An analytical approach to reconstruction of axisymmetric defects in pipelines using T(0,1)guided waves

Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),which is the first order of torsional guided waves,plays the irreplaceable position and role,mainly because of its non-dispersion characteristic property.However,one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy.Taking into account this situation,a quantitative reconstruction method using the torsional guided wave T(0,1)is proposed in this paper.The methodology for defect reconstruction consists of three steps.First,the reflection coefficients of the guided wave T(0,1)scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method(HFEM).Then,applying the boundary integral equation(BIE)and Born approximation,the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T(0,1)and the fundamental solution of the intact pipeline in the frequency domain.Finally,reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain.Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile,the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated.It is noted that the reconstructive error is less than 10%,providing that the defect depth is no more than one half of the pipe thickness.

Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

Exact Traveling Wave Solutions of Nano-Ionic Solitons and Nano-Ionic Current of MTs Using the exp(-φ (ξ ))-Expansion Method

In this work, the exp(-φ (ξ )) -expansion method is used for the first time to investigate the exact traveling wave solutions involving parameters of nonlinear evolution equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. The validity and reliability of the method are tested by its applications to Nano-ionic solitons wave’s propagation along microtubules in living cells and Nano-ionic currents of MTs which play an important role in biology.

Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics

In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.

Investigation of the guided-mode characteristics of hollow-core photonic band-gap fibre with interstitial holes

This paper investigates the guided-mode characteristics of hollow-core photonic band-gap fibre （HC-PBGF） with interstitial holes fabricated by an improved twice stack-and-draw technique at visible wavelengths. Based on the simulation model with interstitial holes, the influence of glass interstitial apexes on photonic band-gaps is discussed. The existing forms of guided-mode in part band gaps are shown by using the full-vector plane-wave method. In the experiment, the observed transmission spectrum corresponds to the part band gaps obtained by simulation. The fundamental and second-order guided-modes with mixture of yellow and green light are observed through choosing appropriate fibre length and adjusting coupling device. The loss mechanism of guided-modes in HC-PBGF is also discussed.

Acoustic scattering mechanism and noise attenuation of circumferentially non-uniform liner with spectral-wave guide method

In this paper,a model is established with application of the spectral-wave guide method,which has higher accuracy and can serve as a rapid calculation tool for sound transmission calculations.Based on this calculation model,some numerical results of circumferentially non-uniform lined annular/circular ducts are carried out,and some physical mechanisms can be discovered.The numerical results show that periodical impedance distributions along the circumferential direction will lead to discontinuous scattered modes with regular spacing;and mirror-symmetric structure liner will converge the energy of opposite modes.Relying on this mechanism,the potential of acoustic scattering can be further developed by suppressing lower or enhancing higher order modes with expressly designed segmented liner configurations.In particular,the intrinsic mechanism of mode redistribution brought about by the non-uniform liner can be subtly utilized to attenuate broadband noise.The present work indeed shows that circumferentially non-uniform liner is conducive to the reduction of the practical broadband sound source.Furthermore,the effects of nonuniform flow are considered in the model,then distinction of noise attenuation and scattered modes energy in different flows is shown.A possible mechanism is proposed that refraction effects in complex flows lead to the distinction.These works show that the current model has profound potential and availability for the research and designs of circumferentially non-uniform liner.

Theoretical investigation of band-gap and mode characteristics of anti-resonance guiding photonic crystal fibres

With the full-vector plane-wave method （FVPWM） and the full-vector beam propagation method （FVBPM）, the dependences of the band-gap and mode characteristics on material index and cladding structure parameter in anti- resonance guiding photonic crystal fibres （ARGPCFs） are sufficiently analysed. An ARGPCF operating in the near- infrared wavelength is shown. The influences of the high index cylinders, glass interstitial apexes and silica structure on the characteristics of band-gaps and modes are deeply investigated. The equivalent planar waveguide theory is used for analysing such an ARGPCF filled by the isotropic materials, and the resonance and the anti-resonance characteristics r：~n h~ w~｜] r^r~dlrtpd

Novel traveling wave solutions and stability analysis of perturbed Kaup-Newell Schrodinger dynamical model and its applications

We study the traveling wave and other solutions of the perturbed Kaup-Newell Schrodinger dynamical equation that signifies long waves parallel to the magnetic field.The wave solutions such as bright-dark(solitons),solitary waves,periodic and other wave solutions of the perturbed Kaup-Newell Schrodinger equation in mathematical physics are achieved by utilizing two mathematical techniques,namely,the extended F-expansion technique and the proposed exp(-φ(ξ))-expansion technique.This dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrodinger equation.In engineering and applied physics,these wave results have key applications.Graphically,the structures of some solutions are presented by giving specific values to parameters.By using modulation instability analysis,the stability of the model is tested,which shows that the model is stable and the solutions are exact.These techniques can be fruitfully employed to further sculpt models that arise in mathematical physics.

改进型密集阵列全聚焦成像算法的碳纤维复合材料板损伤定位研究

本文针对各向异性碳纤维复合材料板的损伤定位问题,提出改进型密集阵列全聚焦成像方法。首先,考虑碳纤维复合材料板的各向异性,通过实验分析超声导波在板中的传播特性,得到沿不同传播方向的群速度值。其次,对密集型传感器阵列的参数进行分析和优化研究,分别对不同阵列参数即阵元间距和阵元数量进行指向性函数的数值分析,优化阵列的参数,以保证阵列主瓣较窄、旁瓣较低且无栅瓣。然后,提出了一种考虑碳纤维复合材料板各向异性的改进型密集传感器阵列板结构缺陷定位算法。使用超声导波在碳纤维复合材料板中沿不同传播方向的群速度值,对全聚焦算法进行修正,并利用虚拟聚焦原理对板结构进行全聚焦成像。最后,通过布置碳纤维复合材料孔洞损伤实验,对基于密集阵列全聚焦成像方法的定位精度进行分析。实验结果表明,改进型密集阵列全聚焦成像算法的定位精度为1.00 mm,相较于使用单一群速度值,该方法在定位孔洞损伤缺陷时具有更高的精度。

三维光波导器件设计中的多重网格法FD-BPM

将一种高效的数值计算方法—多重网格法引入到三维有限差分波束传播法 (FD BPM)中 计算了均匀介质内定向高斯波在不同角度时的传播问题 ,并与解析法的结果进行了比较 最后计算了矩形波导的传播模式 ,并与交替方向迭代法BPM计算的结果进行了比较 证实了此方法的可靠性 ,而且这种方法大大提高了广角三维FD BPM的计算速度 。

光纤MEMS法布里-珀罗压力传感器的准分布式测量

提出了一种基于傅立叶解调法的空分复用系统,实现了光纤微机电系统(M icroE lectroM echan ical System,MEMS)法-珀(FP)压力传感器的准分布式测量.传感器基于FP腔干涉的原理,采用MEMS技术加工制作,用傅立叶方法解调干涉信号,用光开关实现传感器复用.理论分析与实验验证了传感器解调和复用的基本原理.结果表明,该系统具有好的线性、灵敏度、精度和重复性,响应速度快,复用的传感器间无明显串扰,系统复用能力取决于光开关的通道数.

采用矩阵束方法的复合材料圆管周向导波频散数据获取

基于矩阵束算法,提出了一种从弧形阵列采集数据中获取复合材料圆管多模态周向导波频散数据的方法。首先根据留数定理,给出了频率域导波响应信号的多模态周向导波叠加公式,构建了阵列导波信号的Hankel矩阵;然后通过求解Hankel矩阵的广义特征值获取了导波的频散数据,给出了综合利用正向和反向接收弧形阵列处理结果降低频散数据中噪声的方法;最后,设计了碳纤维复合材料圆管中周向传播导波信号的测量实验,利用矩阵束方法获取了圆管周向导波的频散数据,并与采用半解析有限元方法模拟的理论频散曲线进行了对比分析。理论频散曲线与实验数据吻合良好,表明该方法具有很强的鲁棒性,即使采用空气耦合换能器作为发射接收阵列,也可以有效地从弧形阵列波形信号中获取周向导波的频散数据。

PBG-PCF基模特性全矢量平面波多极方法联合数值研究

用全矢量平面波方法与多极方法联合数值研究六重对称带隙型光子晶体光纤的基模特性.通过全矢量平面波方法可确定组成PBG-PCF的二维光子晶体的带隙,基模(束缚模)存在其频率要落在带隙内且须在k0a=βa的直线附近上部区域,在带隙外形成辐射(泄漏模).把频率作为输入变量用多极方法计算,数据导出用MATLAB数学软件作出模场分布图,结果发现,不是所有基模可能存在的区域都有基模存在,为带隙型光子晶体光纤的基模寻找提供一种可行的方法.

基于Wigner-Ville分布的焊缝特征导波信号分析方法

超声导波信号的波形具有多模态、波包混叠严重的问题,因此寻找有效的信号分析和模态识别方法成为超声导波焊缝检测技术中的重要研究内容。利用时-频分析方法中的Wigner-Ville分布及其改进方法对实验获得的焊缝特征导波回波信号进行处理,分析各波包对应的导波模态,有效识别缺陷回波信号,提取焊缝的结构和缺陷信息,实现模态分离和缺陷识别。分析结果与焊缝的实际结构和尺寸参数相吻合,该分析方法可为焊缝特征导波信号的分析处理提供现实依据。

钢绞线导波传播特性研究

导波作为一种有效的无损检测方法,在钢绞线检测中具有广阔的应用前景。钢绞线的特殊螺旋结构,使得导波在钢绞线中的传播性质尚未完全了解。该文研究了导波在七丝钢绞线中频散性质。利用FrenetSerret方法建立了螺旋坐标系,在此基础上对传统半解析有限元方法进行了改进,得到了适用于螺旋结构的波导特征方程。计算了单根高强直钢丝的频散曲线,分析了导波的频散特性,研究了导波在七丝钢绞线中传播的频散特性,得到的频散曲线“陷频”现象中心频率与实验结果一致,并且钢绞线和直钢丝的频散曲线具有很大差异。通过钢绞线超声导波应力测试实验验证了该文所提出的螺旋半解析有限元法的正确性和有效性。结果表明,实验结果与理论群速度吻合良好,并且钢绞线的轴向应力与钢绞线中导波群速度近似线性关系。

Interference coupling analysis based on a hybrid method: application to a radio telescope system

Working in a way that passively receives electromagnetic radiation from a celestial body, a radio telescope can be easily disturbed by external radio frequency interference as well as electro- magnetic interference generated by electric and electronic components operating at the telescope site. A quantitative analysis of these interferences must be taken into account carefully for further electro- magnetic protection of the radio telescope. In this paper, based on electromagnetic topology theory, a hybrid method that combines the Baum-Liu-Tesche （BLT） equation and transfer function is proposed. In this method, the coupling path of the radio telescope is divided into strong coupling and weak cou- pling sub-paths, and the coupling intensity criterion is proposed by analyzing the conditions in which the BLT equation simplifies to a transfer function. According to the coupling intensity criterion, the topological model of a typical radio telescope system is established. The proposed method is used to solve the interference response of the radio telescope system by analyzing subsystems with different coupling modes separately and then integrating the responses of the subsystems as the response of the entire system. The validity of the proposed method is verified numerically. The results indicate that the proposed method, compared with the direct solving method, reduces the difficulty and improves the efficiency of interference prediction.

An Efficient High-Resolution Shock-Capturing Scheme for Multi-Dimensional Flows I. Hydrodynamics

Many problems at the forefront of theoretical astrophysics require a treatment of dynamical fluid behavior. We present an efficient high-resolution shock-capturing hydrodynamic scheme designed to study such phenomena. We have implemented a weighted, essentially non-oscillatory （WENO） scheme to fifth order accuracy in space, lILLE approximate Riemann solver is used for the flux computation at cell interface, which does not require spectral decomposition into characteristic waves and so is computationally friendly. For time integration we apply a third order total variation diminishing （TVD） Runge-Kutta scheme. Extensive testing and comparison with schemes that re.quire characteristic decomposition are carried out demonstrating the ability of our scheme to address challenging open questions in astrophysics.

Numerical Investigation of Ultrasonic Guided Wave Dynamics in Piezoelectric Composite Plates for Establishing Structural Self-Sensing

This article presents a numerical investigation of guided wave generation, propagation, interaction with damage, and reception in piezoelectric composite plates for the purpose of establishing structural self-awareness.This approach employs piezoelectric composite materials as both load bearing structure and sensing elements.Finite element modal analysis of a plate cell with Bloch-Floquet boundary condition(BFBC) is performed to understand the wave propagation characteristics in piezoelectric composite plates. A comparative study is carried out between a standard composite plate and a piezoelectric composite plate to highlight the influence of piezoelectricity on guided wave dispersion relations. Subsequently, a transient dynamic coupled-field finite element model is constructed to simulate the procedure of guided wave generation, propagation, interaction with damage, and reception in a piezoelectric composite plate. Active sensing array is designed to capture the structural response containing the damage information. Three engineering scenarios, including a pristine case, a one-damage-location case and a two-damage-location case, are considered to demonstrate the ultrasonic sensing capability of the piezoelectric composite system. Finally, time-reversal method is utilized to locate and image the damage zones. This research shows that piezoelectric composite material possesses great potential to establish structural self-awareness, if it serves both as the load bearing and structural sensing components.

钢轨中超声导波模式激励方法研究

超声导波具有传播距离长、探测范围大的优点,可应用于铁路快速、远距离的检测。较为单一导波模式的激发和传播有利于信号处理和损伤识别。本文基于正交模式展开方法对钢轨中较单一波模式的激励方法开展研究,给出考虑切向激励的横截面振幅因子经验公式,分析不同位置激励时钢轨中不同导波模式的振幅因子;通过有限元仿真对激励方法进行验证,使用上述激励方法对轨头和轨底缺陷进行检测,结果表明该激励方法激励的波模式较为单一,可明显识别伤损回波信号。该方法可用于开发适用于损伤识别的单一波模式激励策略,显示无损检测和结构健康监测应用的潜力。

A One-Dimensional Relativistic Shock Model for the Light Curve of Gamma-ray Bursts

We investigate the forming of gamma-ray burst pulses with a simple onedimensional relativistic shock model. The mechanism is that a ＂central engine＂ drives forward the nearby plasma inside the fireball to generate a series of pressure waves. We give a relativistic geometric recurrence formula that connects the time when the pressure waves are produced and the time when the corresponding shocks occurred. This relation enables us to relate the pulse magnitude with the observation time. Our analysis shows that the evolution of the pressure waves leads to a fast rise and an exponential decay pulses. In determining the width of the pulses, the acceleration time is more important than that of the deceleration.