基于裂纹诱导弦挠度的简支外伸梁裂纹损伤识别

基于梁横向开裂纹的线性扭转弹簧模型,给出了具有任意裂纹数目的简支外伸梁弯曲挠度的显式解析解,研究了集中载荷作用下简支外伸梁裂纹诱导弦挠度函数的性质,给出了裂纹位置和裂纹等效扭转弹簧柔度的近似表达式,从而实现了梁横向裂纹位置及裂纹损伤程度的识别．在此基础上,为利用裂纹梁的测量挠度识别裂纹损伤,提出了分段线性函数的最佳拟合法,实现了简支外伸梁裂纹的损伤参数识别．通过数值试验验证了该识别方法的适用性和可靠性,考察了识别结果对梁挠度测量误差和裂纹深度的敏感性,结果表明随着挠度测量误差的增大,裂纹损伤参数识别误差增大,但裂纹损伤识别方法具有较强的鲁棒性,在工程实际中具有一定的应用性．     

Étude du comportement d'une fissure humide soumise à une élévation de température

We have been interested in the role of water inside a material crack, during heating. We have established an original analytical solution giving, the liquid–vapour repartition in the crack and the crack tip stress intensity factor, as functions of crack's length, water molecules contained in the inner of the crack and temperature. Then, we are able to study the crack stability.     

On irregularity-based damage detection method for cracked beams

A new damage detection technique using irregularity profile of a structural mode shape is proposed in this paper. The mode-shape of a cracked beam is first obtained analytically by using a general function. Its irregularity profile is then extracted from the mode shape by a numerical filter. The location and size of the crack in the beam can be determined by the peak value appearing on the irregularity profile. Two types of numerical filters, i.e., triangular and Gaussian, are examined. It has been found that the former filter is more effective in damage detection than the latter one. Numerical simulations suggest that the irregularity-based method requires a relatively low measurement resolution. Noise stress tests are carried out to demonstrate the effectiveness and robustness of this method under the influence of noise. As a validation, the proposed method is applied to detect crack damage in an E-glass/epoxy laminated composite beam. The successful detection of the crack in the composite beam demonstrates that the irregularity-based method is capable of assessing both the location and size of the crack and can be used efficiently and effectively in damage identification and health monitoring of beam-type structures.     

Identification of multiple open and fatigue cracks in beam-like structures using wavelets on deflection signals

A novel method for damage detection of multi-cracked beam-like structures by analyzing the static deflection is presented. The damage incurred produces a change in the stiffness of the beam. This causes a localized singularity which can be identified by a wavelet analysis of the displacement response. The existence and location of the cracks can be revealed by positions of the peaks in the continuous wavelet transform (CWT). To achieve this, the static profile of beams is analyzed with Gauss2 wavelet to identify the cracks. Beams under some ideal boundary and prescribed load conditions are considered. The deflected shape of the beam with open and fatigue cracks has been simulated under static loading using lumped crack models adopted from fracture mechanics and involving various degrees of complexity. The deflection of cracked beam in closed form for several cases of loads, crack sizes, and crack locations is calculated, and an explicit expression for the damage index (DI), based on CWT, is developed; it is demonstrated that the proposed damage index does not depend on mechanical properties of a homogeneous beam, and that the DI of one crack does not depend on the size and location of other cracks in a multiple cracked beam. Hence, the obtained expression for the DI can be used to find the size of each crack independently. Numerical results show that the method can detect cracks of small depth and is also applicable under the presence of measurement noise.     

基于裂纹附加模态Timoshenko梁的裂纹损伤识别

将梁中横向裂纹等效为无质量扭转弹簧，并忽略其对梁剪切变形的影响，得到的具有任意裂纹数目Timoshenko 梁自振模态的统一显示解析表达式．将裂纹梁的自振模态分为基本模态和裂纹附加模态，利用最小二乘拟合，建立了利用裂纹附加模态函数的梁裂纹损伤识别方法．通过数值模拟开展了简支单裂纹梁以及悬臂和固支双裂纹梁等的裂纹损伤识别，考察了测量误差对损伤识别的影响，数值结果表明本文所提出的裂纹损伤识别方法对裂纹位置的识别精度高于对裂纹损伤程度的识别精度；随着测量误差的增加，裂纹位置及裂纹损伤程度的识别误差增加，但仍在可接受的范围内，故该裂纹损伤识别方法在实际工程中具有一定的应用价值．     

悬臂梁中开闭裂纹的损伤识别

利用裂纹诱导弦挠度函数,建立了悬臂Euler-Bernoulli中开闭裂纹位置、深度、初始张开角等损伤参数的识别方法.为此,首先将梁中开闭裂纹等效为单向扭转弹簧,给出了考虑裂纹缝隙效应的裂纹梁等效抗弯刚度,并得到悬臂Euler-Bernoulli开闭裂纹梁弯曲挠度的显式闭合解及裂纹诱导弦挠度函数,证明了裂纹诱导弦挠度的...     

Experiments on crack identification in cantilever beams

In this paper we present an experimental investigation of the identification of crack location and size. By providing the first three natural frequencies through vibration measurements, curves of crack equivalent stiffness versus crack location are plotted, and the intersection of the three curves predicts the crack location and size. In the experiments, the cracked specimens were made using a wire-cut electrical discharge machine, and the cantilever beams were excited next to the free end by means of an impulse force hammer. In order to obtain the accurate natural frequencies from the transient signal measured, the method of zoom fast Fourier transform is adopted to improve frequency resolution. From experimental results, it is observed that the identification errors of crack location and size are less than 2% and 4%, respectively. The effectiveness of crack identification through vibration measurements is verified.     

Crack identification in beams using wavelet analysis

In this paper a simple method for crack identification in beam structures based on wavelet analysis is presented. The fundamental vibration mode of a cracked cantilever beam is analyzed using continuous wavelet transform and both the location and size of the crack are estimated. The position of the crack is located by the sudden change in the spatial variation of the transformed response. To estimate the size of the crack, an intensity factor is defined which relates the size of the crack to the coefficients of the wavelet transform. An intensity factor law is established which allows accurate prediction of crack size. The viability of the proposed method is investigated both analytically and experimentally in case of a cantilever beam containing a transverse surface crack. In the light of the results obtained, the advantages and limitations of the proposed method as well as suggestions for future work are presented and discussed.     

基于裂纹诱导弦挠度的梁开闭裂纹损伤识别

考虑裂纹缝隙效应,建立了Euler-Bernoulli梁中开闭裂纹位置、深度和初始张开角等损伤参数的识别方法．首先,基于梁中开闭裂纹的等效单向扭转弹簧模型,给出了开闭裂纹Euler-Bernoulli梁静力弯曲挠度的显式闭合解．在此基础上,证明了裂纹诱导弦挠度函数由分段三次多项式组成,并基于其构造特征,建立了基于测量挠度的梁中开闭裂纹位置、裂纹等效扭转弹簧柔度、裂纹初始张开角和裂纹上下侧属性等参数的数值识别方法．最后,通过数值实验考察了挠度测量误差和裂纹位置等对裂纹识别结果的影响,结果表明：裂纹位置、裂纹等效扭转弹簧柔度和裂纹初始张开角等的识别误差随挠度测量误差增大而增大,但裂纹识别结果具有较强的鲁棒性,在工程实际中具有一定的应用前景．     

小波分析在悬臂梁裂纹识别中的应用

基于空间信号的小波分析理论,将含裂纹悬臂梁前四阶振型信息直接用于小波变换,小波系数在空间域上的突变反映了裂纹的存在并指出了裂纹的位置.本文分析了前四阶振型对小波识别结果的敏感性,利用小波系数模极大值在尺度上的表现与Lipschitz指数之闻的关系建立了集中因子和裂纹深度之间的关系,以此来估计裂纹深度.鉴于实测信号往往是含噪声信号,分析了噪声对识别结果的影响规律.数值算例表明利用sym4小波对含裂纹梁的四阶振型信息进行小波分析可以准确地识别出裂纹的位置和深度;高阶振型对结构损伤较为敏感,高阶振型更适合于微裂纹和含噪声信息的处理,但高阶振型的非线性也会给裂纹识别带来一定的困难.使用本文方法进行结构裂纹参数识别,噪声对裂纹位置的影响只是指示清晰度的影响,基本不会产生错误的识别,而对裂纹深度的影响远比对位置的影响复杂,由于小波系数混入了噪声成分,从而增加了集中因子的取值,致使识别结果总是比真实结果偏大.     

基于等效弹簧模型的裂纹Euler-Bernoulli梁弯曲变形分析

考虑裂纹的缝隙效应,研究了开闭裂纹Euler-Bernoulli梁的弯曲变形．首先,将裂纹等效为内部旋转弹簧,利用广义函数,给出了考虑裂纹缝隙影响的Euler-Bernoulli梁的等效抗弯刚度,推导了具有任意数目开闭裂纹梁弯曲变形的显式通解．在此基础上,研究了均布载荷作用下上侧单裂纹简支梁以及裂纹处承受集中力和集中力偶共同作用的固支梁的弯曲变形,分析了梁长细比、裂纹深度和位置以及载荷等对裂纹开闭状态和梁弯曲变形的影响。结果表明：梁挠度分布在裂纹处存在尖点,而转角分布存在跳跃;梁挠度与载荷的响应关系一般为双折线形式,分别对应于裂纹的张开和闭合状态;且裂纹张开时,裂纹梁的柔度随着梁长细比的增加和裂纹深度的减小而减小。这些结果对梁裂纹无损检测具有指导意义．     

基于模态数据的长细结构小损伤精确识别研究

本文针对现有的损伤识别方法不能满足部分结构损伤识别精度要求的现状,对结构的小损伤精确识别方法开展研究．以长细结构为研究对象,对具有不同损伤位置和损伤程度的圆柱形的轻阻尼梁结构进行了数值分析和实验研究,应用数值计算方法和实验确定的特征向量和特征频率对长细结构裂缝参数进行识别计算．本文在研究过程中编制了一个创新性的预测程序,通过其一次性生成目标函数图来选择合适的初始参数,从而对识别结果进行分析．研究结果表明,应用本文提出的识别方法,裂缝位置的识别误差可以控制在0.05 %~0.28 %范围内,裂缝深度识别误差低于7 %．     

An Experimental Investigation of Condition Monitoring for Notched Rotors Through Transient Signals and Wavelet Transform

Experimental studies considering the dynamic transient signals of a notched rotor (i.e. a rotor with a transverse open crack) are investigated in order to examine the possibility of detecting the presence of open cracks in rotating machinery for low or high rotor accelerations. Firstly, the orbital patterns, spectrum cascade plots of the Power Spectral Density, evolutions of the 2× amplitudes of rotor with and without an open transverse crack are compared and discussed in the case of low accelerations of the rotor system. Secondly, the non-stationary vibration signals of the rotor with an open transverse crack at high accelerations are investigated. The timefrequency features and a tool based on the Continuous Wavelet Transform (CWT) to detect open cracks in a rotor system are discussed. It is demonstrated that both the Continuous Wavelet Transform (CWT) and changes on the 2× harmonic components are robust indicators for crack detection.     

辅助质量块—单裂纹悬臂梁耦合系统固有频率的理论研究及其应用

论文研究了辅助质量块—单裂纹悬臂梁耦合系统的固有频率,用无缺陷悬臂梁固有振型叠加一个多项式来近似拟合含单裂纹悬臂梁的振型,由动力学方法推导了辅助质量块—单裂纹悬臂梁系统的固有频率方程的解析形式,系统频率随着质量块在梁上位置改变而改变,即可得到固有频率曲线,此频率曲线包含了缺陷信息,因此可对固有频率曲线进行平稳小波变换来识别梁上的缺陷.同时用有限元计算结果对上述固有频率理论推导进行验证,有限元结果与论文理论推导结果相一致.最后论文数值计算了质量块大小、缺陷深度、位置等因素对系统固有频率的影响,也探讨了平稳小波变换用于识别损伤,结果验证了该理论推导的可靠性和损伤识别的准确性.     

Flexural model for a notched beam: Direct and inverse problems

Matching conditions simulating a transverse notch in a beam are proposed. These conditions are used to determine the location and size of the notch. The notch is identified from beam deflections at several points in the static case and from the first eigenfrequencies of the beam in the dynamic case. Dependences of the first eigenfrequencies on the characteristic parameters of the problem are obtained. The effect of the relative error of frequency measurements on the relative error of calculation of the notch parameters is studied. It is shown that the use of the first eigenfrequencies of flexural vibrations of the beam with respect to different axis provides a more accurate identification than the use of eigenfrequencies of flexural vibrations relative to one axis. Since local defects such as hollows, local corrosion, and an open crack can be simulated by a notch, the results can also be used to identify these defects.     

Dynamic instability and steady-state response of an elliptical cracked shaft

An elliptical front crack has been found to be more accurate and realistic for modeling the transverse surface crack in rotating machinery compared with the widely used straight front crack. When the shaft rotates, the elliptical crack opens and closes alternatively, due to gravity, and thus, a “breathing effect” occurs. This variance in shaft stiffness is time-periodic, and hence, a parametrically excited system is expected. Therefore, the dynamic instability and steady-state response of a rotating shaft containing an elliptical front crack are studied in the paper. The local flexibility due to the crack is derived, and the governing equations of the crack shaft system are established using the assumed modes method. Utilizing the Bolotin’s method and harmonic balance method, the boundaries of two typical instability regions and maximum response amplitude of the cracked shaft could be computed numerically. The elliptical crack parameters (depth, shape factor and position) and damping are, respectively, considered and discussed for their effects on the dynamic behavior of the elliptical cracked shaft. Some research results might be helpful for the crack detection in rotating machinery.     

Static fracture testing of PMMA plates having flawed fastener holes

Results of static fracture tests on PMMA plates with part-elliptical cracks at fastener holes are presented. Experimental configurations include three crack locations with respect to both open and loaded holes. During static testing, slow growth prior to specimen separation allows for calculation of the maximum stress-intensity factor and identification of the location on the crack border at which it occurs. The testing techniques developed produce a simple, economical means of experimentally validating theoretical analyses of crack problems.     

Waveform fractal dimension for mode shape-based damage identification of beam-type structures

Mode shape-based structural damage identification has been a research focus during the last couple of decades. Most of the existing methods need a numerical or measured baseline mode shape serving as a reference to identify damage, and this requirement extremely limits the practicability of the methods. Recently, waveform fractal dimension such as Katz’s waveform fractal dimension (KWD) has been explored and applied to mode shape for crack identification without a baseline requirement. In this study, different from the popular KWD, an approximate waveform capacity dimension (AWCD) is formulated first, from which an AWCD-based modal abnormality algorithm (AWCD-MAA) is systematically established. Then, the basic characteristics of AWCD-MAA on abnormality detection of mode shapes, e.g., crack localization, crack quantification, noise immunity, etc., are investigated based on an analytical crack model of cantilever beams using linear elastic fracture mechanics. In particular, from the perspective of isomorphism, a mathematical solution on the use of applying waveform fractal dimension to higher mode shapes for crack identification is originally proposed, from which the inherent deficiency of waveform fractal dimension to identify crack when implemented to higher mode shapes is overcome. The applicability and effectiveness of the AWCD-MAA is validated by an experimental program on damage identification of a cracked composite cantilever beam using smart piezoelectric sensors/actuators (i.e., Piezoelectric lead–zirconate–titanate (PZT) and polyvinylidene fluoride (PVDF)). The proposed AWCD-MAA provides a novel, viable method for crack identification of beam-type structures without baseline requirement, and it largely expands the scope of fractal in structural health monitoring applications.     

Detection of a slant crack in a rotor bearing system during shut-down

Abstract

The transient response of a slant-cracked rotor system during shut-down has been analyzed while it is decelerating through the critical speed. Vibration response has been simulated by using finite element method (FEM) for flexural vibrations. An unbalance force and a harmonically-varying torque is applied on the rotor system. Subharmonic frequency components at an interval frequency corresponding to torsional frequency were found in the frequency domain (Fast Fourier Transform (FFT) plot). These peaks are centered on the critical speed of the rotor system when a slant crack is present and can be used to detect the crack. The fundamental mode shapes of the rotor bearing systems are wavelet transformed to identify the crack location. A peak is observed at the crack location in the spatial variation of the wavelet-transformed fundamental mode shape. A few suggestions for the detection of slant cracks in the rotor during shut-down are described.     

Monitoring structural damage of components using an effective modulus approach

This paper describes a novel nondestructive damage detection method that was developed to study the influence of a crack on the dynamic properties of a cantilever beam subjected to bending. Experimental measurements of transfer functions for the cracked cantilever beam revealed a change in the natural frequency with increasing crack length. A finite element model of a cracked element was created to compute the influence of severity and location of damage on the structural stiffness. The proposed model is based on the response of the cracked beam element under a static load. The change in beam deflection as a result of the crack is used to calculate the reduction in the global component stiffness. The reduction of the beam stiffness is then used to determine its dynamic response employing a modal analysis computational model. Euler–Bernoulli and Timoshenko beam theories are used to quantify the elastic stiffness matrix of a finite element. The transfer functions from both theories compare well with the experimental results. The experimental and computational natural frequencies decreased with increasing crack length. Furthermore the Euler–Bernoulli and Timoshenko beam theories resulted in approximately the same decrease in the natural frequency with increasing crack length as experimentally measured.