Experimental investigation of transient flexural waves in beams with discontinuities of cross section

There has been little experimental work on flexural wave propagation in general and on flexural wave propagation in beams with discontinuities of cross section in particular. Experimental data are obtained for various test beams subjected to eccentric longitudinal impact. The bending strain versus time results are presented for several positions along a uniform beam and finite beams (of circular cross section) with discontinuities of cross section. Bending strain histories are recorded at several positions before and after the discontinuity. The effect of reflections on the propagated flexural wave is illustrated. The dispersion of the traveling flexural wave caused several alternating peaks within the duration of the original positive input pulse. The importance of investigating discontinuities of cross section in structures subjected to impact loading is clearly manifested.     

Experimental wavelet analysis of flexural waves in beams

The wavelet transform (WT) is applied to the time-frequency analysis of flexural waves in beams. The WT with the Gabor wavelet decomposes a dispersive wave into each frequency component in the time domain, which enables one to determine the traveling time of a wave along the beam at each frequency. By utilizing this fact, a method is developed to identify the dispersion relation and impact site of beams.     

铁木辛柯梁中的卸载弯曲波及二次断裂

半无限长梁承受恒定弯矩作用后, 如果自由端的初始弯矩突然释放, 将在梁中激发出一列卸载弯曲应力波. 采用铁木辛柯梁和瑞利梁来研究突然卸载所激发出的弯曲波的传播特征. 利用拉普拉斯变换方法进行分析, 首先推导出铁木辛柯梁和瑞利梁中的卸载弯曲波的像函数解析解, 采用数值反变换方法给出了时域上波传播的响应解, 并研究了梁中各点的横向位移、弯矩和剪力随时间的变化规律. 计算结果表明: 与简化的欧拉梁不同, 旋转惯性的引入使铁木辛柯梁和瑞利梁中的弯曲波传播具有强烈的局部化效应, 特别是梁中各点经历的弯矩变化, 和其距离自由端的位置相关, 不同时刻的弯矩峰值大小不同;瑞利梁中离自由端不同距离各点的峰值弯矩先增大后降低, 最后达到一个渐近值;铁木辛柯梁中各点的峰值弯矩总体上随着时间单调增大到同一个渐近值, 该渐近值与欧拉梁中的峰值弯矩值相同, 均为1.43.切应力效应的引入进一步降低了铁木辛柯梁中卸载弯曲波的波速, 同时也使得铁木辛柯梁中弯矩峰值的最大值小于瑞利梁中的最大值. 对于脆性细长梁的纯弯曲断裂, 铁木辛柯梁可以较好地预测二次断裂的发生位置, 相应的碎片尺寸约为7倍梁横截面厚度.      

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。     

Wave dispersion in gradient elastic solids and structures: A unified treatment

Analytical wave propagation studies in gradient elastic solids and structures are presented. These solids and structures involve an infinite space, a simple axial bar, a Bernoulli–Euler flexural beam and a Kirchhoff flexural plate. In all cases wave dispersion is observed as a result of introducing microstructural effects into the classical elastic material behavior through a simple gradient elasticity theory involving both micro-elastic and micro-inertia characteristics. It is observed that the micro-elastic characteristics are not enough for resulting in realistic dispersion curves and that the micro-inertia characteristics are needed in addition for that purpose for all the cases of solids and structures considered here. It is further observed that there exist similarities between the shear and rotary inertia corrections in the governing equations of motion for bars, beams and plates and the additions of micro-elastic (gradient elastic) and micro-inertia terms in the classical elastic material behavior in order to have wave dispersion in the above structures.     

Transient thermoelastic waves in an anisotropic hollow cylinder due to localized heating

This paper presents a theoretical study of transient ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic hollow circular cylinder. Generalized thermoelastic theory proposed by Lord and Shulman is adopted to model the dynamic thermoelastic behavior of the cylinder. The concentrated heat source model used is to represent heating due to a pulsed laser beam, which is focused on the outer surface of the cylinder. A semi-analytical finite element (SAFE) method is employed to evaluate guided wave modes in the cylinder. Using integral transform techniques, the modal wave forms are obtained in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying inverse Fourier transformation in the time domain. Numerical results showing the dispersion curves for the group velocities of the propagating modes and transient radial displacements are presented. For this purpose it is assumed that the cylinder is made of transversely isotropic silicon nitride (Si₃N₄). Attention is focused on the propagation characteristics of longitudinal and flexural modes separately.     

弯曲波彩虹捕获效应及其在能量俘获中的应用

弹性波在色散关系经过设计的梯度结构中传播时会产生空间分频现象和波场能量增强现象,即不同频率的弹性波会在结构的不同位置停止向前传播并发生能量聚集,这就是弹性波彩虹捕获效应.其相关研究成果可以促进结构健康监测、振动控制以及能量俘获等领域的发展.本文通过所设计的梯度结构梁,系统地研究了弯曲波彩虹捕获效应及其在压电能量俘获中的应用.首先,利用传递矩阵法获得了梯度结构梁元胞能带结构的解析解,进而分析了弯曲波彩虹捕获效应的产生机理:不同频率的弯曲波会在不同元胞附近群速度减小到零,从而停止向前传播并发生反射;入射波和反射波的叠加,以及群速度减小带来的能量聚集,会显著增强反射处的波场能量.其次,通过有限元仿真和实验验证了弯曲波彩虹捕获效应的空间分频现象和波场能量增强现象.最后,通过有限元多物理场耦合仿真和实验,研究了粘贴PVDF压电薄膜的梯度结构梁相对于均匀梁的弯曲波能量俘获效果及其随入射波频率的变化规律.结果表明,在弯曲波彩虹捕获效应发生频带内,粘贴在梯度结构梁上的PVDF压电薄膜的输出电压约为粘贴在均匀梁相应位置处的PVDF压电薄膜的输出电压的2倍.     

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.     

Stress-concentration factors for multiple semielliptical notches in beams under pure bending

Uniformly spaced semielliptical notches in rectangular beams under pure bending are examined photoelastically. Minimum stress-concentration factors, produced by multiple elliptical notching of beams, are obtained for wide ranges of notch width, semiminor elliptical axis, notch depth, notch pitch and depth of beam. In particular, the geometries of the optimum elliptical notch producing the least stress concentration are obtained for a practical range of parameters. Stress-concentration factors for beams with multiple semi-elliptical notches are compared to those for beams with single semielliptical notches and to those for beams with semicircular notches. The maximum reduction of stress-concentration factor for beams with multiple semielliptical notches is to approximately 37 percent of the stress-concentration factor for beams with single semielliptical notches. Within the range of parameters investigated, the stress-concentration factor for beams with multiple semielliptical notches was 15 to 37 percent less than that for multiple semicircular notches.     

Effects of compressive load and support damping on the propagation of flexural waves in beams resting on elastic foundation

The contributions of compressive load and support damping are included into the formulation of flexural wave motion in beams lying on elastic (Winkler) foundation. The beam is modeled by both Euler–Bernoulli’s and Timoshenko’s theories. First, dispersion analysis is performed, which reveals that, for a fixed wavenumber, phase velocity decreases as the intensity of the compressive force or the value of the support damping is increased. Secondly, the transverse displacement of a semi-infinite beam excited by a velocity step pulse at its finite end is examined in the transient regime by adopting Laplace transform approach. This latter study sustains the validity of the dispersion analysis outcomes and shows that compressive load and support damping cause an amplification and a diminution, respectively, of the displacement amplitudes at the various positions of the beam.     

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.     

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.      

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.     

Mode II fracture-parameter estimates for concrete from beam specimens

At the present time, work on determination of fracture parameters for concrete subjected solely to mode I deformation states has advanced to the point where standard methods of testing and data evaluation have been proposed. Thus, many researchers are now considering the dual problems of (1) determination of fracture parameters for mode II deformation and (2) the need for this information (or put another way—the possible application of this information). In fact, the physical testing arrangements for mode II testing with no influence of mode I are not obvious; compromises must be made which will lead to approximations—perhaps fairly gross—in the estimates of mode II fracture parameters. Herein are presented experimental and analytical results for fracture parameters for beams loaded in antisymmetric four-point bending with a single-edge starter notch located in a region of high-shear and low-bending moment. This study complements another, presented elsewhere, in which beams in three-point bending were used with notches located off center. From this study, which included tests on 18 beam specimens, the following conclusions are reached. The beams must be tested in strain control. Crack initiation started in mode II but quickly changed to a mixed mode (although finite-element calculations indicate mode I is dominant). The fracture energy associated with the onset of unstable crack propagation is much larger than normally obtained for mode I—this is thought to be due to extensive aggregate interlock forces not present in normal bending or direct tension tests. Probably this type of testing arrangement is not suitable for determination of mode II fracture parameters because propagation does not occur under mode II conditions.     

Wave characteristics in functionally graded piezoelectric hollow cylinders

Based on linear three-dimensional piezoelasticity, the Legendre orthogonal polynomial series expansion approach is used for determining the wave characteristics in hollow cylinders composed of the functionally graded piezoelectric materials (FGPM) with open circuit. The displacement and electric potential components, expanded in a series of Legendre polynomials, are introduced into the governing equations along with position-dependent material constants so that the solution of the wave equation is reduced to an eigenvalue problem. Dispersion curves for FGPM and the corresponding non-piezoelectric hollow cylinders are calculated to show the piezoelectric effect. The influence of the ratio of radius to thickness is discussed. Electric potential and displacement distributions are used to show the piezoelectric effect on the flexural torsional mode. The influence of the polarizing direction on the piezoelectric effect is illustrated. For the radial and axial polarization, the piezoelectric effect reacts mostly on the longitudinal mode. For circumferential polarization, the piezoelectric effect reacts mostly on the torsional mode. In the FGPM hollow cylinder, piezoelectricity can weaken the guided wave dispersion.     

Discriminating linear from nonlinear elastic damage using a nonlinear time reversal DORT method

The DORT method is a selective detection and focusing technique originally developed to detect defects and damages which induce linear changes of the elastic moduli. It is based on the time reversal (TR) where a signal collected from an array of transducers is time reversed and then back-propagated into the medium to obtain focusing on selected targets. TR is based on the principle of spatial reciprocity. Attenuation, dispersion, multiple scattering, mode conversion, etc. do not break spatial reciprocity. The presence of defects or damage, may cause materials to show nonlinear elastic wave propagation behavior that will break spacial reciprocity. Therefore the DORT method will not allow focusing on nonlinear elastic scatterers. This paper presents a new method for the detection and identification of multiple linear and nonlinear scatterers by combining nonlinear elastic wave spectroscopy, time reversal and DORT method. In the presence of nonlinear hysteretic elastic scatterers, forcing the solid with a harmonic excitation, the time reversal operator can be obtained not only at the fundamental frequency of excitation, but also at the odd harmonics. At the fundamental harmonic, either inhomogeneities and linear damages can be individually selected but only at odd harmonics nonlinear hysteretic elastic damages exist. A procedure was developed where by decomposing the operator at the odd harmonics, it was possible to focus on nonlinear scatterers and to differentiate them from the linear inhomogeneities. A complete mathematical nonlinear DORT formulation for 1 and 2D structures is presented. To model the presence of nonlinear elastic hysteretic scatterers a Preisach–Mayergoyz (PM) material constitutive model was used. Results relative to 1 and 2 dimensional structures are reported showing the capability of the method to focus and discern selectively linear and nonlinear scatterers. Furthermore, an analysis was conducted to study the influence of the number of sources and their location on the imaging process showing that using a higher numbers of sensors does not automatically bring to a minor uncoupled behaviour between the nonlinear targets.     

ANALYSIS ON IMPACT RESPONSES OF UNRESTRAINED PLANAR FRAME STRUCTURE(Ⅱ)-NUMERICAL EXAMPLE ANALYSIS

By using the formula derived in Part (Ⅰ), the instant response of an unrestrained planar frame structure subjected to the impact of a moving rigid-body are evaluated and analysed.The impact force-time history between the structure and the moving rigid-body, shear force and bending moment distribution along the beams, axial force distribution along the bars were calculated. The wave propagation phenomena of the longitudinal wave in the bars, the flexural and shear waves in the beams were also analysed. The numerical results show that the time duration of impact force is controlled by the flexural wave and the longitudinal wave; the shear effect in beams should not be neglected in the impact response analysis of structures.     

ANALYSIS ON IMPACT RESPONSES OF UNRESTRAINED PLANAR FRAME STRUCTURE(Ⅱ)—NUMERICAL EXAMPLE ANALYSIS

By using the formula derived in Part （ Ⅰ ）, the instant response of an unrestrained planar frame structure subjected to the impact of a moving rigid-body are evaluated and analysed. The impact force-time history between the structure and the moving rigid-body, shear force and bending moment distribution along the beams, axial force distribution along the bars were calculated. The wave propagation phenomena of the longitudinal wave in the bars, the flexural and shear waves in the beams were also analysed. The numerical results show that the time duration of impact force is controlled by the flexural wave and the longitudinal wave ; the shear effect in beams should not be neglected in the impact response analysis of structures.     

利用兰姆波对板状结构中隐蔽腐蚀缺陷的检测

在石油、天然气、化工和石化行业中,许多大型容器和储罐常用来储存带有腐蚀性液体或气体,其内壁极易被腐蚀变薄而影响其使用寿命。为了激励出合适的导波模态检测容器内壁的隐蔽腐蚀缺陷,本文对一块2.76mm厚并蚀刻了一个人工腐蚀缺陷的钢板进行了检测。实验中,采用了一发一收法,并分别激励了对称模态S1和反对称模态A1对该缺陷进行了检测。利用短时傅立叶变换对接收到的时域信号进行了时频分析,得到各导波模态的模态转换,频散和衰减结果。通过对比可以看出,S1模态更适用于检测隐蔽腐蚀缺陷。结果显示,通过选取合适的模态,导波检测方法有可能用于大型容器和储罐内壁腐蚀缺陷的检测。     

一种基于深度学习的超声导波缺陷重构方法

超声导波检测因其传播效率高、耗能少等优势成为了无损检测领域的重要研究方向.目前已有的利用超声导波进行结构缺陷探测和定量化重构的方法主要由相关的导波散射理论推导得出.然而,由于导波散射问题本身的高复杂性,使得在推导上述理论方法时引入一些近似假设,降低了重构结果的质量.另外,有些方法通过优化迭代的方式提高重构精度,又会增加...