Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.     

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal(MPFC) model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.     

Laser-induced thermoelastic Leaky Lamb waves at the fluid–solid interface

A model based on the theory of fluid–structure interaction is developed to simulate the laser thermoelastic generation and propagation of Leaky Lamb waves at the water–aluminum interface. Each component of displacement, stress, and temperature are derived in transform domain by the photothermoelastic transfer matrix method. The time domain solutions are obtained by numerically inverting the transforms while the dispersion curves and attenuation curves for the leaky waves are also calculated. Then the propagation characteristics of different modes are analyzed. The model establishes a quantitative relation between the laser parameters, the material parameters, the corresponding waveforms, and the dispersion curves, which provides a useful tool for the Leaky Lamb waves applied to nondestructive evaluation.     

The propagation of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates

Based on linear three-dimensional elasticity theory, the wave equations of coupled Lamb waves in multilayered arbitrary anisotropic composite laminates are derived using a Legendre orthogonal polynomial approach. The elastodynamic solution for the propagation of coupled Lamb waves in composite plates is also presented to determine the characteristics of coupled Lamb waves. To verify the applicability and validity of the method, two cases of bi-layered plates formed with isotropic components and anisotropic components, respectively, are primarily manipulated for comparison with earlier known results. Next, the dispersion curves, displacements and stress distributions of Lamb waves in multilayered anisotropic laminates are calculated. The effects of coupling and fiber orientation on the characteristics of the Lamb waves are illustrated. The potential usefulness of the fundamental modes of the coupled Lamb waves is discussed in detail.     

Hybridization of acoustic waves in piezoelectric plates

The interaction (hybridization) of different types of acoustic waves of zero and higher orders propagating in lithium niobate piezoelectric plates is theoretically investigated. Different crystallographic orientations of the plates and different directions of wave propagation in them are considered. It is shown that, for an electrically free plate with the propagation direction along any of the crystallographic axes, the dispersion curves have intersection points and hybridization is absent. However, when the propagation direction slightly changes or when one of the plate surfaces is short-circuited, the dispersion curves separate and the waves become coupled. A quantitative coefficient characterizing the degree of wave hybridization with allowance for both mechanical and electric coupling is introduced. It is shown that the dependence of this coefficient on the product of the plate thickness by the wave frequency determines the extent of separation of the dispersion curves of interacting waves. The phenomenon under study is of both fundamental and practical interest, for example, in connection with the problem of an efficient excitation of nonpiezoactive acoustic waves in piezoelectric plates.     

Mechanical and elastic properties of amorphous hydrogenated silicon films studied by broadband surface acoustic wave spectroscopy

Mechanical and elastic properties of a-SiH films were measured by broadband Surface Acoustic Wave Spectroscopy (SAWS). In the frequency range achieved, the SAW dispersion curves extend to 300 MHz, which allowed the density, Young's modulus, and Poisson's ratio to be evaluated for films grown by laser CVD or plasma CVD with different hydrogen concentrations. The films deposited by either method have the best mechanical and elastic properties. at a hydrogen concentration of about 10 at. %. For this material, a density of (2300±20) kg/m³ and Young's modulus of (134±5) GPa was determined. The network structures of amorphous silicon are discussed by applying the constraint-counting model to estimate the mean coordination number.     

Numerical study on surface acoustic wave method for determining Young's modulus of low-k films involved in multi-layered structures

The surface acoustic waves (SAWs) technique is becoming an attractive tool for accurately and nondestructively characterizing the mechanical property of the brittle low dielectric constant (low-k) thin film. The theoretical equations for describing SAWs propagating on the multi-layered structure are derived in this study. The dispersion features of SAWs propagating on different structures of low-k/SiO₂/Si substrate, SiO₂/low-k/Si substrate, low-k/Si substrate, and low-k/Cu/Si substrate are investigated to instruct an accurate and facile fitting process for determining Young's modulus of low-k films. The dependence of dispersion relation on the film thickness, elastic modulus of low-k materials as well as frequency are provided and discussed in detail. The study shows an obvious influence of layered structure on the dispersion relation of SAWs. For a fixed structure, the dispersion curvature increases with the decrease of Young's modulus of low-k films.     

液态金属快堆主管道中超声导波传播特性研究

讨论了钠冷快堆(Sodium-cooled Fast Reactor,SFR)主管道的整体温度和内部液态金属钠流动速度的变化对管道导波传播特性的影响。推导了充液管道中导波频散方程的一般形式,并给出了管道内液态金属钠处于流动状态下的导波频散方程。采用数值计算方法获得了管内液态金属钠处于不同温度和不同流速时的导波纵向模式频散曲线和导波时域波形。结果表明,温度变化对基阶纵向模式的影响较小,但对高阶纵向模式的影响较大;液态钠流速增大会使导波频散曲线向高频轻微移动,但在实际检测中可以忽路管内液体流动速度的影响。通过对时域接收波形的模拟计算,进一步考察了液态金属钠的温度及流动速度变化对导波传播的影响,并通过对比不同模态的激发特点和不同频段的导波时域波形特点,结合导波频散曲线,给出了适用于SFR管道超声无损检测的导波模态和声源激发频段选择方案。      

The effect of surface stress on the propagation of Lamb waves

This work investigates the possibility of the propagation of Lamb waves in thin solid layers with external traction free surfaces, in the presence of surface elasticity, inertia and residual stress. It is demonstrated that such waves do exist and that their characteristics can be quite different from their classical counterparts. The governing equations with non-classical boundary conditions involving the bulk and surface stress are solved exactly in the frequency-wavenumber domain. This solution is utilized to compute the Lamb wave modes for different layer thicknesses. An efficient strategy to capture all the modes of Lamb waves within a given frequency window is outlined. It is shown that the effect of surface elasticity and inertia becomes significant with increasing frequency and decreasing layer thickness, where the number of modes participating within a given frequency window is more than that permitted by the classical theory. Further, it is observed that the nature of the Lamb wave modes (in terms of negative dispersion) in the presence of surface stress is similar to what predicted by the nonlocal theory and microstructure based continuum theory.     

Characterization of mechanical properties of a hollow cylinder with zero group velocity Lamb modes

Hollow cylinders used in the industry must be regularly inspected. Elastic guided waves, similar to Lamb modes in a plate, can propagate in the axial direction or around the circumference. They are sensitive to geometrical and mechanical parameters of the cylindrical shell. The objective of this paper is to show that zero group velocity (ZGV) Lamb modes can be used to bring out anisotropy and to measure elastic constants of the material. This study provides experimental and numerical investigations on a Zirconium alloy tube extensively used by the nuclear industry in reactor core components. A non-contact method, based on laser ultrasound techniques and ZGV Lamb modes, demonstrates that the difference observed between axial and circumferential guided waves cannot be explained by an isotropic model. Then, a transverse isotropic model is used for the Zircaloy tube. Four of the five elastic constants are directly extracted from ZGV resonance frequencies. The last one is deduced from the measured dispersion spectra. With this complete set of constants, a good agreement is obtained between theoretical and experimental dispersion curves for both axially and circumferentially propagating guided waves.     

有限元仿真兰姆波评价胶接接头界面弹性模量的研究

金属薄板检测中,声-超声检测方法可激发多模式的兰姆波,兰姆波能够评价金属胶接后结构质量,正确认识兰姆波传播特性与胶接接头弹性模量的关系是有效应用该技术的基础。本文采用有限元仿真法分析这种关系,得出随着胶层弹性模量的降低,各模式兰姆波通过胶接接头后能量有不同程度的衰减,频率为0.5 MHz和1 MHz时,兰姆波主要模式A₀、S₀能量值与接头弹性模量具有一定的线性关系。实验结果表明,低频时随着胶接接头的人工老化,接头中主要模式兰姆波能量均发生一定程度的衰减,其能量变化曲线与有限元仿真结果趋势一致。本方法能为实验研究、实际检测提供有效参考依据。     

Quantum and geometric effects on the symmetric and anti-symmetric modes of the surface plasma wave

The propagation of the surface quantum plasma waves is investigated in a thin quantum plasma slab. The symmetric and anti-symmetric dispersion modes of the quantum surface wave are obtained by the plasma dielectric function with the kinetic dispersion model for the slab geometry. The quantum mechanical and slab geometric effects on the symmetric and anti-symmetric modes are also discussed.     

Circumferential waves for a cylindrical shell in smooth contact with a continuum

Dispersion relations are determined for circumferential waves propagating in a layered, circular cylinder by using shell equations to approximate the behavior of the outer layer. These equations include the effects of transverse shear deformation and rotatory inertia. The cylinder consists of an elastic core in smooth contact with a hollow, circular cylinder of distinctly different elastic properties. Two distinct modes exist as the shell thickness reduces to zero. One mode is recognized to be surface waves on the convex cylindrical surface of the core; the second mode is associated with long longitudinal waves in the shell. The approximate dispersion curves for these modes are compared with curves obtained by employing elasticity equations for the layer. As the curvature increases, the agreement of the two theories becomes progressively poorer whether or not any disagreement exists for the case of no curvature. The agreement of the two theories is better when the layer is relatively stiff than when the layer is relatively soft. The shell equations simplify the calculations necessary to produce the dispersion curves.     

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.     

Wave propagation along transversely periodic structures

The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for NDE ultrasonic applications. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width. Periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation. This method allows a complete investigation of the dispersion curves and of displacement/stress fields for guided modes in anisotropic and absorbing periodic structures. Among other examples, that of a grooved aluminum plate is theoretically and experimentally investigated, indicating the presence of specific and original guided modes.     

Influence of oxygen on the elastic properties of nanocrystalline diamond films studied by laser-induced surface acoustic waves

Laser-induced surface acoustic waves (SAWs) were used to study the influence of oxygen on the elastic properties of nanocrystalline diamond films. A series of samples was grown by chemical vapor deposition (CVD) on the (100) plane of p-type silicon for 3h under different O(2)/(CH(4)+H(2)) flow ratios from 0% to 8%. The elastic properties of these nanocrystalline diamond films were determined from the SAW dispersion curves. The maximum frequency realized was about 310 MHz in wideband SAW experiments and about 700 MHz using a narrowband mask method with several higher harmonics. It was found that the densities of all samples were surprisingly high, approaching the ideal value of diamond, whereas the Young's modulus increased from 700 to 950 GPa with the addition of oxygen. It is concluded that oxygen has a significant positive effect on the elastic properties of nanocrystalline diamond.     

Non-destructive evaluation of the mechanical behaviour of TiN-coated steels by laser-induced ultrasonic surface waves

Measuring the propagation velocity of ultrasonic surface waves has been used to determine the Young's modulus of TiN films on steel. Wide-band surface-wave pulses are generated by a pulsed nitrogen laser and detected by a piezoelectric PVDF-foil transducer. A spectrum of the surface-wave phase velocity is obtained from the Fourier transformation of the surface-wave signals. The TiN films were deposited after different presputtering times with argon ions to vary the adhesion on the steel substrate. The adhesion behaviour of the films was investigated with the scratch tester. A correlation was found between the Young's modulus of the film material and the acoustic emission activity in the scratch test, which has been shown to be a suitable measure for adhesion.     

Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation

In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves.     

铝板中Lamb波检测的实验研究

Lamb波在传播过程中具有频散及多模态特性,若相关参数选择不当,会导致在实际应用中信号相互叠加而无法识别。本文基于Lamb波的频散曲线是其频散方程实数解分布的特点,采用二分法绘制了铝板中Lamb波的频散曲线、波结构曲线和入射角曲线。根据曲线选择S0模态的Lamb波对1mm厚铝板中不同类型的缺陷进行检测。实验结果表明,S0模态的Lamb波对裂纹型缺陷和贯穿型缺陷十分敏感,但对于裂纹型缺陷,其幅值变化并不与缺陷大小成线性关系,并且S0模态Lamb波的声场指向性十分集中,在偏离声束轴线时无法检测到缺陷。     

Soliton Transmission and Reflection Due to the Inhomogeneity

A new approach to nonlinear wave in one-dimensional discontinuous fluid-filled elastic tube is presented. As-a model, an elastic tube which has a discontinuity of radius, thickness and Young's modulus is considered. The incident, reffe cted and transmitted waves are described by KdV equations. The reflected and transmitted waves are constructed from incident wave analytically. Fission and reflection of a soliton due to the discontinuity are explicitly shown in the lowest order