高频纵向导波在钢杆中传播特性的研究

计算了钢杆中纵向轴对称导波模态的衰减频散曲线和群 速度频散曲线. 分析了1~3MHz范围内高频纵向轴对称超声导波在钢杆中的传播特 性. 理论分析表明,各高阶纵向模态都存在一个衰减最小值,在此衰减最小值所对应频率下 的高阶模态能传播较远距离,可用于钢杆导波检测. 建立实验系统,采用轴对称同端激 励接收的方法,根据第1次端面回波做出群速度和端面回波幅值随频率变化曲线,实验结 果与理论分析基本吻合. 表明考虑材料衰减特性的钢杆频散曲线可以作为实验指导依据.     

Investigation of guided waves propagation in orthotropic viscoelastic carbon–epoxy plate by Legendre polynomial method

The effect of viscoelasticity on the guided waves propagation in viscoelastic plate has been investigated according to multi-aspect. To this purpose, an extension of the Legendre polynomial method is proposed to formulate the guided waves equation in orthotropic viscoelastic plate composed of carbon–epoxy. The validity of the proposed Legendre polynomial method is illustrated by comparison with available data. The convergence of the method is discussed through a numerical example. The hysteretic and Kelvin–Voigt viscoelastic models are used to integrate the imaginary part of the complex stiffness matrix associated with the viscoelastic plate in this study. Accordingly, both viscoelastic models do not affect on the dispersion curves results. However, appreciable effects are seen in the attenuation curves. Also, the sensitivity of the guided waves propagation caused by variations of elastic and viscoelastic modulus has been studied in detail. Finally, the advantages of the Legendre polynomial method are described.     

THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH 1)

近年来, 超声导波因其衰减小, 传播距离远和信号覆盖范围广, 成为无损检测领域快速发展的方向之一. 然而, 基于超声导波的高温在线检测和激光超声技术却发展缓慢, 其关键在于热弹耦合波动方程求解难度大、传播与衰减特性研究困难. 作为一种有效的求解方法, 勒让德正交多项式方法已广泛应用于导波传播问题, 但该方法在求解热弹导波传播时存在两个不足, 限制其进一步的发展和应用. 这两个缺陷是: (1)求解过程中大量积分的存在, 致使计算效率低下; (2)仅能处理等热边界条件的热弹导波传播. 针对两项不足之处, 提出一种改进的勒让德正交多项式方法, 以求解分数阶热弹板中的导波传播. 推导求解方法中积分的解析表达式, 以提高计算效率; 引入温度梯度展开式, 发展适合勒让德多项式级数的绝热边界条件处理方法. 与已有文献结果对比表明改进方法的正确性; 与已有方法的计算时间对比说明改进方法的高效性. 最后将改进的方法用于求解分数阶热弹板中的导波传播, 研究分数阶次对频散、衰减曲线和应力、位移、温度分布等的影响.     

Characteristics of elastic waves in FGM spherical shells,an analytical solution

In this paper, we investigate the propagation characteristics of elastic guided waves in FGM spherical shells with exponentially graded material in the radial direction. A new separation of variables technique to displacements is proposed to convert the governing equations of the wave motion to the second-order ordinary differential equations with variable coefficients. By further a variables transform technique, these equations are transformed to the Whittaker equations so that analytic solutions can be obtained. For the spherical shell case, by satisfying the traction-free boundary conditions on both the inner and outer surfaces of the shell, we obtain the dispersion equations, which show that both the SH and Lamb-type wave modes are generated in the structure. The calculated dispersion curves in the functionally graded shell demonstrate a clear influence of the gradient coefficient as compared to those of the homogeneous shell, with the Lamb-type waves more sensitive to the gradient coefficient. The mode shapes and the distributions of stresses in the shells for various gradient coefficients are also presented to illustrate their dependence on the gradient coefficient.     

板中热弹波传播:一种改进的勒让德多项式方法

近年来,超声导波因其衰减小,传播距离远和信号覆盖范围广,成为无损检测领域快速发展的方向之一.然而,基于超声导波的高温在线检测和激光超声技术却发展缓慢,其关键在于热弹耦合波动方程求解难度大、传播与衰减特性研究困难.作为一种有效的求解方法,勒让德正交多项式方法已广泛应用于导波传播问题,但该方法在求解热弹导波传播时存在两个不足,限制其进一步的发展和应用.这两个缺陷是:(1)求解过程中大量积分的存在,致使计算效率低下;(2)仅能处理等热边界条件的热弹导波传播.针对两项不足之处,提出一种改进的勒让德正交多项式方法,以求解分数阶热弹板中的导波传播.推导求解方法中积分的解析表达式,以提高计算效率;引入温度梯度展开式,发展适合勒让德多项式级数的绝热边界条件处理方法.与已有文献结果对比表明改进方法的正确性;与已有方法的计算时间对比说明改进方法的高效性.最后将改进的方法用于求解分数阶热弹板中的导波传播,研究分数阶次对频散、衰减曲线和应力、位移、温度分布等的影响.     

功能梯度圆柱板中的周向衰逝导波

与传播波模态不同,衰逝波模态波数为纯虚数或复数,它们随传播距离呈指数或阻尼式衰减。复数根描述的衰逝波对结构缺陷形状和尺寸的导波检测具有重要作用,但其求解却是非常困难的,通常要借助于各种迭代技术。本文提出一种计算求解衰逝波问题的改进的Legendre正交多项式方法,该方法可将复杂的变系数微分方程组计算转换为特征值求解问题,无需迭代便能计算得到包含实波数域、虚波数域和复波数域的完整的频散曲线。通过具体算例验证了提出方法的正确性。应用提出方法计算了不同梯度圆柱板中的衰逝导波,绘制了三维频散曲线,研究了不同径厚比和梯度场对衰逝导波频散的影响,分析了衰逝导波的位移和应力分布,讨论了衰逝导波的传播特性。     

PROPAGATION CHARACTERISTICS OF HIGH ORDER LONGITUDINAL MODES IN STEEL STRANDS AND THEIR APPLICATIONS

Propagation characteristics of high order longitudinal modes of ultrasonic guided waves in seven-wire steel strands are investigated theoretically and experimentally. According to these analysis results, proper longitudinal modes are selected for defect detection in steel strands. Dispersion curves for helical and central wires in a 17.80 mm nominal diameter seven-wire steel strand are numerically obtained firstly, and propagation characteristics of high-order longitudinal modes, such as wave structures, attenuation and dispersion, are analyzed. In experiments, the signals of ultrasonic guided wave at different high frequencies are excited and received at one end of a steel strand by using the same single piezoelectric transducer. The identification of longitudinal modes in the received signals is achieved based on short time Fourier transform. Furthermore, appropriate L（0, 5） mode at 2.54 MHz is chosen for detecting an artificial defect in a helical wire of the steel strand. Results show that high order longitudinal modes in a high frequency range with low dispersion and attenuation whose energy propagates mainly in the center of the wires can be used for defect detection in long range steel strands.     

Effect of rotation on generalized thermo-viscoelastic Rayleigh–Lamb waves

The present paper is aimed at studying the effects of rotation on the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate rotating about the normal to its faces with uniform angular velocity. This facilitates the decoupling of anti-plane/in-plane motion which is not possible, in general. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The formulation is applied according to three theories of the generalized thermoelasticity: Lord-Shulman with one relaxation time, Green–Lindsay with two relaxation times, as well as the coupled theory. Secular equations are derived for the plate in closed form isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms. In the absence of mechanical relaxations (Rotation and viscous effects), the results for generalized and couple theories of thermoelasticity were obtained as particular cases from the derived secular equations. In the absence of thermomechanical coupling, the analysis for a viscoelastic plate can be deduced from the present one. Finally the numerical solution is carried out for copper material. The function iteration numerical scheme is used to solve the complex secular equations, in order to obtain phase velocity and attenuation coefficients of propagating wave mode. The dispersion curves and attenuation coefficients profiles so obtained for symmetric and skew-symmetric wave modes are presented graphically to illustrate and compare the theoretical results in the presence and absence of rotation. The study may be useful in the construction and design of gyroscopes and rotation sensors as well as in the application in diverse fields.     

功能梯度空心圆柱体中的周向超声导波

为了更有效地使用超声技术检测功能梯度管道中纵向缺陷,基于3维弹性理论,采用一种正交多项式法研究无限长功能梯度材料管道中的周向导波。为验证方法的正确性与适用性,首先采用该方法计算均匀各向异性管道中的周向导波,并与已有数据相比较。其次,计算了不同梯度函数下管道周向导波的频散曲线,并与均匀管道进行了比较,说明了梯度材料管道中周向导波的特点以及梯度函数变化对频散曲线的影响。最后,求解了不同径厚比下功能梯度材料圆柱壳周向导波的频散曲线,分析了径厚比的变化对频散曲线的影响。     

Quantitative guided wave testing by applying the time reversal principle on dispersive waves in beams

A method for the localization and characterization of defects in waveguide-like structures is presented in this paper. In contrast to traditional ultrasound and guided wave techniques, a broadband signal is used to enforce strong dispersion of the flexural wave mode. Since dispersion is well compensated in a time reversal experiment we use a time reversal numerical simulation to identify the origin and the original shape of the flexural wave excited at a local non-uniformity due to mode conversion. Limitations of the time reversal process for broadband signals due to multimode and evanescent behavior of guided waves are discussed and eliminated using a Timoshenko beam model. The resulting novel process which uses both flexural and longitudinal wave information allows detection, localization and size estimation of several defects in a beam with only a single measurement. The method proposed is experimentally validated on rectangular solid beams and cylindrical hollow beams with notches of different sizes and positions. Up to three notches could be localized from one measurement, with a maximum error of 3% with respect to the propagation distance. The size was accurately predicted for notches as small as 0.5 mm depth or 8.3% of the cross section, using a generalized spring model of a crack.     

分数阶粘弹性地基上薄板波动和振动特性分析

本文研究了粘弹性地基上薄板的波动和振动问题.主要讨论了基于分数导数理论的粘弹性地基模型上薄板弯曲波的传播特性以及固有频率对地基的依赖特性.推导了三种经典粘弹性地基模型的复模量.并利用分数导数的性质得到分数阶粘弹性地基上Kirchhoff板中弯曲波的传播速度、衰减系数以及自由振动的复固有频率.数值算例表明粘弹性地基对弯曲波传播特性存在显著影响,不同粘弹性模型所对应的色散和衰减特性也存在较大差别.分数阶导数可以实现相邻整数阶导数之间的光滑过渡.利用分数导数的本构关系可以更加真实地描述粘弹性地基的历史依赖行为,更准确地表现出粘弹性地基板中弯曲波的色散和衰减特性.     

Resonances of three transverse standing-wave modes in a waveguide with periodic wall undulations

Interactions of three transverse modes are investigated in a waveguide with periodic walls. Resonances of two guided wave modes always result in forbidden bands for wave propagations when the wavenumber matching conditions are satisfied. As a third mode is involved due to the selected wall corrugations, we find that a single high-order mode can penetrate through the forbidden band based on the complex interactions. A method for generating a single high-order transverse mode is proposed by manipulating the multimode interactions. The numerical simulations on acoustic waveguides, showing the extreme suppression of the unwanted modes in the Bragg and non-Bragg gaps, demonstrate the validity and the efficiency of the proposed method.     

Propagation of guided waves in pressure vessel

Pressure vessels usually operate under extremes of high/low temperatures and high pressures. Defect, such as crack and corrosion, can result in leakage or rupture failures, even catastrophic incidents. Guided wave-based structural health monitoring (SHM) technology is one of the most prominent options in non-destructive evaluation and testing (NDE/NDT) techniques. Propagation of guided waves in a typical pressure vessel is systematically investigated in this study for the application of guided wave-based SHM. Shape of the pressure vessel is a cylinder with two end caps. Because of geometric similarity, theory of guided wave propagation in the cylinderical structure is analyzed to study dispersive features of guided waves in the pressure vessel. Dispersion curves of three different types of guided wave modes, viz. the longitudinal, torsional and flexural modes, are calculated using theoretical method. Based on the analyses and experimental wave signals, central frequency and wave parameters of incident wave are optimized. Effect of contained liquid on propagation of guided waves, especially the L(0, 2) mode, in the pressure vessel is further investigated to minimize energy leakage of the wave to the contained liquid. The analytical method, finite element analysis (FEA) and experiments are applied to study propagation characteristics of guided waves in the pressure vessel, so as to demonstrate the feasibility of guided wave-based non-destructive evaluation and testing (NDE/NDT) for such kind of complex structures.     

Wave propagation in graded rings with rectangular cross-sections

In this paper, a double orthogonal polynomial series method is proposed to investigate the guided wave propagation in a two-dimensional (2-D) structure, namely, a FGM ring with a rectangular cross-section. Two kinds of graded rings are considered: material gradient directions being in the radial direction and in the axial direction respectively. Numerical comparison with available reference results for a straightly homogeneous rectangular bar illustrates the validity of the proposed method. The dispersion curves and displacement distributions of various FGM rings, which have different radius to thickness ratios, different material gradient directions and different thickness to height ratios, are calculated to reveal the guided wave characteristics.     

Generation of acoustic solitary waves in a lattice of Helmholtz resonators

This paper addresses the propagation of high amplitude acoustic pulses through a 1D lattice of Helmholtz resonators connected to a waveguide. Based on the model proposed by Sugimoto (1992), a new numerical method is developed to take into account both the nonlinear wave propagation and the different mechanisms of dissipation: the volume attenuation, the linear viscothermal losses at the walls, and the nonlinear absorption due to the acoustic jet formation in the resonator necks. Good agreement between numerical and experimental results is obtained, highlighting the crucial role of the nonlinear losses. Different kinds of solitary waves are observed experimentally with characteristics depending on the dispersion properties of the lattice.     

Effect of a viscous liquid loading on Love wave propagation

This paper describes a theory of surface Love waves propagating in a layered elastic waveguide loaded on its surface by a viscous (Newtonian) liquid. An analytical expression for the complex dispersion equation of Love waves has been established. The real and imaginary parts of the complex dispersion equation were separated and resulting system of nonlinear algebraic equations was solved numerically. The influence of the viscosity of liquid on the dispersion curves of phase velocity, the wave attenuation and the distribution of the Love wave amplitude is analyzed numerically. The propagation loss is produced only by the viscosity of liquids. Elastic layered waveguide is assumed to be loss-less. The numerical solutions show the dependence of the phase velocity change, the wave attenuation and the wave amplitude distribution in terms of the liquid viscosity and the wave frequency. The results of the investigations are fundamental and can be applied in the design and development of liquid viscosity sensors and biosensors, in Non-Destructive Testing (NDT) of materials, in geophysics and seismology.     

Multi-mode wave propagation in ribbed plates. Part II: Predictions and comparisons

This paper addresses dispersion curve numerical computations for specific ribbed plates. Precisely, wave propagation in the direction parallel to the ribs is the main objective. First, analytical calculations are performed for such ribbed plates after which the results are compared to a more general numerical procedure. This procedure reuses a reduced finite element model of the ribbed plate and extracts guided multi-mode propagation parameters. Comparisons of analytical and numerical estimations show very good agreement. Finally, the experimental results obtained in the companion paper are considered. Specifically, experimental and numerical dispersion curves are compared over a wide frequency range. Close concordance is obtained allowing the dispersion curves to be fully interpreted.     

Surface waves in a piezoelectric–semiconductor composite structure

The present work deals with the propagation of interfacial surface waves in a composite consisting of homogeneous, transversely isotropic, piezoelectric halfspace underlying a thin layer of non-piezoelectric semiconductor material. The mathematical model of the problem is depicted by partial differential equations of motion for the structure and boundary conditions to be satisfied at the interface and free surface of the composite. After obtaining formal wave solution of the model the secular equation that governs the propagation of surface waves in the considered composite structure has been derived in compact form. The numerical solution of secular equation is being carried out for the composites Si–CdSe, Ge–CdSe and Ge–PZT by employing functional iteration method along with irreducible Cardano method using MATLAB programming. The computer simulated results in respect of dispersion curves, attenuation coefficient and specific loss factor of energy dissipation are presented graphically for Si–CdSe composite to illustrate the analytical developments. We have extended our analysis to Ge–CdSe and Ge–PZT composites also. However, to avoid clustering of profiles and also to have clear understanding of the variations, the computer simulated values of phase velocity and attenuation coefficient are presented in tabular form for all three considered composite structures. This work may be useful for designing and construction of surface acoustic wave (SAW) devices and electronics industry.     

基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。