含孔隙分层半空间中瑞利波的传播特性研究

为了研究含孔隙介质分层半空间中瑞利波的传播规律,分析孔隙介质参数对瑞利波频散曲线的影响,本文进行了数值模拟研究。采用传递矩阵算法,计算了含孔隙分层半空间中一定频率范围内瑞利波所有模式的频散及激发强度曲线,并与均匀弹性固体分层半空间情况作了类比分析,在含孔隙覆盖层的两层模型和含低速孔隙夹层的三层模型下,详细研究了孔隙度、渗透率、层厚度等参数对瑞利波各模式的影响,发现孔隙度及层厚度的变化对频散曲线影响较大,而渗透率的变化对频散曲线影响较小。      

激光激发瑞利波检测表面倾斜缺陷的研究

研究激光激发瑞利波检测样品的表面倾斜缺陷。基于频域热弹耦合方程,采用有限元方法建立激光激发瑞利波检测倾斜缺陷的数值模型,研究倾斜缺陷的检测机理。数值计算含不同的长度及倾斜角度缺陷的样品中瞬态位移波形,分析瑞利波在倾斜缺陷处模式转换的过程,研究各种瑞利波的传播路径。在此基础上,研究缺陷宽度与材料黏性对瑞利波传播及缺陷检测的影响。结果表明:瑞利波在缺陷处产生的反射及透射瑞利波的到达观测点的时间可以检测缺陷位置和长度,瑞利波在缺陷的底部发生模式转换产生的切变波可以检测缺陷倾斜角度。数值结果和已有的实验结果一致,从而为表面倾斜缺陷的检测提供有效的理论依据。      

分层结构中兰姆波二次谐波发生的模式展开分析

采用二阶微扰近似和模式展开方法,对分层结构中兰姆波的二次谐波发生问题进行了深入研究,得到了二次谐波声场的一般表达式。兰姆波在分层结构中传播时,固体板材的体弹性非线性效应导致在各固体层的内部及表面出现二倍频的体驱动力及面驱动应力,其作用是在分层结构中激发出一系列二倍频兰姆波的简正模式,这些简正模式的叠加即构成分层结构中兰姆波的二次谐波声场。当构成二次谐波声场的某一二倍频兰姆波简正模式的相速度等于基频兰姆波的相速度时,该二倍频兰姆波简正模式分量表现出随传播距离积累增长的性质。本文还就铝板-环氧粘接层-铝板结构中兰姆波的二次谐波声场进行了数值分析,结果显示,软粘接层性质对二次谐波声场的影响很大。     

二维矩形波导管中的非线性声传播

本文采用部分波和二阶微扰理论对二维矩形波导管内声波的非线性传播问题进行了研究。由二次谐波的边界条件和初始条件，可得到物理图象清晰、便于计算的二次谐波声场解析式。结果表明，不同基波传播模式间的相互作用不存在二阶非线性，管内任意振幅分布的稳态激发源产生的二次谐波为各个模式二次谐波之和，且二次谐波声场分布具有对称性。     

圆管结构中周向导波非线性效应的模式展开分析

在二阶微扰近似条件下, 采用导波模式展开分析方法研究了圆管结构中周向导波的非线性效应. 伴随基频周向导波传播所发生的二次谐波, 可视为由一系列二倍频周向导波模式叠加而成. 从动量定理出发, 结合柱坐标系下非线性应力张量及其散度的数学表达式, 针对圆管中某一基频周向导波模式, 推导出相应的二倍频应力张量及二倍频彻体驱动力的数学表达式, 建立了确定二倍频周向导波模式展开系数的控制方程, 得到了伴随基频周向导波传播所发生的二次谐波声场的形式解. 理论分析和数值计算表明, 当构成二次谐波声场的某一二倍频周向导波模式与基频周向导波的相速度匹配时, 该二倍频周向导波模式的位移振幅表现出随传播周向角积累增长的性质; 当两者的相速度失配时, 二倍频周向导波的振幅随传播周向角表现出“拍”效应.     

固体板中SH板波非线性效应的实验观察

采用微扰近似和导波的模式展开分析方法,从理论上简要分析了SH板波的二次谐波发生效应;尽管在无限大固体介质中单个切变波的二次谐波发生效应非常微弱,但在一定条件下由两个切变波构成的SH板波可具有强烈的非线性效应;本文的主要工作就是对此结论加以实验验证。试制了激发SH板波的切变波斜劈换能器和接收二次谐波信号的液体斜劈换能器,建立了非线性SH板波的实验研究系统;通过详细的理论分析和对比实验研究,阐明了在一定条件下实验观察到的显著二次谐波信号来源于SH板波传播过程中的强烈非线性效应。此外,针对不同的SH板波传播距离,在远场条件下分别测量了相应的二次谐波幅频曲线;在基频SH板波与二倍频对称兰姆波相速度相等所对应的频率值附近,分析了二次谐波的振幅随传播距离的变化关系,结果证明在一定条件下SH板波的二次谐波振幅可随传播距离积累增长,即SH板波可具有强烈的非线性效应。      

黏弹性胶粘涂层-基底结构中激光激发类瑞利波的传播特性

研究黏弹性胶粘涂层/基底结构中激光激发类瑞利波的传播特性。考虑涂层及基底的黏弹性,在频域中建立环氧树脂涂层/铝基底、环氧树脂涂层/铜基底、环氧树脂涂层/泡沫基底等结构中激光激发类瑞利波的有限元数值模型,研究类瑞利波的波形及传播特性,并分析环氧树脂涂层的透明性、厚度、黏性与基底的黏性对类瑞利波传播特性的影响,在此基础上,结合理论计算的色散与衰减曲线进行验证。研究结果表明,涂层的黏性引起类瑞利波高频成分的衰减,而对低频成分没有影响;基底的黏性对类瑞利波的高频与低频成分的衰减均有影响,其中对低频成分影响较大,此外,类瑞利波的模式及频散特性与基底材料密切相关。本研究为反演黏弹性胶粘涂层/基底结构的力学参数及评估结构的粘接质量提供理论指导。     

黏弹性胶粘涂层-基底结构中激光激发类瑞利波的传播特性

研究黏弹性胶粘涂层/基底结构中激光激发类瑞利波的传播特性。考虑涂层及基底的黏弹性,在频域中建立环氧树脂涂层/铝基底、环氧树脂涂层/铜基底、环氧树脂涂层/泡沫基底等结构中激光激发类瑞利波的有限元数值模型,研究类瑞利波的波形及传播特性,并分析环氧树脂涂层的透明性、厚度、黏性与基底的黏性对类瑞利波传播特性的影响,在此基础上,结合理论计算的色散与衰减曲线进行验证。研究结果表明,涂层的黏性引起类瑞利波高频成分的衰减,而对低频成分没有影响;基底的黏性对类瑞利波的高频与低频成分的衰减均有影响,其中对低频成分影响较大,此外,类瑞利波的模式及频散特性与基底材料密切相关。本研究为反演黏弹性胶粘涂层/基底结构的力学参数及评估结构的粘接质量提供理论指导。      

超声Lamb波二次谐波发生效率分析与模式选择

在导波模式展开分析方法的基础上,提出激发效率参量来定量表征超声Lamb波积累二次谐波的发生效率。以P92钢板为例,理论计算得到了与频散曲线对应的理论激发效率参量分布图谱,从图谱中选择理论激发效率参量大小不同的两种基频Lamb波模式:纵波型S1模式和交点型A2/S2模式,分别测量这两种基频Lamb波模式在钢板中传播时产生的二次谐波信号。理论计算和实验测量结果表明,这两种基频Lamb波模式的理论和实验激发效率参量的比值基本一致,且激发效率参量较大的纵波型S1模式能激发出效率更高的二次谐波信号。研究结果表明激发效率参量可以有效的用于Lamb波二次谐波发生效率的表征及模式选择。      

分层介质半空间瑞利波的时频分析

对分层介质半空间瑞利波的频散特性,用一种时频分析方法——重排的平滑伪魏格纳维尔分布(RSPWVD,Reassign- ment of Smooth Pseudo-Wigner Ville Distribution)进行了分析和研究。对均匀半空间和两层介质半空间的理论和实验研究表明,由于层状介质中瑞利波的频散曲线存在多个模式,所获得的群速度频散曲线在不同的频段显示出来的模式是对应表面位移幅度占主导作用的模式。频散曲线的这种模式判定对利用层状半空间的瑞利波反演介质参数是必须预先了解的。     

Rayleigh wave and detection of low-velocity layers in a stratified half-space

The excitation and propagation of the guided waves in a stratified half-space and a Rayleigh wave exploration method in shallow engineering seismic exploration are studied in this paper. All the modes of the guided waves are calculated by the bisection method in the case where the low velocity layers are contained in a stratified half-space. Cases when the formation shear wave velocity gradually decreases from the top to the bottom layers are also studied. The dispersion curves obtained in actual Rayleigh wave exploration are usually noncontinual zigzag curves, but the dispersion curves given by the elastic theory for given modes of the guided waves are smooth and continual curves. In this paper, the mechanism of zigzag dispersion curves in Rayleigh wave exploration is investigated and analyzed thoroughly. The zigzag dispersion curves can give not only the possible positions of the low-velocity layers but also the other information on the formation structure (fractures, oil, gas, etc.). It is found that the zigzag dispersion curves of the Rayleigh wave are the result of the leap of the modes and the existence of low velocity layers in a stratified half-space. The effects of the compressional wave velocity, shear wave velocity, and density of each layer on zigzag dispersion curves and the relationship of the low velocity layers to zigzag dispersion curves are also investigated in detail. Finally, the exploration depth of the Rayleigh wave is discussed. The exploration depth of the Rayleigh wave is equal to the wavelength multiplied by a coefficient that is variable and usually given by the work experience and the formation properties of the local work area.     

Numerical solutionsfor acoustic Rayleigh wave problems in anisotropic and layered media

A finite difference iterative formulation which has already been applied successfully to acoustic surface wave scattering problems in homogeneous and layered isotropic as well as non-linear media, is extended to cover Rayleigh type mode propagation in anisotropic materials. The transmission, reflection and conversion into bulk modes of Rayleigh waves are studied as a function of relative step height. The waves are incident normally at upward and downward step discontinuities formed by the sudden termination of an uniform aluminium layer on a semi-infinite fused quartz substrate. In terms of the severity of Rayleigh wave scattering, the layered upward step has the most drastic effects, followed by the layered downward and the homogeneous downward steps respectively. Rayleigh wave scattering at a break in a layered waveguide is discussed.     

Response features of nonlinear circumferential guided wave on early damage in inner layer of a composite circular tube

A theoretical model to analyze the nonlinear circumferential guided wave(CGW) propagation in a composite circular tube(CCT) is established. The response features of nonlinear CGWs to early damage [denoted by variations in third-order elastic constants(TOECs)] in an inner layer of CCT are investigated. On the basis of the modal expansion approach, the second-harmonic field of primary CGW propagation can be assumed to be a linear sum of a series of double-frequency CGW(DFCGW) modes. The quantitative relationship of DFCGW mode versus the relative changes in the inner layer TOECs is then investigated. It is found that the changes in the inner layer TOECs of CCT will obviously affect the driving source of DFCGW mode and its modal expansion coefficient, which is intrinsically able to influence the efficiency of cumulative second-harmonic generation(SHG) by primary CGW propagation. Theoretical analyses and numerical simulations demonstrate that the second harmonic of primary CGW is monotonic and very sensitive to the changes in the inner layer TOECs of CCT, while the linear properties of primary CGW propagation almost remain unchanged. Our results provide a potential application for accurately characterizing the level of early damage in the inner layer of CCT through the efficiency of cumulative SHG by primary CGW propagation.     

Effect of the surface free energy on the behaviour of surface and guided waves

The aim of this paper is to evaluate the influence of the surface free energy upon the propagation of the eigenmodes of structures, by studying successively (a) the Rayleigh wave for an elastic half-space, (b) the Lamb waves for an elastic layer, and (c) the guided modes for a tri-layer structure (e.g., metal/adhesive/metal). The surface free energy is a parameter which appears in the jump conditions of stresses and displacements at each interface, and which consequently modifies the eigenmodes, solutions of the boundary conditions system. As expected, the Rayleigh wave is dispersive and its velocity increases when the surface free energy increases. In the same way, the velocity of Lamb waves also increases except at normal angle of propagation where the surface free energy does not arise. Moreover, near the Rayleigh angle, the behaviour of the A₀ and S₀ Lamb modes varies strongly according to the surface free energy. Similar results are observed for the tri-layer structure.     

Acoustic field excited by a pulsed laser line source in a cylinder

The excitation and propagation of the acoustic waves in an elastic cylinder are studied by laser ultrasonics both theoretically and experimentally. The theoretical analysis of the two-dimensional acoustic field excited by a pulsed laser line source impacting on the generatrix of an elastic cylinder is presented. The dispersive properties for both cylindrical Rayleigh wave and the higher modes--whispering gallery (WG) modes are analyzed in detail. The numerical transient displacement waveforms for a detecting point located another terminal of the cylinder diameter opposite the source are calculated. The experimental excitation and detection of the acoustic waves in an aluminum cylinder are carried out on a laser ultrasonic system, which mainly consists of a Q-switched Nd:YAG laser and a laser interferometer. The wave components of bulk waves and surface waves (cylindrical Rayleigh waves and WG modes) are analyzed by comparing the numerical and experimental waveforms. The results are in good agreement.     

Nonlinear waves and shocks in a rigid acoustical guide

A model is developed for the propagation of finite amplitude acoustical waves and weak shocks in a straight duct of arbitrary cross section. It generalizes the linear modal solution, assuming mode amplitudes slowly vary along the guide axis under the influence of nonlinearities. Using orthogonality properties, the model finally reduces to a set of ordinary differential equations for each mode at each of the harmonics of the input frequency. The theory is then applied to a two-dimensional waveguide. Dispersion relations indicate that there can be two types of nonlinear interactions either called "resonant" or "non-resonant." Resonant interactions occur dominantly for modes propagating at a rather large angle with respect to the axis and involve mostly modes propagating with the same phase velocity. In this case, guided propagation is similar to nonlinear plane wave propagation, with the progressive steepening up to shock formation of the two waves that constitute the mode and reflect onto the guide walls. Non-resonant interactions can be observed as the input modes propagate at a small angle, in which case, nonlinear interactions involve many adjacent modes having close phase velocities. Grazing propagation can also lead to more complex phenomena such as wavefront curvature and irregular reflection.     

Circumferential waves in a composite circular cylinder

Circumferential waves propagating in a layered, circular cylinder are studied. The cylinder consists of an elastic circular core encased in a hollow, circular cylinder of distinctly different elastic properties. Both smooth and bonded contact are considered. The effect of curvature and layer thickness on the phase velocity of the lowest mode(s) is investigated for both an acoustically softer and an acoustically stiffer layer. When the outer radius of the composite cylinder is unbounded, Stoneley waves are a limiting case as the ratio of the radius of the core to the wavelength increases beyond bounds. When the outer radius is finite, waves in a layer and a half-space result for this limit. Some attention is also directed to the limiting case of small layer thickness to the wavelength ratio. In the limit as this ratio vanishes, the motion of the core reduces to that of Rayleigh waves on the curved surface. For smooth contact, the motion of the core becomes uncoupled from that of the layer for this limiting case, and two distinct modes are seen to exist.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.