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.     

激光在管道中激发周向导波的有限元模拟

以超声的热弹激发机理为基础，建立了模拟激光在管道中激发周向导波的有限元模型.为了验证模型的正确性，根据Gao等人报道的实验条件［J. Appl. Phys. 91, 6114 (2002)］进行了模拟，理论模拟结果与Gao等人的实验结果符合很好，说明本数值模型的正确性.在此基础上，模拟激光在不同厚度、不同曲率半径的管道内激发的周向导波波形，同时分析了激光在管道中激发的周向导波波形与平板中激发Lamb波的差异，以及管道厚度和曲率半径对激光激发周向导波的影响.     

Analysis of flexural mode focusing by a semianalytical finite element method

Focusing is one of the most promising techniques for the detection of small defects in pipe works, in which guided waves including longitudinal and flexural modes are tuned so that ultrasonic energy can be focused at a target point in a pipe, and analysis of reflected waves gives information on defects such as location and size. In this paper, the focusing technique is discussed by way of a simulation of guided wave propagation in pipe by a semianalytical finite element method (SAFE). Experiments and SAFE calculations were compared for waveforms transmitted by a single transducer and received at different circumferential positions initially, and then the focusing phenomena were experimentally observed using focusing parameters obtained by calculations. Calculation and visualization were conducted to clarify focusing phenomena in pipe in investigating the potential of the focusing technique. These results show that the time-reversal idea helps in understanding focusing and that resolution of focusing is strongly affected by incident waveforms as well as the number of channels available in an experiment.     

基于周向SH0导波的管道轴向缺陷定量表征*

随着管道服役时间的增加,其损伤逐渐累积,最终导致泄漏或爆炸事故。引入导波在线监测管道损伤是确保其安全运行的重要保障。周向零阶水平剪切(CSH0)波具有不易频散、对管道轴向缺陷敏感等优秀特性,非常适用于管道轴向缺陷的定量表征。该文 基于周向SH0导波在管道的传播特性,通过有限元模拟和试验对管道周向SH0模态导波与轴向缺陷的定量关系展开研究。结果表明：管道曲率半径越大,周向SH0模态的传播特性越接近板中SH0模态的传播特性;导波信号的反射系数和透射系数对轴向缺陷的长度和深度均呈现单调变化。依此建立了缺陷定量表征的关系云图,可用于评估缺陷尺寸。     

Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method

In typical Lamb wave simulation practices, effects of plate edge reflections are often not considered in order to simplify the wave signal interpretations. Methods that are based on infinite plates such as the semi-analytical finite element method is effective in simulating Lamb waves as it excludes the effect of plate edges. However, the inclusion of plate edges in a finite plate could render this method inapplicable, especially for transient response simulations. Here, by applying the ratio of Lamb mode reflections at plate edges, and representing the reflection at plate edges using infinite plate solutions, the semi-analytical finite element method can be applied for transient response simulation, even when the plate is no longer infinite.     

板状结构Lamb波频散补偿与聚焦接收成像检测

对板状结构中Lamb波的频散和多模现象进行了理论分析,采用有限元仿真方法获取了Lamb波与缺陷作用后的回波信号,对信号进行聚焦接收处理,即在一定距离范围内利用导波频散特性对各个模式信号进行频散补偿,提取补偿后信号的幅值,结果表明当所得信号幅值最大时,所对应的补偿距离等于缺陷与换能器之间的实际距离.利用这一结论,提出了以...     

Natural beam focusing of non-axisymmetric guided waves in large-diameter pipes

The propagation of non-axisymmetric guided waves in larger diameter pipes is studied in this paper by treating the guided waves as corresponding Lamb waves in an unwrapped plate. This approximation leads to a simpler method for calculating the phase velocities of hollow cylinder guided waves, which reveals a beam focusing nature of non-axisymmetric guided waves generated by a partial source loading. The acoustic fields in a pipe generated by a partial-loading source includes axisymmetric longitudinal modes as well as non-axisymmetric flexural modes. The circumferential distribution of the total acoustic field, also referred as an angular profile, diverges circumferentially while guided waves propagate with dependence on such factors as mode, frequency, cylinder size, propagation distance, etc. Exact prediction of the angular profile of the total field can only be realized by numerical calculations. In particular cases, however, when the wall thickness is far less than the cylinder diameter and the wavelength is smaller than or comparable to the pipe wall thickness, the acoustic field can be analyzed based on the characteristics of Lamb waves that travel along a periodic unwrapped plate. Based on this assumption, a simplified model is derived to calculate the phase velocities of non-axisymmetric flexural mode guided waves. The model is then applied to discussions on some particular characteristics of guided-wave angular profiles generated by a source loading. Some features of flexural modes, such as cutoff frequency values are predicted with the simpler model. The relationship between the angular profiles and other factors such as frequency, propagation distance, and cylinder size is obtained and presented in simple equations. The angular profile rate of change with respect to propagation distance is investigated. In particular, our simplified model for non-axisymmetric guided waves predicts that the wave beam will converge to its original circumferential shape after the wave propagates for a certain distance. A concept of "natural focal point" is introduced and a simple equation is derived to compute the 1st natural focal distance of non-axisymmetric guided waves. The applicable range of the simplified equation is provided. Industrial pipes meet the requirement of wall thickness being far less than the pipe diameter. The approximate analytical algorithms presented in this paper provides a convenient method enabling quick acoustic field analysis on large-diameter industrial pipes for NDE applications.     

Characterization of mechanical and geometrical properties of a tube with axial and circumferential guided waves

Guided waves propagating in cylindrical tubes are frequently applied for the characterization of material or geometrical properties of tubes. In a tube, guided waves can propagate in the axial direction and called axial guided waves, or in the circumferential direction called circumferential guided waves. Dispersion spectra for the axial and circumferential guided waves share some common behaviors and however exhibit some particular behaviors of their own. This study provides an investigation with theoretical modeling, experimental measurements, and a simplex-based inversion procedure to explore the similarity and difference between the axial guided waves and circumferential guided waves, aiming at providing useful information while axial and circumferential guided waves are applied in the area of material characterization. The sensitivity to the radius curvature for the circumferential guided waves dispersion spectra is a major point that makes circumferential guided waves different from axial guided waves. For the purpose of material characterization, both axial and circumferential guided waves are able to extract an elastic moduli and wall-thickness information from the dispersion spectra, however, radius information can only be extracted from the circumferential guided waves spectra.     

Guided waves in a plate with linearly varying thickness: experimental and numerical results

The aim of this work is to give experimental and numerical results on the behaviour of guided waves that propagate downslope in a free elastic plate with slowly linearly varying thickness. We show experimentally the propagation of adiabatic modes, which are guided waves that adapt to the varying thickness of the plate. As the thickness is decreasing, a given guided wave will reach its thickness cut-off. When this happens, we show that two phenomena occur: the reflection of this wave and its propagation backward in the plate, its conversion into a different guided wave which goes on propagating downslope in the plate. The numerical study is done with the software Ansys, based on the finite element method. The results obtained confirm the experimental ones.     

长骨中振动声激发超声导波的方法

为了实现一定频段内任意低频下在长骨中激励导波信号,本文提出一种采用聚焦高频(5 MHz)超声换能器在长骨皮质骨中激发低频(150 kHz)超声导波的振动声方法.首先介绍了板状超声导波理论和双声束共聚焦法与单声束调幅法激发振动声的基本原理;进而采用三维有限元仿真方法分析振动声激发低频超声导波的基本现象,然后结合牛胫骨板离体实验,验证振动声激发低频超声导波的可行性.结果均表明,双声束共焦与单声束振动超声均可在骨板中激发低频超声导波.相关研究方法有助于提高空间域长骨中超声导波测量精度,以及在一定频段内实现任意频率激励等,对发展低频超声导波在体测量长骨皮质骨的新技术具有一定的指导意义.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

套管中模式波的响应特征*

在固井质量评价中主要利用套管中模式波的幅度或衰减变化反映水泥的胶结状况,不同测井仪器在套管中激发的模式波的类型不同,研究套管中各模式波的传播特征和影响因素可充分挖掘测量数据的潜在应用价值。CBL和SBT等测井仪器在套管中主要激发拉伸波,类同于平板中的零阶对称Lamb波,水泥环封隔测井仪器的斜入射模式在套管中主要激发套管弯曲波,类同于平板中的零阶反对称Lamb波,垂直入射模式激发套管共振波,类同于平板中的高阶对称Lamb波。该文重点分析了这些模式波的衰减特征及其对微环的响应,套管弯曲波在套后耦合轻质水泥时对微环不敏感,但在套后耦合常规水泥或重水泥时,其衰减明显高于胶结良好的状况;拉伸波对微环的存在最为敏感;套管共振波对微环不敏感。     

3D analysis of interaction of Lamb waves with defects in loaded steel plates

The objective of the research presented here is the investigation of the interaction of guided waves with welds, defects and other non-uniformities in steel plates loaded by liquid. The investigation has been performed using numerical simulation for 2D and 3D cases by the finite differences method, finite element method and measurement of 3D distributions of acoustic fields. Propagation of the S(0) mode in a steel plate and its interaction with non-uniformities was investigated. It was shown that using the measured leaky wave signals in the water loading of the steel plate and by application of signal processing, the 3D ultrasonic field structure inside and outside of the plate can be reconstructed. The presence of leaky wave signals over the defect caused by the mode conversion of Lamb waves has been proved using the numerical modelling and experimental investigations. The developed signal and data processing enables to visualise dynamics of ultrasonic fields over the plate, and also to estimate spatial positions of defects inside the steel plates.     

Mode propagation in curved waveguides and scattering by inhomogeneities: application to the elastodynamics of helical structures

This paper reports on an investigation into the propagation of guided modes in curved waveguides and their scattering by inhomogeneities. In a general framework, the existence of propagation modes traveling in curved waveguides is discussed. The concept of translational invariance, intuitively used for the analysis of straight waveguides, is highlighted for curvilinear coordinate systems. Provided that the cross-section shape and medium properties do not vary along the waveguide axis, it is shown that a sufficient condition for invariance is the independence on the axial coordinate of the metric tensor. Such a condition is indeed checked by helical coordinate systems. This study then focuses on the elastodynamics of helical waveguides. Given the difficulty in achieving analytical solutions, a purely numerical approach is chosen based on the so-called semi-analytical finite element method. This method allows the computation of eigenmodes propagating in infinite waveguides. For the investigation of modal scattering by inhomogeneities, a hybrid finite element method is developed for curved waveguides. The technique consists in applying modal expansions at cross-section boundaries of the finite element model, yielding transparent boundary conditions. The final part of this paper deals with scattering results obtained in free-end helical waveguides. Two validation tests are also performed.     

Wave based analysis of the Green's function for a layered cylindrical shell

Cylindrical shells composed of concentric layers may be designed to affect the way that elastic waves are generated and propagated, particularly when some layers are anisotropic. To aid the design process, the present work develops a wave based analysis of the Green's function for a layered cylindrical shell in which the response is given as a sum of waves propagating in the axial coordinate. The analysis assumes linear Hookean materials for each layer. It uses finite element discretizations in the radial coordinate and Fourier series expansions in the circumferential coordinate, leading to linear equations in the axial wavenumber domain that relate shell displacements and forces. Inversion to the axial domain is accomplished via a state-space formulation that is evaluated using residue integration. The resulting expression for the Green's function for each circumferential harmonic is a summation over the natural waves of the shell. The finite element discretization in the radial direction allows the approach to be used for arbitrarily thick shells. The approach is benchmarked to results from an isotropic shell and numerical examples are given for a shell composed of a fiber-reinforced material. The numerical examples illustrate the effect of fiber orientation on the Green's function.     

无限流体中孔隙介质圆柱周向导波的传播特性

为研究无限大流体约束的孔隙圆柱中周向导波的传播规律,分析孔隙参数对导波传播特性的影响,建立了无限流体中孔隙介质圆柱的理论模型,利用孔隙介质弹性波动理论,建立了周向导波频散方程,通过数值模拟计算得到无限流体中孔隙介质圆柱的频散曲线,探讨了圆柱半径和孔隙参数对导波传播特性的影响,并对导波的衰减特性进行了分析;通过数值计算,得到了周向导波的时域波形,讨论了孔隙参数对波形的影响.结果表明,孔隙介质圆柱半径的改变影响圆柱尺度,孔隙度的改变影响孔隙介质中体声波的波速,都对周向导波频散曲线产生一定的影响,所得到的频散曲线特征及衰减曲线与时域波形吻合.研究结果对开展无限流体中孔隙介质圆柱的超声无损评价提供了一定的理论参考.     

A numerical approach for the computation of dispersion relations for plate structures using the Scaled Boundary Finite Element Method

In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.     

A combined finite element and modal decomposition method to study the interaction of Lamb modes with micro-defects

This paper presents a combined finite element and modal decomposition method to study the interaction of Lamb waves with damaged area. The finite element mesh is used to describe the region around the defects. On the contrary to other hybrid models already developed, the interaction between Lamb waves and defects is computed in the temporal domain. Then, the modal decomposition method permits to determine the wave reflected and transmitted by the damaged area. Modal analysis allows also identifying the mode conversions induced by the defects. These numerical results agree with previous finite element results concerning the interaction of Lamb modes with a notch. Experiments, carried out with gauged defects on an aluminum plate, are also compared to numerical predictions to validate the simulation. Compared to classical techniques of simulation, this new method allows us to investigate the interaction of Lamb modes generated at high frequency-thickness product with micro-defects as corrosion pitting.     

Lamb wave tomography of pipe-like structures

Lamb waves are guided ultrasonic plate waves that can follow the curvature of pipe-like structures. By transmitting and receiving many helically propagating Lamb waves via longitudinal transducers in contact with the surface of a pipe, crosshole tomographic geometries can be mimicked and tomographic reconstructions performed in order to locate and size flaws. We describe here a meridional-array scheme which mimics a single line of transducers along the exterior surface of the pipe in the axial direction, and show proof of concept results on a pipe sample with an internal wall-thinning. We also demonstrate improved reconstructions for the other helical ultrasound tomography geometry where the transmitters and receivers lie along parallel circumferential rings. We find frequency compounding smoothes out some of the noise and artifacts that appear in the reconstructions.     

The radiation Q factors obtained from the partial derivatives of the phase of the reflection coefficient of an elastic plate

The phase gradient method is applied to study the partial derivatives of the phase of the reflection coefficient of a fluid-loaded elastic plate. We consider the derivatives with respect to the frequency f, the incidence angle theta, the phase velocities of the longitudinal and transverse waves propagating in the plate, cL and cT, respectively, and the phase velocity in the fluid cF. The partial derivatives with respect to f, cL, cT, cF are linked by a relation involving products of one of these variables with the corresponding partial derivative. At a resonance frequency, the product of frequency with the frequency phase derivative can be identified as a radiation quality factor. By analogy, the other products correspond to quality factors. It can be shown that the product assigned to the fluid phase velocity corresponds to an angular radiation quality factor. The products assigned to the longitudinal and transverse phase velocities are identified as longitudinal and transverse radiation quality factors. These quality factors are shown to be related to stored energies associated with either standing waves across the plate, guided waves, longitudinal waves or transverse waves. A reactive power balance between the plate and the fluid is also established.