基于小波有限元的悬臂梁裂纹识别

研究了悬臂梁裂纹识别中的正反问题．即通过裂纹位置和尺寸求解梁的固有频率以及利用梁的固有频率．识别裂纹位置和尺寸。以矩形截面裂纹悬臂梁为例，利用小波有限元方法建立了梁自由振动的有限元模型．其中裂纹被看作为一刚度已知的扭转线弹簧，求解出了系统的固有频率；通过行列式变换，将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题，分别做出了以不同固有频率作为输入值时裂纹位置与弹簧刚度之间的解曲线，曲线交点预测出裂纹的位置与尺寸。数值算例证实了算法的有效性，为工程结构裂纹故障预示与诊断提供了新的方法。     

不同温度下裂纹悬臂梁的模态和疲劳寿命分析

基于扭转弹簧模型和修正Paris公式,提出了一种在不同外界温度下含初始裂纹悬臂梁的疲劳寿命估算方法。在模态分析过程中,通过弹性模量引入温度模块,利用扭转弹簧等效该裂纹,将悬臂梁转化为由扭转弹簧联接的两段弹性梁;推导出不同温度下含裂纹梁固有振型的特征方程,分析温度和裂纹几何参数对裂纹梁固有频率的影响。在疲劳寿命分析过程中,利用复弹性模量引入阻尼损耗因子,基于修正Paris方程和同步分析法,考虑裂纹梁振动与疲劳裂纹扩展的相互作用,分析温度、阻尼和悬臂梁根部区域裂纹几何参数对裂纹梁疲劳寿命的影响。结果表明:随着裂纹相对位置的减小以及裂纹相对深度的增大,裂纹悬臂梁的固有频率和疲劳寿命则逐渐降低;而外界温度的升高也会导致裂纹悬臂梁固有频率和疲劳寿命的降低;同时随着阻尼损耗因子的逐渐增大,裂纹悬臂梁的疲劳寿命也会逐渐增加。     

悬臂梁裂纹参数识别方法研究

基于Bernoulli-Euler梁振动理论,以等效弹簧来模拟裂纹引起的局部软化效应,推导了含裂纹悬臂梁振动频率的特征方程,直接利用该特征方程,提出一种有效估计裂纹参数的优化方法,通过测量频率和分析频率误差,用目标函数最小化可识别裂纹参数-裂纹位置和裂纹深度.最后,应用含裂纹悬臂梁实验来说明本文方法的有效性.实验结果表明只需梁结构前三阶频率即可识别裂纹位置和深度.在测量频率存在较小误差情况下,该方法能给出比较准确的裂纹参数识别结果,在误差较大情况下,仍可为更精确的局部探测给出大致范围,此外,利用高阶频率来识别裂纹参数可能使该目标函数产生不规律的变化,甚至得到错误的识别结果.     

矩形梁裂纹柔度测量方法研究

为了描述裂纹引起的矩形梁结构损伤程度,提出了一种基于固有频率的裂纹柔度测量方法。首先通过动力学分析求解矩形梁的前3阶固有频率,建立对应于不同裂纹位置和裂纹柔度的固有频率数据库,并将其拟合为固有频率影响曲面。然后对矩形梁进行振动测试,利用获得的前3阶固有频率去截取固有频率影响曲面,绘制出前3阶频率影响曲线,基于3条频率影响曲线的交点可以得到裂纹柔度和裂纹位置。研究结果表明该方法可以有效地测量出裂纹柔度及对应的裂纹位置。从测量过程可以看出,求解固有频率数据库的输入参数是一系列包含裂纹位置和裂纹柔度的样本点,并没有涉及裂纹的类型、形状以及裂纹柔度的计算公式。因此,该方法适用于矩形梁中不同类型和形状裂纹的柔度测量,对于含裂纹的梁结构的动力学分析和损伤识别研究具有重要的参考意义。     

圆柱类金属构件表面裂纹的激光超声识别方法研究

为了利用激光超声技术有效地识别圆柱表面裂纹,提出利用圆柱表面波信号增强和小波包-奇异值分解(WPT-SVD)方法识别圆柱类金属构件表面裂纹的位置和深度。建立了圆柱的激光超声显式有限元模型,分析了圆柱表面裂纹对表面波的模式转化作用。利用圆柱表面裂纹在激发源位置附近时激光超声扫描信号增强的现象,识别圆柱表面裂纹的位置。在已识别圆柱表面裂纹位置的基础上,通过分析圆柱表面裂纹检测信号的时频特点,利用WPT-SVD提取圆柱表面信号的时频特征,定义参数k r表征裂纹深度的变化,识别圆柱表面裂纹深度。搭建了激光超声圆柱表面裂纹检测实验系统,开展了实验研究,实验结果表明所提出的圆柱表面信号增强和WPT-SVD方法可以识别出圆柱表面裂纹的位置和深度。     

基于小波有限元的悬臂梁裂纹遗传优化辨识

利用小波有限元法求解了裂纹悬臂梁的前三阶固有频率,并将其拟合成以裂纹位置和深度作为变量的频响函数曲面。将裂纹识别中的匹配追踪问题转化为多维优化问题,以实测固有频率作为输入,利用遗传算法寻优求解出与输入值相差最小的样本点,进而预测出裂纹的位置和深度。试验研究表明,所提出的裂纹识别方法具有较好的精度和鲁棒性,且易于推广到诸如转子、叶片等复杂结构的裂纹监测诊断场合。     

蒙皮裂纹点阵夹芯梁振动特性分析及裂纹识别

主要研究了含蒙皮呼吸裂纹金字塔型点阵夹芯梁的振动特性。基于夹芯结构折线理论,考虑呼吸效应引起的刚度周期性变化,推导出系统的动力学方程。分析裂纹深度和裂纹位置对裂纹夹芯梁固有频率的影响,运用频率响应曲线、波形图和相图研究了裂纹参数对夹芯梁强迫振动响应的影响。研究结果显示,超谐共振响应对裂纹参数的变化较为敏感,可以利用其相图的几何特征识别裂纹参数。     

裂缝悬臂梁的振动特性及其裂缝参数识别

结构中裂缝的存在使其局部刚度减小、阻尼增大、固有频率降低。本文利用扭曲弹簧模型，对裂缝悬臂梁前三阶固有频率的变化与裂缝位置和深度的关系进行了计算和分析，并且利用特征方程以及前三阶固有频率，通过作图法对裂缝参数进行识别。并以悬臂梁为例证明了这种识别方法精度较高，可以作为进一步研究无损诊断的理论基础。     

裂纹对空间框架固有频率影响的数值分析

利用有限元方法,对不同位置、不同深度和不同方位裂纹引起的空间框架结构固有频率改变进行了比较分析,将有限元分析得到的梁单元模态应变能力分解为拉压、扭转和弯曲模态应变能,并对结构固有频率改变量随裂纹位置变化的曲线与这些模态应变能分布曲线进行了对比分析。     

裂纹梁无效损伤位置的理论分析和实验研究

以两端固支裂纹梁为例,通过理论和实验方法探讨无效损伤位置。首先将梁的裂纹模拟为无质量的等效扭转弹簧,得到裂纹梁的特征方程,并求解特征方程解得固有频率。数值计算结果表明,某阶模态的无效损伤位置就是该阶模态固有频率与裂纹深度无关的位置,并且该位置出现裂纹时无法通过计算相应模态的曲率模态差来判断是否出现损伤。不同阶模态的无效损伤位置也会不同。随后用质量块模拟裂纹进行实验研究,利用移动质量块的方法模拟不同损伤位置得到的梁固有频率曲线,与健康梁固有频率对比,从而得到梁的无效损伤位置。最后将质量块放置在梁无效损伤位置上模拟裂纹,实验测得该梁的曲率模态,实验结果表明:当质量块布置在梁某阶无效损伤位置时,梁该阶固有频率几乎不发生变化,且相应模态的曲率模态差无法检测出损伤信息,与数值计算结果相符。     

Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 3. Analytical and numerical determination of natural frequencies of longitudinal and bending vibrations of beams with transverse cracks. Solution

Based on the concepts of linear fracture mechanics, we derive analytical expressions for the determinational of natural frequencies of longitudinal and bending vibrations of beams which are rectangular in cross section, are fixed in different ways, have variable ratios of the section height to the beam length, and have transverse cracks of various types. The results of the analytical solution are compared with those obtained by the finite-element method as well as with experimental data obtained by the authors and other scientists. The analytical solution under consideration is shown to be quite simple and provide a fairly good accuracy of the results obtained. Using a cantilever beam with one or two symmetrical edge cracks or a central through crack as an example, we consider the possible dependence of the relative change in natural frequencies of vibration on the relative crack length, crack location, and the vibration mode of a beam. We discuss the possible methods of evaluating the crack size and location from the results of experimental determination of the change in natural vibration frequencies of a cracked beam. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 19–31, July–August, 1999.     

简支梁裂纹位置识别的一种简单方法

由等效线弹簧来模拟裂纹引起的软化效应,基于铁摩辛柯梁理论得到含裂纹简支梁横向振动的频率计算式,由此获得识别裂纹位置的一种近似方法。文中利用梁的二维有限元模态分析数据进行裂纹位置的识别,结果表明该法在较宽的高跨比范围内,有好的效果;裂纹的深度对识别精度影响不大。     

典型损伤对复合材料机翼振动特性的影响

利用大型商用软件MSC.Patran建立了某型无人机复合材料机翼的有限元模型。在机翼中分别模拟了蒙皮分层、蒙皮与翼梁翼肋脱粘以及翼梁裂纹这3种典型损伤,通过与无损伤复合材料机翼固有振动频率进行比较,分析了损伤位置和大小对机翼振动特性的影响。结果表明:3种典型损伤一般不会引起机翼各阶振动模态的改变,但会使各阶振动频率发生变化;对各阶振动频率的影响既与损伤位置有关,也与主承力结构的损伤程度有关;蒙皮分层和翼梁裂纹出现在机翼根部时对机翼振动频率的影响最明显。     

Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam

This paper presents a detailed investigation on the modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam with hollow circular cross-section. To consider multiple crack effects, a cantilever beam including cracks is considered for six damage scenarios. Finite element models are constituted in ANSYS software for numerical solutions. The results are validated by experimental measurements. Ambient vibration tests are performed to extract the dynamic characteristics using Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) methods. Calculated and measured natural frequencies and mode shapes for undamaged and damaged beams are compared with each other. Automated model updating is carried out using the modal sensitivity method based on Bayesian parameter estimation to minimize the differences for damage detection. In addition, modal assurance criterion (MAC) and coordinated modal assurance criterion (COMAC) factors are obtained from the mode shapes and two set of measurements to establish the correlation between the measured and calculated values for damage location identification.     

基于神经网络的短粗转轴裂纹诊断研究

构造Rayleigh-Timoshenko区间B样条小波梁单元,建立短粗转子系统小波有限元模型。求解与不同裂纹相对位置和相对深度相对应的裂纹转子前三阶固有频率。将裂纹相对位置、相对深度、前三阶固有频率作为神经网络的训练样本,训练出用于裂纹定量诊断的神经网络。以实测固有频率作为训练好的神经网络的输入,定量诊断测出裂纹的相对位置和深度。试验研究表明,所提出的裂纹诊断方法具有较好的精度和鲁棒性,且易于在工程实践中进行短粗裂纹转子定量诊断。     

Detection of multiple cracks using frequency measurements

A method for detection of multiple open cracks in a slender Euler-Bernoulli beams is presented based on frequency measurements. The method is based on the approach given by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841], transverse vibration modelling through transfer matrix method and representation of a crack by rotational spring. The beam is virtually divided into a number of segments, which can be decided by the analyst, and each of them is considered to be associated with a damage parameter. The procedure gives a linear relationship explicitly between the changes in natural frequencies of the beam and the damage parameters. These parameters are determined from the knowledge of changes in the natural frequencies. After obtaining them, each is treated in turn to exactly pinpoint the crack location in the segment and determine its size. The forward, or natural frequency determination, problems are examined in the passing. The method is approximate, but it can handle segmented beams, any boundary conditions, intermediate spring or rigid supports, etc. It eliminates the need for any symbolic computation which is envisaged by Hu and Liang [J. Franklin Inst. 330 (5) (1993) 841] to obtain mode shapes of the corresponding uncracked beams. The proposed method gives a clear insight into the whole analysis. Case studies (numerical) are presented to demonstrate the method effectiveness for two simultaneous cracks of size 10% and more of section depth. The differences between the actual and predicted crack locations and sizes are less than 10% and 15% respectively. The numbers of segments into which the beam is virtually divided limits the maximum number of cracks that can be handled. The difference in the forward problem is less than 5%.     

Influence of Crack on Structure Vibration of Gear Tooth

This paper presents a theoretical model for analyzing the dynamic characteristic such as natural frequencies and vibration mode shapes of cracked gears. The influence of crack position and crack size on the dynamic characteristic of gears is thoroughly investigated using the proposed theoretical model as well as the finite element method (FEM) for the sake of model validation. The theoretical analysis and numerical simulation show that the influence of crack size and crack position on the dynamic responses of cracked gears is significant and that the influence of crack position is larger than that of crack size. The natural frequencies drop with the increase of crack size and the low order natural frequencies drop more notably. The natural frequencies drop more significantly when crack is located at tooth root than at tooth tip. The vibration mode shapes of cracked gear tooth are very different from those of gear tooth without crack, and the vibration amplitude increases significantly in crack neighborhood. These observations are very valuable for damage detection and fault diagnosis of gear system.