Propagation behaviour of guided waves in tapered sandwich structures and debonding identification using time reversal

Fundamental symmetric and anti-symmetric Lamb wave modes are characterised in terms of their velocity and magnitude variation as they encounter a gradual change in the thickness of a composite sandwich plate with a high density foam core (Dyvinicell HP100). Wave mode selection is optimised to enhance the sensitivity of guided waves for debonding inspection of tapered sandwich structures, and the conversion in wave modes after interaction with the taper is also studied. A taper change in the sandwiched structure can induce a clear change in the wave magnitude when the guided waves are excited at relatively low frequency (below around 150 kHz), while there is less effect on the velocity of the propagating waves. The effect of the taper on the signal magnitude and velocity is reduced when the excitation frequency is increased beyond 200 kHz. An imaging algorithm based on time reversal is developed to detect multiple debonding in tapered composite sandwich panels, using guided waves at different excitation frequencies ranging from 150 to 200 kHz, from an active sensor network. Correlation coefficients between the original and reconstructed time reversal signals are calculated to define a damage index for individual sensing paths, which are subsequently used in a fusion process to identify the presence of multiple debonded areas.     

Leaky and non-leaky behaviours of guided waves in CF/EP sandwich structures

The aim of this study is to investigate the leaky and non-leaky behaviours of guided waves, between the composite skin and the core in CF/EP sandwich structures, focusing on the fundamental symmetric like and anti-symmetric like guided wave modes and Rayleigh waves. In investigating the core effect on the guided wave propagation different types of cores are used, namely Nomex honeycomb (HRH 10 1/8-3) 10 and 20 mm in thickness and foam (Divinycell^®  PVC). The behaviour of the guided wave modes is characterised and the conversion mechanism to the Rayleigh wave is investigated. Further, leaky and non-leaky behaviours of guided waves upon interacting with debonded areas are explored, where the ability of guided waves to identify debonding of different sizes was assessed. Finite element analysis simulations are presented to support the experimental analysis, where propagation of ultrasonic waves and their interaction with debonded areas are quantitatively examined.     

钢轨轨底垂直振动模式导波检测技术的实验研究

现有铁路钢轨超声探伤车技术无法检测线路钢轨轨底缺陷,给铁路运输安全带来很大隐患.本文开展了钢轨轨底超声导波传播特性和垂直振动模式导波检测技术研究,采用半解析有限元方法分析了我国60型钢轨轨底的各振动模态导波频散曲线和波结构.应用模态锤技术对自由状态钢轨轨底垂直振动模态导波传播特性进行了实验测量,结果表明,在0～100kHz频率范围内,钢轨轨底垂直振动模态优势模式与厚度为14 mm板中的A0模式兰姆波具有等效性.进一步研究了激励频率、激励脉冲周数、传播距离对轨底垂直振动模态导波传播的影响,设计了导波斜探头,选择合适的参数在钢轨轨底激励出垂直振动模态导波并检测出了轨底的人工缺陷.本文的研究结果为线路钢轨轨底的导波检测技术奠定了一定的基础.     

Anti-symmetric waves in pre-stressed imperfectly bonded incompressible elastic layered composites

The effect of an imperfect interface on the dispersive behavior of in-plane time-harmonic symmetric waves in a pre-stressed incompressible symmetric layered composite, was analyzed recently by Leungvichcharoen and Wijeyewickrema (2003). In the present paper the corresponding case for time harmonic anti-symmetric waves is considered. The bi-material composite consists of incompressible isotropic elastic materials. The imperfect interface is simulated by a shear-spring type resistance model, which can also accommodate the extreme cases of perfectly bonded and fully slipping interfaces. The dispersion relation is obtained by formulating the incremental boundary-value problem and using the propagator matrix technique. The dispersion relations for anti-symmetric and symmetric waves differ from each other only through the elements of the propagator matrix associated with the inner layer. The behavior of the dispersion curves for anti-symmetric waves is for the most part similar to that of symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress for perfectly bonded and imperfect interface cases, a finite phase speed may exist only for the fundamental mode while other higher modes have an infinite phase speed. However, for a fully slipping interface in the low wavenumber region it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds. For the higher modes which have infinite phase speeds in the low wavenumber region an expression to determine the cut-off frequencies is obtained. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the phase speeds of the surface wave or the interfacial wave or the limiting phase speed of the composite. The bifurcation equation obtained from the dispersion relation yields neutral curves that separate the stable and unstable regions associated with the fundamental mode or the next lowest mode. Numerical examples of dispersion curves are presented, where when the material has to be prescribed either Mooney–Rivlin material or Varga material is assumed. The effect of imperfect interfaces on anti-symmetric waves is clearly evident in the numerical results.     

Damage detection based on the propagation of longitudinal guided wave in a bimetal composite pipe

This paper investigates the damage detection based on the propagation of guided wave in bimetal composite pipes, which can identify damage locations in both axial and circumferential directions. The feasibility of the method is showed by numerical simulations using FEM code ANSYS. Mode analysis is used to evaluate the guided wave mode and its structure, which can provide the basis of the mode selection in measurements scheme. The guided wave propagation in a damaged pipe is computed by transient analysis. 16 nodes around the pipe wall, as probes, are used to record the guided wave signal. When Pseudo Margenau—Hill distribution (PMHD) for each signal is carried out, three types of modes could be found, which are led mode, excited mode and lag mode in sequences. Based on the results, the arrival time of the excited mode could be used to locate damage in axial direction, and the energy distribution around the pipe of lag mode is consistent with the damage in circumferential direction. The simulation illustrated the possibility of detecting damage location in both axial and circumferential directions based on longitudinal ultrasonic guided waves only.     

Modeling the sound transmission through complex structures with attached noise control materials

This paper discusses three extensions of the Transfer Matrix Method (TMM). The first deals with the modeling of the transmission loss of sandwich–composite panels. A wave based model is recalled and used to derive a simpler model based on identifying effective properties of an equivalent orthotropic panel. An experimental case study is presented to show the accuracy of these models when used to predict practical sound transmission problems involving single wall sandwich–honeycomb panels and double wall sandwich–honeycomb with an absorbing material filling the cavity between the two panels. In the second extension, the use of the TMM to predict the response of panels under various types of excitations is discussed. A wave based method is presented and compared with Finite Element Method (FEM) predictions for two types of excitations: Turbulent Boundary Layer (TBL) and point source. The comparison shows that the method allows for accurate predictions of the frequency averaged Transmission Loss (TL). Finally, the use of the TMM to model double wall systems with mechanical links is presented and numerically validated using FEM. It is found that the method captures well the decrease of the TL due to the insertion of the links and the effect of the excitation nature on this decrease.     

Structuring of suspended sediments in periodic vortex flow over a vortex ripple

The formation of spatially ordered structures in a suspended sediment under the action of two-dimensional standing surface gravity waves is studied experimentally for the first time in a rectangular vessel oscillating in the vertical direction. The parameters of the structured regions in vessels with individual vortex ripples and groups of ripples are found for the first and second wave modes. Isolated structured regions of the suspended sediment appear over the bottom topography and gradually reach the free surface. The corresponding spatial horizontal scales are determined by the sand ripple dimensions, while the vertical scale of the clouds increases with time. In all experiments, the structures formed remained unchanged during the whole interval of the fluid wave motion and disappeared when the parametric excitation of the waves stopped.     

Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer

The dispersive behavior of small amplitude waves propagating along a non-principal direction in a pre-stressed, compressible elastic layer is considered. One of the principal axes of stretch is normal to the elastic layer and the direction of propagation makes an angle θ with one of the in-plane principal axes. The dispersion relations which relate wave speed and wavenumber are obtained for both symmetric and anti-symmetric motions by formulating the incremental boundary value problem for a general strain energy function. The behavior of the dispersion curves for symmetric waves is for the most part similar to that of the anti-symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress and propagation angle, it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds, while other higher modes have an infinite phase speed. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the Rayleigh surface wave speed and the limiting wave speeds of the layer, respectively. Numerical results are presented for a Blatz–Ko material and the effect of the propagation angle is clearly illustrated.     

Vortical structure evolutions and spreading characteristics of a plane jet flow under anti-symmetric long-wave excitation

The vortical evolutions and spreading characteristics of a low-speed plane jet under anti-symmetric long-wave excitations are investigated experimentally. The perturbation is introduced with two oscillating strips located at the nozzle exit. The experiments were operated at Reynolds number of 8.2 × 10³ based on the nozzle exit height. Mixing and spreading properties are influenced obviously by long-wave excitation after the end of potential core. The increments of half-width, momentum thickness, and volume flow rate depend on the excitation frequency. The results of flow visualization also reveal the dependence of excitation frequency. The power spectra of fluctuating velocities shows that the evolution of coherent structure is significantly influenced by the long-wave excitation in the downstream, but it is similar to the natural jet in the near field. The long-wave excitation at certain frequencies can promote large-scaled anti-symmetric vortical structures in the far field.     

Two fundamental modes of disturbances and their development in a plane plume above a horizontal heat source

Experimental investigations are conducted on development of the disturbances which appear in the transition to turbulence in a natural convection plume above a horizontal line heat source in air. Both the power spectra of velocity and temperature in natural transition show that there seem to be two fundamental modes of disturbances. One is an outstanding peak about 0.8 Hz and the other a small one about 1.1 Hz in the spectra. The disturbances of these fundamental frequencies are observed as anti-symmetric modes around the entrance to the transition region. The disturbance of the first fundamental frequency is a selectively amplified anti-symmetric mode in that area. In contrast, the disturbance of the second fundamental frequency is thought to be originated from a symmetric mode and then transformed into an anti-symmetric mode of the same frequency during its growth.     

Scattering of guided waves by circumferential cracks in composite cylinders

A somewhat generalized numerical procedure is used in this paper to study the problem of wave scattering by circumferential cracks in composite pipes. The study is motivated by the need to develop a model for the quantitative, ultrasonic non-destructive evaluation of cracks in pipes. For this purpose, a stiffness-based Rayleigh–Ritz type approach is employed first to obtain the approximate wave numbers and wave modes. Using the wave function expansions of the incident and scattered fields in the axial direction and decomposing the problem into separate symmetric and anti-symmetric problems, a three-dimensional wave scattering problem is reduced to two, independent two-dimensional problems over the circular cross-section. Both these problems can be reduced further to quasi-one-dimensions by discretizing the cross-section into finite elements and using a transfer matrix approach in the circumferential direction. This simplification greatly reduces the computational time. A comparison of the results for an isotropic pipe demonstrates the reliability and accuracy of the modified numerical procedure. Numerical results for the reflection and transmission coefficients of different incident wave modes are also presented for a 2-ply composite pipe with a crack. The crack may have an arbitrary circumferential length and radial depth. Simple extrapolations from one wave to another wave, separately incident on a crack, are demonstrated to be impossible due to different mode conversions by the crack.     

Symmetric and anti-symmetric Rayleigh–Lamb modes in sinusoidally corrugated waveguides: An analytical approach

The wave propagation analysis in corrugated waveguides is considered in this paper. Elastic wave propagation in a two-dimensional periodically corrugated plate is studied here analytically. The dispersion equation is obtained by applying the traction free boundary conditions. Solution of the dispersion equation gives both symmetric and anti-symmetric modes. In a periodically corrugated waveguide all possible spectral order of wave numbers are considered for the analytical solution. It has been observed that the truncation of the spectral order influences the results. Truncation number depends on the degree of corrugation and the frequency of the wave. Usually increasing frequency requires increasing number of terms in the series solution, or in other words, a higher truncation number. For different degrees of corrugation the Rayleigh–Lamb symmetric and anti-symmetric modes are investigated for their non-propagating ‘stop bands’ and propagating ‘pass bands’. To generate the dispersion equation for corrugated plates with a wide range of the degree of corrugation, appropriate truncation of the spectral orders has to be considered. Analytical results are given for three different degrees of corrugation in three plates. Resonance of symmetric and anti-symmetric modes in these plates, their ‘cut-off’, ‘cut-on’, ‘branch-point’, ‘change-place’, ‘mode conversion’ and ‘pinch points’ at various frequencies are also studied.     

周向导波在空心圆柱体中传播的数值模拟研究

在石油、化工、食品和城市供水等行业,由于腐蚀等原因而引起泄漏事故,造成巨大的经济损失和资源浪费.因此,能够预先检测到管道缺陷避免事故发生显得十分重要.基于弹性动力学理论,利用Matlab编程实现周向导波在空心圆柱体中传播的数值模拟.利用特征函数展开法计算出周向导波的频散曲线及0.6MHz和1MHz各个模态的时域波形图并据此分析激励方式同周向导波传播的关系,频率为1MHz或0.6MHz时,1和2模态在空心圆柱壳中传播的周向导波中处于主导地位:各模态的径向或周向位移幅度会受到激励入射角的影响而变化并且周向导波的位移幅度随着激励入射角的增加而增加:得到特定频率下,周向导波各模态径向、周向位移的变化关系.本文结果为进一步利用实验方法研究周向导波在空心圆柱体中传播特性和缺陷检测奠定了基础.     

竖直振动无黏液滴的法拉第不稳定性分析

由于外部周期性的振动而在液滴表面产生的Faraday不稳定效应广泛存在于超声雾化、喷涂加工等应用中,对Faraday不稳定性进行分析对研究振动液滴的表面动力学有着重要意义.本文将Faraday不稳定性问题从径向振动拓展到竖直振动,研究了竖直振动无黏液滴表面波的不稳定性.竖直方向的振动使得液滴动量方程为含有空间相关项和时...     

双介质耦合刚性基弹性层平面应变型导波模式及界面散射能量分配

过渡段动力稳定性问题已成为制约400 km/h及以上高铁路基设计的关键难题,亟需从波动和能量的角度探究由基础非均匀引发的线路系统动力响应放大机理.文章将轨下基础简化为上表面自由、底端固定的刚性基弹性层,将高铁过渡段车致弹性波传播问题提炼为非均匀介质刚性基弹性层中波的散射问题,建立双介质耦合刚性基弹性层平面应变模型,优化该类波导结构频散方程在复平面求根方法,并结合岩土类介质特征展开刚性基弹性层频散分析,以明确其多模式导波特性及散射能量分配,最后,围绕弹性层厚度、刚度比等影响因素开展对比分析.结果表明:刚性基弹性层各模式导波均具有截止频率,弹性层厚度越小,杨氏模量越大,各阶导波模式的截止频率越高;入射波在双介质刚性基弹性层发生散射后,透射场基阶模式导波会占据主体能量,随着高阶导波模式被逐一激发,反射场及透射场高阶模式能量占比会在全频率范围呈现“此消彼长”状态;交换两侧弹性层材料,改变弹性层厚度及两弹性层刚度比不会显著改变能量分布规律,但总体来看,能量更易集中在较软侧弹性层中,各模式导波在激发初始频段会更为活跃,可分配到更多能量.     

Influence of Horizontal Excitations on Dynamic Stability of a Slender Beam Under Vertical Excitation

Experimental studies have been conducted to clarify the influence of horizontal harmonic excitations on the dynamic stability of a slender cantilever beam under vertical harmonic excitation. Three kinds of aluminum test beams with rectangular cross section have been used. The test beam being clamped at one end and free at the other end, was vertically stood, and was harmonically excited to both vertical and horizontal directions simultaneously. The direction of the horizontal excitation was taken parallel to one of the beam side faces, i.e. two directions were considered as X and Y directions which have the largest and smallest flexural rigidity, respectively. By varying the horizontal excitation amplitude, keeping the amplitude of excitation in the vertical direction, the influence of the horizontal excitation has been investigated on the principal instability regions in which unstable vibration of the fundamental vibration mode occurs. The excitation frequency in the vertical excitation was taken around twice the fundamental natural frequency 2f _{Y 1} in smallest rigidity direction, while that in the horizontal direction was taken around both the fundamental natural frequency f _{Y 1} and twice of it 2f _{Y 1}. Obtained experimental results present useful fundamental data for aseismatic design of structures under earthquake containing both vertical and horizontal excitation components.     

Volume and surface stability of uniformly compressed transversely isotropic linearly elastic materials

The stability loss of a transversely isotropic linearly elastic medium is studied. The medium is uniformly compressed in both horizontal directions, and the initial stress in the vertical direction is equal to zero. The standard analysis based on the Hadamard condition is used. The bifurcation equation divides into two parts, and therefore, two kinds of buckling modes are possible. The critical initial compression is found, but the buckling modes remain indefinite (as the wave length so the relation between the wave numbers is arbitrary). The stability loss of a compressed half-space with a free surface is studied. Only one kind of buckling mode localized near the free surface is possible, and as for an entire space, the buckling mode and the wave length are indefinite. In these problems, linear as well as non-linear approaches are used. In the linear approach, the pre-buckling deformations are ignored. It is shown that for some values of parameters, the linear approach leads to qualitatively incorrect results. The stability loss of an uniformly compressed plate lying on a soft elastic half-space is studied. By using the non-linear post-critical analysis, it is shown that the buckling mode is a chessboard-like one.     

基于导波技术的螺柱轴力无损检测

根据弹性动力学理论,采用纵向导波与弯曲导波相结合的方法对螺柱所受轴向应力进行无损检测。计算了M22螺柱中纵向导波和弯曲导波的群速度频散曲线。根据频散曲线,确定了采用导波对螺柱轴向应力进行无损检测的最优检测信号频率范围(50~80 kHz),此频率范围的纵向导波与弯曲导波模态单一,并且频散性较低。分别计算了不同轴向应力σ作用下,多种频率的纵向导波和和弯曲导波在螺柱中传播的群速度值cgσrL和cgσrF。结果表明,随着轴向应力的增大,同频率纵向导波和弯曲导波的群速度皆呈线性递减趋势。利用纵向导波和弯曲导波群速度与轴向应力的线性关系及纵向导波和弯曲导波在轴向应力作用螺柱端面的反射时间tLσ和tσF,可以迅速确定螺柱所受轴向应力值。     

Whirling of a forced cantilevered beam with static deflection. III: Passage through resonance

Nonstationary excitations of slender, elastic, cantilevered beams with equal principal moments of inertia are considered. The excitation frequency is slowly increased or decreased through a resonance of the first mode at a constant rate. Three resonances are investigated: primary resonance, superharmonic resonance of order two and subharmonic resonance of order two. After application of Galerkin's method with three modes, the nonlinear, nonstationary response of the first mode of the beam is determined by two methods: integration of the modulation equations obtained from the method of multiple scales, and direct numerical integration of the temporal equations of motion. Time histories are presented and the effects of excitation amplitude, rate of acceleration or deceleration through resonance, damping and initial conditions of the disturbance on the maximum response are studied. The effect of a persistent random disturbance is also examined. Although the excitation acts in the vertical plane, whirling occurs if the beam is subjected to out-of-plane disturbances.     

四边固支蜂窝夹层板1:3内共振非线性动力学分析

基于经典叠层板理论和几何大变形理论,将铝基蜂窝芯层等效为一正交异性层,等效弹性参数由修正后的Gibson公式得出,对四边固支蜂窝夹层板非线性动力学特性进行了分析。考虑横向阻尼的影响,建立了四边固支蜂窝夹层板受横向激振力作用的受迫振动微分方程,通过振型正交化将蜂窝夹层板受迫振动微分方程简化成双模态下的动力学控制方程,利用同伦分析方法对双模态下蜂窝夹层板的动力学控制方程进行研究,得到了1:3内共振下的幅频特性曲线,研究了不同结构尺寸对动力学特性的影响以及蜂窝夹层板作稳态运动时的稳定性问题。本文得到的结果为蜂窝夹层板的设计和实际应用提供了理论依据和数值参考。