multiphoton induced fluorescence from organic molecules. The concept is based on frustrating the energy transfer between a fluorescent donor and one or more acceptors in conjugated molecules. The nonlinearity is not based on higher order molecular susceptibilities but entirely on their linear properties. Therefore, in contrast to nonresonant multiphoton absorption, this method does not require high local intensities. Likewise, the production of visible fluorescence does not require an infrared excitation wavelength. Hence, when applied to scanning microscopy this property is predicted to increase spatial resolution. Instead of the ∼10 GW/cm² required in non-resonant multiphoton excitation, focal intensities ∼10 MW/cm² are expected to produce an equally strong nonlinear signal. The predicted resolution is up to 30% greater than that of an ideal confocal microscope operating at the same fluorescence wavelength. The resolution improvement over non-resonant two-photon absorption microscopes is about two-fold in all directions.     

Localization in the model of contacting media with specific nonlinearity and interface interaction

In this paper, we consider the new model of nonlinear contacting media based on nonlinear Schrodinger equation with point potential and term, which is depended stepwise on field amplitude. Such a model theoretically describes a change in properties of the boundary regions along the interface between a Kerr-type crystal with cubic nonlinearity and a nonlinear medium characterized by abruptly change in dielectric constant depending on field amplitude. The short-range local interaction between wave and interface is taken into account by point potential in nonlinear Schrodinger equation. We obtain two new types of localized states characterized by composite structure consisting of three parts of the field distributions. We find exact and approximate solutions of dispersion equations. We described new properties of the spectrum of localized states arising as a result of the interaction of the wave with the interface and the presence of threshold field of the switching between the medium constants. All results are obtained in an analytical form. The proposed theory can be used to describe the propagation features of intense light beams localized along media interfaces in nonlinear optics, and to describe Bose-Einstein condensates with cubic nonlinearity.     

On the spectral and conservation properties of nonlinear discretization operators

Following the study of Pirozzoli [1], the objective of the present work is to provide a detailed theoretical analysis of the spectral properties and the conservation properties of nonlinear finite difference discretizations. First, a Nonlinear Spectral Analysis (NSA) is proposed in order to study the statistical behavior of the modified wavenumber of a nonlinear finite difference operator, for a large set of synthetic scalar fields with prescribed energy spectrum and random phase. Second, the necessary conditions for local and global conservation of momentum and kinetic energy are derived and verified for nonlinear discretizations. Because the nonlinear mechanisms result in a violation of the energy conservation conditions, the NSA is used to quantify the energy imbalance. Third, the effect of aliasing errors due to the nonlinearity is analyzed. Finally, the theoretical observations are verified for two simple, thought relevant, numerical simulations.     

非线性Bragg微腔的双稳态研究

研究了一维Bragg微腔中的光学增强效应,并对F-P腔中Kerr介质的双稳态特性进行了理论分析,并得到相应的数学表达式.研究表明,对聚焦型Kerr介质（χ(3)>0）,要产生双稳态特性必须给入射光波预置一定的红移量,若是散焦型介质（χ(3)<0）则要预置一定的蓝移量.红移量（或蓝移量）的临界值与光子晶体的介质折射率、周期数、F-P腔长度、缺陷模的线宽（FWHM）等因素密切相关,它随介质折射率比、周期数、F-P腔长的增大而减小,随缺陷模的线形变窄而降低.要有效地降低非线性介质的双稳态开关阈值,除了尽可能选择较小的合适红移（或蓝移）量外,还要选择｜χ(3)｜较大的Kerr介质以增强腔内的非线性光学效应.     

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N(N−1)/2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.     

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.     

Physics-based modeling techniques of a twelve-string Portuguese guitar: A non-linear time-domain computational approach for the multiple-strings/bridge/soundboard coupled dynamics

The Portuguese guitar is a pear-shaped instrument with twelve metal strings which is widely used in Portuguese traditional music. Unlike most common guitars, it has a curved top-plate and a specific violin-like bridge which is not rigidly fixed to the soundboard of the instrument. From the dynamical point of view, if the bridge transmits the strings vibrations to the instrument body in order to maximize the radiated energy, it also couples all the component parts of the instrument which therefore interact by structural coupling. This can originate various audible effects such as beating behavior and the excitation of numerous sympathetic resonances enhanced by the large number of strings of the instrument, and this is certainly why the Portuguese guitar has such distinct sound compared to other guitars. In this paper, a fully coupled time-domain model of the Portuguese guitar is developed and a series of simulations are presented to emphasize the various coupling phenomena involved in sound production. To reproduce the main musical features, the model includes the coupled dynamics of the twelve strings supported by a bridge which interact with the body of the instrument, described through Finite-Element modeling of the soundboard of a typical Portuguese guitar. Further simple models have been devised for the string/fret interaction and the pluck excitation. Since nonlinear effects are quite apparent in the behavior of string musical instruments, the string dynamics is modeled by the Kirchhoff–Carrier equations which describe large-amplitude string vibrations, and includes the coupling between both polarizations of string motion. The coupling between the strings and the soundboard at the bridge is provided by a model of the bridge kinematics, built on the basis of simple geometrical rationale, so that the two perpendicular string motions can exchange energy back and forth. By a close examination of the energy transfers between the various subsystems of the model, we first assess the correct behavior of the physical model and then examine the respective influence of the string nonlinearity and the bridge on the nonplanar motion of the string. The fully coupled model which pertains to the restricted group of studies which deals with the complete physical-based modeling of a multi-stringed instrument, captures many important phenomena observed in practice, among which the pitch glide effect and the mutual excitation of sympathetic vibrations.