固体中二维纵波非线性方程的摄动解

针对二维纵波非线性方程的求解问题进行了研究.从二维纵波非线性方程出发,围绕声马赫数对该方程的解进行二阶摄动展开,求解出二维非线性纵波方程的二阶摄动解.根据计算结果定义二次谐波沿x轴的传播分量和沿y轴的传播分量与入射基波的振幅比为非线性系数,并对基波和二次谐波的传播特性进行详细讨论,探究了二维纵波在固体中传播时其入射波振...     

Second harmonic generation of shear waves in crystals

Nonlinear self-interaction of shear waves in electro-elastic crystals is investigated based on the rotationally invariant state function. Theoretical analyses are conducted for cubic, hexagonal, and trigonal crystals. The calculations show that nonlinear self-interaction of shear waves has some characteristics distinctly different from that of longitudinal waves. First, the process of self-interaction to generate its own second harmonic wave is permitted only in some special wave propagation directions for a shear wave. Second, the geometrical nonlinearity originated from finite strain does not contribute to the second harmonic generation (SHG) of shear waves. Therefore, unlike the case of longitudinal wave, the second-order elastic constants do not involve in the nonlinear parameter of the second harmonic generation of shear waves. Third, unlike the nonlinearity parameter of the longitudinal waves, the nonlinear parameter of the shear wave exhibits strong anisotropy, which is directly related to the symmetry of the crystal. In the calculations, the electromechanical coupling nonlinearity is considered for the 6 mm and 3 m symmetry crystals. Complement to the SHG of longitudinal waves already in use, the SHG of shear waves provides more measurements for the determination of third-order elastic constants of solids. The method is applied to a Z-cut lithium niobate (LiNbO/sub 3/) crystal, and its third-order elastic constant c/sub 444/ is determined.     

Explosive collapse of vapor film under conditions of intensive heat fluxes

The stability is investigated (linear and nonlinear analysis) of the interface between a thin vapor film and a layer of liquid in the presence of a steady heat flux from a metal surface heated to a high temperature to the vapor film and then from vapor to subcooled liquid. In view of thermal disequilibrium which takes into account the temperature dependence of saturation pressure, boundary conditions on the vapor-liquid interface are derived, which generalize the known correlations on the free surface of liquid in the gravity field. A number of new effects arise in the problem under consideration, as distinct from the classical problem. The thermal processes, which occur on the phase boundary and are possible in the absence of the force of gravity as well, lead to the generation of weakly decaying periodic waves of low amplitude, whose velocity may exceed significantly that of gravity waves. The heat flux through the interface may cause on this surface periodic waves of small length (ripple) which are not capillary. The processes of phase transition on the interface are capable of providing for the stability of vapor film under the layer of liquid in the gravity field. Along with periodic waves and solitons, the mode of explosive instability may arise in the nonlinear stage because of a weak variation of the film thickness, where the amplitude of an initially low-amplitude plane wave rises to infinity during a finite period of time.     

广义兰姆波的积累二次谐波发生研究

借助色散导波的部分波分析方法、二阳微扰理论及同的声非线性反射处理技术,本文对声波导中广义兰姆波的积累二次谐波发生进行了理论研究。结果表明,在一定条件下,源于声波导介质的体非线性、由文义兰姆波的部分波非线性相互作用所发生的二次谐波具有随传播距离积累增长的性质,文中给出了广义兰姆波的积累二次谐波发生所要满足的条件,并求解出相应的积累二次谐波之解析式。     

Wave beams in crystals with dislocations and quadratic nonlinearity

Nonlinear elastic waves in dislocated crystals are considered in terms of equations with constant coefficients, which involve a quadratic nonlinearity. A nonlinear modulation equation with a cubic nonlinearity is obtained for the first harmonic amplitude, a dispersion equation is derived, and the absorption coefficient is determined. The stability and focusing (self-focusing) of a wave beam are studied.     

超声导波混频表征和定位早期局部损伤的研究进展

超声导波具有远距离传输的特性，能够快速、有效地大范围检出薄板中的损伤或缺陷。非线性超声导波相较于传统超声导波，主要研究基波与材料中微观组织演化相互作用而产生的高阶谐波，对尺寸远小于基波波长的损伤或缺陷比较敏感。其中，超声导波的二次谐波相对容易激发，已被用于定量评估早期损伤。但是，超声导波的二次谐波容易受到测量系统非线性的干扰，并且无法定位材料中的局部损伤。超声导波混频在频率、模式、传播方向的选择上具有一定的灵活性，克服了二次谐波的缺点。目前，超声导波混频在理论、模拟和实验上取得了一定的进展，已被用于表征和定位金属材料中处于早期阶段的疲劳、热老化、微裂纹、冲击损伤和局部塑性变形等。高频段超声导波混频、兰姆波相向混频和非共线混频中差频谐波或和频谐波的传播性，以及更多类型损伤的定位和表征仍有待进一步研究。     

利用非线性表面波评价材料疲劳损伤

采用非线性Rayleigh表面波检测方法,实现了不同疲劳阶段下钢试样拉伸和腐蚀疲劳损伤的测试与评价;基于楔块\换能器激发与接收声波方式,搭建非线性Rayleigh波检测系统,测量了不同激励水平下基波幅值平方与二次谐波幅值间的线性关系以及Rayleigh表面波二次谐波的累积效应;分别在拉伸载荷和腐蚀疲劳载荷下,采集非线性时域信号并进行频谱分析,测量声学非线性系数在不同疲劳阶段下变化趋势,并分析不同疲劳载荷对钢试样声学非线性系数的影响。实验结果表明:超声非线性系数与疲劳周期数呈单调递增关系,可以用声学非线性系数来表征材料的表面疲劳损伤程度;相比较周期性拉伸疲劳损伤,腐蚀疲劳试样的声学非线性系数会增大,是由于腐蚀环境会加重实验中钢试样的疲劳损伤程度。研究成果可为疲劳损伤无损检测与评价提供一定的指导意义。     

Backscattering of Scholte waves and near-grazing underwater acoustic waves by a trench at a liquid/solid interface

Ultrasonic modeling results are presented on backscattering of broadband pulsed Scholte waves and grazing underwater acoustic waves from a trench at a liquid/solid interface. The backscattered waves are characterized by interference of diffracted waves reflected from the trench bottom and the trailing steep side. The effects of trench width and depth are demonstrated.     

一维复合波入射的固-固界面接触特性分析

基于弹性波理论,针对接触面非线性相互作用,建立了一个非线性刚度模型,利用接触应力描述非线性刚度特性。引入包含基波和谐波的一维复合波入射,在二阶微扰近似以及非线性边界条件下,给出了界面的反射波和透射波的表达式,得到反射系数和透射系数。结合界面线性刚度和接触应力的幂律关系,定义了四个非线性系数。通过数值计算分析了固-固界面的非线性特性以及谐波对于接触应力的依赖性。     

Directional scholte wave generation and detection using interdigital capacitive micromachined ultrasonic transducers

Directional generation and detection of Scholte waves and other guided modes in liquids and microfluidic channels by capacitive micromachined ultrasonic transducers (cMUTs) is reported. An interdigital transducer structure along with a phased-excitation scheme is used to enhance the directionality of Scholte interface waves in microfluidic environments. Finite element models are developed to predict the performance of the devices in both fluid half-spaces and microchannels. Experiments on the interdigital cMUTs show that a five-finger-pair device in a water half-space has 12 dB of directionality in generating Scholte waves at the design frequency of 10 MHz. A 10-finger device operating at 10 MHz in a water-filled microchannel has 13.4 dB of directionality. These directionality figures agree well with the modeling results. Using the results of the finite element model of a cMUT in a fluid half-space, it was determined that 41% of the acoustic power radiated into the fluid is contained in the Scholte wave propagating in the desired lateral direction. Transducers are demonstrated to perform bidirectional pumping in fluid channels with input power levels in the milliwatt range. Interdigital cMUTs fabricated using low temperature processes can be used as compact ultrasonic transducers with integrated electronics for sensing and actuation in fluidic environments.     

Large amplitude vibration analysis of composite beams: Simple closed-form solutions

Large amplitude vibration analysis of laminated composite beam with axially immovable ends is investigated with symmetric and asymmetric layup orientations by using the Rayleigh–Ritz (R–R) method. The displacement fields used in the analytical formulation are coupled by using the homogeneous governing static axial equilibrium equation of the beam. Geometric nonlinearity of von-Karman type is considered which accounts for the membrane stretching action of the beam. The simple closed-form solutions are presented for the nonlinear harmonic radian frequency as function of central amplitude of the beam using the R–R method. The nonlinear harmonic radian frequency results obtained from the closed-form solutions of the R–R method in general show good agreement with the results obtained from simple iterative finite element formulation. Furthermore, the closed-form expressions are corrected for the harmonic motion assumption from the available literature results on the existence of quadratic and cubic nonlinearity. It is interesting to note that the composite beams can result in asymmetric frequency vs. amplitude curves depending upon the nature of direction of displacement in contrast to isotropic beams which exhibit cubic nonlinearity only and leads to symmetric frequency vs. amplitude curves with respect to sign of the amplitude.     

Harmonic generation at an unbonded interface—I. Planar interface between semi-infinite elastic media

An analysis is made of the nonlinear dynamics of a system composed of an unbonded planar interface separating two semi-infinite linear elastic media. The unbonded interface, by definition, cannot support tension and hence opens up in the tension phase of a propagating disturbance, if it is not already open. The opening and closing of the interface is the origin of the nonlinearity. This is perhaps the simplest nonlinear problem involving continuous media, since the problem reduces to the consideration of a pair of independent first order ordinary differential equations involving the center of gravity and width of the gap. In the case of an incident sinusoidal wave the second harmonic generation efficiency is determined as a function of the ratio of the ambient hydrostatic pressure to the stress amplitude of the incident wave.     

Transient evolution of weakly nonlinear sloshing waves: an analytical and numerical comparison

The problem of water waves generated in a horizontally oscillating basin is considered, with specific emphasis on the transient evolution of the wave amplitude. A third-order amplitude evolution equation is solved analytically in terms of Jacobian elliptic functions. The solution explicitly determines the maximum amplitude and nonlinear beating period of the resonated wave. An observed bifurcation in the amplitude response is shown to correspond to the elliptic modulus approaching unity and the beating period of the interaction approaching infinity. The theoretical predictions compare favorably to fully nonlinear simulations of the sloshing process. Due to the omission of damping, the consideration of only a single mode, and the weakly nonlinear framework, the analytical solution applies only to finite-depth, non-breaking waves. The inviscid numerical simulations are similarly limited to finite depth.     

液浸多层薄膜-基底结构中Scholte界面波特性研究

多层薄膜-基底结构在工业领域有广泛应用，其中薄膜的厚度与弹性参数等特性对结构与器件性能有显著影响。但对多层薄膜材料参数进行无损定征较为困难。考虑界面波对界面附近材料特性敏感的特点，以及分层薄膜导致液固界面Scholte波频散与分层材料速度分布密切相关等因素，文章首先利用全局矩阵理论分析了分层结构中的声传播，并给出界面上脉冲激励的声压表达式，据此对水浸双层薄膜-基底三层结构材料声速呈正梯度、负梯度、随机分布三种结构中液固界面Scholte波的频散曲线进行数值计算。进一步详细计算了法向脉冲线源激发的界面波瞬态信号随薄膜厚度的变化。结果显示，三种结构中两层薄膜厚度均对液-固界面波频散特性有显著影响，同时不同膜厚对不同频段的Scholte波的“捕获”作用(频率选择性)十分明显。该结果为进一步利用Scholte波频散特性进行多层薄膜厚度定征提供了理论依据。     

Non-linear dynamic coupled equations on controlling patterns of the solid/liquid interface

In non-equilibrium non-linear region, assuming that there is a local equilibrium at the solid/liquid interface, the non-linear dynamics coupled equations of the time dependence of the perturbation amplitude and wave number of the solid/liquid interface during the solidification of a dilute binary alloy are established.     

On finite amplitude waves in heterogeneous elastic solids

The perturbation technique of the ‘stretching of the coordinates’ is used to obtain first and second order perturbation solutions of finite amplitude plane waves which propagate into an elastic half-space whose material property varies in the direction of the propagation. The interaction between nonlinearity and heterogeneity is discussed, and the results are illustrated by means of two examples: the longitudinal waves propagating in an elastic half-space with harmonic heterogeneity; the shear wave in a half-space whose property varies as A[1 + ?(X/L)ⁿ], where A, ? ? 1, L, and n are constants, and X denotes the initial particle position measured normal to the plane boundary.     

Effect of disperse phase on instability in systems with combustion

The dynamics of weak perturbations with finite amplitude in a two-phase homogeneous medium (gas with suspended solid particles) featuring a nonequilibrium chemical reaction has been studied. Using an asymptotic approach, a weakly nonlinear model of the evolution of one-dimensional perturbations is developed that takes into account the kinetic wave interactions and dissipative properties including the interphase exchange of heat and momentum. Conditions for the loss of stability of the homogeneous state of the system are analyzed. Numerical solutions of the evolution equation are obtained in the form of established self-sustained oscillations. The stabilizing effect of the inert disperse phase is described.     

On dissipation coefficients in a rectangular wave tank

Summary An alternative approach to determination of the complex dissipation coefficients at the solid boundaries of a wave tank is suggested. The proposed method is based on the balance between the apparent energy consumption in the wall boundary layer and the full complex energy flux to this layer from the potential core. The present technique allows one to incorporate easily the dissipation in the nonlinear model describing the evolution of standing waves of finite amplitude in a rectangular tank. The relative importance of wavemaker dissipation in this case is discussed.     

Evaluation of Fatigue Specimens Using EMATs for Nonlinear Ultrasonic Wave Detection

It is suggested that the waveform of the received ultrasonic wave is slightly different from that of the incident ultrasonic wave when the displacement of an ultrasonic wave and the opening width of a crack are almost same. Thus, as regarding the incident ultrasonic wave, its harmonic frequency components change as it penetrates the crack. Since, the nonlinearity of a solid material is very small compared to that of a liquid medium with a high nonlinear efficiency when used as a coupling medium, we applied an electromagnetic acoustic transducer (EMAT), which does not require a coupling medium. In addition, we tried to develop the EMAT that could alternately drive S₀-Lamb wave and fundamental Shear Horizontal (SH₀)-plate wave to detect any nonlinearity in an ultrasonic wave. We actually tested the performance using the fatigue specimens we fabricated. As a result, we observed that the harmonic components changed when we used the specimen with a specific loading condition and a specific ultrasonic mode. This is indicated that the harmonic components detection using the trial EMAT could also provide useful information on the degree of damage to any structures or any materials.     

Comparative study of different nonconserving time integrators for wave propagation in hyperelastic waveguides

This paper addresses the formulation and numerical efficiency of various numerical models of different nonconserving time integrators for studying wave propagation in nonlinear hyperelastic waveguides. The study includes different nonlinear finite element formulations based on standard Galerkin finite element model, time domain spectral finite element model, Taylor–Galerkin finite element model, generalized Galerkin finite element model and frequency domain spectral finite element model. A comparative study on the computational efficiency of these different models is made using a hyperelastic rod model, and the optimal computational scheme is identified. The identified scheme is then used to study the propagation of transverse and longitudinal waves in a Timoshenko beam with Murnaghan material nonlinearity.