阶梯悬臂梁的双裂纹参数两步识别法

以等效弹簧模拟裂纹引起的局部软化效应,应用Bernoulli-Euler梁理论建立双裂纹阶梯悬臂梁的振动特征方程.鉴于方程含有较多的未知量,提出联合小波变换和结构测量频率的裂纹参数识别两步法.首先,含裂纹悬臂梁的一阶模态作为信号用于连续小波变换,通过小波系数的局部极值可以清楚地确定结构的裂纹位置.其次,将识别得到的裂纹位置代入双裂纹阶梯悬臂梁的特征方程,最后通过绘制两个裂纹的等效柔度的等值线图,通过交点确定满足特征方程的两个裂纹的等效柔度,并进一步确定裂纹深度.最后利用数值算例验证该方法的有效性.     

悬臂梁裂纹参数的识别方法

以梁振动理论作为基础 ,将含裂纹梁的振动问题转化为由弹性铰联接两个弹性梁系统的振动问题 ,得到理论计算含裂纹梁振动频率的特征方程。由此特征方程计算得到裂纹深度参数和位置参数变化时悬臂梁振动固有频率的变化规律。利用计算裂纹悬臂梁振动固有频率的特征方程 ,提出一种辩识裂纹深度和位置参数的数值计算方法。并通过对模拟悬臂梁裂纹的分析说明文中方法的有效性。     

悬壁梁裂纹参数的识别方法

以梁振动理论作为基础，将含裂纹梁的振动问题转化为由弹性铰联接两个弹性梁系统的振动问题，得到理论计算含裂纹梁振动频率的特征方程。由此特征方程计算得到裂纺深工参数和位置参数变化时悬臂梁振动固有频率的变化规律。利用计算裂纹悬臂梁振动固有频率的特征方程，提出一种辩识裂纹深度和位置参数的数值计算方法。并通过对模拟悬臂梁裂纹的分析说明文中方法的有效性。     

裂纹悬臂梁的扭转弹簧模型及其实验验证

将含裂纹悬臂梁转化为由扭转弹簧联接两段弹性梁构成的连接体,得到理论计算含裂纹梁振动频率的特征方程。确立了求解裂纹梁固有频率的数值计算流程．计算得到了裂纹深度和位置变化时裂纹悬臂梁振动固有频率的变化规律。进行了裂纹悬臂梁的弯曲振动台架实验,验证了本文提出的扭转弹簧模型及固有频率数值计算方法的有效性。     

梁结构裂纹参数的识别方法

以Bernoulli-Euler梁振动理论为基础,引入断裂力学中能量释放率的概念,得到承弯梁出现横向裂纹时其固有频率的变化与裂纹参数的简化表达式,讨论梁裂纹参数、几何参数对固有频率的影响。利用这一表达式,提出一种识别裂纹位置和深度的数值方法,最后,用含裂纹等截面悬臂梁的实验验证所提方法。结果表明,在固有频率误差较小的情况下,文中方法可给出梁结构中裂纹位置和深度,可为更精确的局部探伤指出探测范围。     

基于小波分析的悬臂梁裂纹参数识别方法研究

通过对含裂纹悬臂梁的应变能信号进行小波分析,悬臂梁的裂纹位置可由小波系数的局部极大值给出,并通过小波系数局部极大值定义集中因子和裂纹深度之间的关系,以此估计裂纹深度.数值算例表明, 利用sym4小波对含裂纹梁的应变能信号进行小波分析,可以准确识别出裂纹的位置和深度,这一方法很容易推广应用到结构的在线监测中.     

多裂纹梁不确定性损伤识别和实验研究

对于多裂纹梁识别过程中的测试数据的不确定性问题,基于传递矩阵法推导了悬臂裂纹梁的频率特征方程,构建损伤参数(损伤位置和损伤深度)和动态特征参量(频率和模态)的映射关系。基于贝叶斯推断理论建立了损伤参数识别的贝叶斯模型,选择均匀分布作为损伤参数的先验分布,以悬臂裂纹梁固有频率和模态振型的测试值作为样本信息,建立损伤参数的后验概率分布。采用马尔科夫链蒙特卡洛模拟方法来解决贝叶斯方程中存在的高维积分的问题,通过仿真算例分析和实验研究,实现了对多裂纹梁损伤参数的有效识别。     

简支梁中裂纹参数的识别

结构中的裂纹对系统振动特性将产生一定的影响 ,一般来讲 ,裂纹参数与振动特性的改变之间很难有直接的函数关系 ,通过振动参数的改变来识别裂纹有一定的困难 ,本文经过计算证明 :对于受弯的两端简支梁 ,当裂纹较小时 ,梁的自振频率的变化率与裂纹参数之间存在明确的函数关系 ,利用这一函数关系 ,梁中的裂纹深度与裂纹位置可由自振频率的变化率计算得出。同时证明 :对于简支梁而言 ,单纯利用自振频率无法唯一地确定裂纹位置 ,只能唯一地确定裂纹的深度     

含任意数目裂纹梁的振动分析

基于递推方法研究多种边界条件下含任意数目裂纹梁的振动分析。将梁的裂纹模拟为无质量的等效扭转弹簧。通过递推方法可以把裂纹梁的特征微分方程转换成递归代数公式,然后利用边界条件和裂纹位置的连续性条件推导可以得到该裂纹梁的无量纲固有频率以及相应的振形函数解析表达式。通过与参考文献中的计算结果相比较,验证了方法的正确性和有效性。文中还给出了具体的算例,计算出了简支梁的模态振型,并分别讨论了裂纹的数量和深度对于固有频率的影响。     

传动轴结构损伤识别的数值模拟试验

在带有裂纹的轴结构件中,当裂纹较小时,传动轴的裂纹参数与其固有频率的变化率相关联。通过对由固有频率的变化率确定轴结构件裂纹参数的理论分析和通过截取频率变化率趋势图的等高线并取其交点来反推出裂纹的位置和深度的方法,可识别其裂纹位置和深度。文中给出了有关计算公式,并进行了数值模拟。从模拟结果看,这种方法可以很好地识别传动轴的损伤程度,从而为轴结构件的改进设计及含裂纹的轴结构件剩余寿命的估算提供了理论依据。     

基于固有频率的悬臂梁裂缝识别

结构中裂缝的存在使其模态参数发生改变 ,如局部刚度减小、阻尼增大、固有频率降低。把裂缝梁模拟成由扭曲弹簧连接 ,并对其前三阶固有频率的变化与裂缝位置和深度之间的关系进行计算和分析 ;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。识别结果证明 ,这种方法精度较高、简单可行 ,可用于机械工程实时监测。     

Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions

An analytical approach for crack identification procedure in uniform beams with an open edge crack, based on bending vibration measurements, is developed in this research. The cracked beam is modeled as two segments connected by a rotational mass-less linear elastic spring with sectional flexibility, and each segment of the continuous beam is assumed to obey Timoshenko beam theory. The method is based on the assumption that the equivalent spring stiffness does not depend on the frequency of vibration, and may be obtained from fracture mechanics. Six various boundary conditions (i.e., simply supported, simple–clamped, clamped–clamped, simple–free shear, clamped–free shear, and cantilever beam) are considered in this research. Considering appropriate compatibility requirements at the cracked section and the corresponding boundary conditions, closed-form expressions for the characteristic equation of each of the six cracked beams are reached. The results provide simple expressions for the characteristic equations, which are functions of circular natural frequencies, crack location, and crack depth. Methods for solving forward solutions (i.e., determination of natural frequencies of beams knowing the crack parameters) are discussed and verified through a large number of finite-element analyses. By knowing the natural frequencies in bending vibrations, it is possible to study the inverse problem in which the crack location and the sectional flexibility may be determined using the characteristic equation. The crack depth is then computed using the relationship between the sectional flexibility and the crack depth. The proposed analytical method is also validated using numerical studies on cracked beam examples with different boundary conditions. There is quite encouraging agreement between the results of the present study and those numerically obtained by the finite-element method.     

Four-beam model for vibration analysis of a cantilever beam with an embedded horizontal crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton's principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.     

Frequency error based identification of cracks in beam-like structures

A crack identification method of a single edge cracked beam-like structure by the use of a frequency error function is presented in this paper. First, the dynamic theory of Euler-Bernoulli beams was employed to derive the equation of the natural frequency for a single edge cracked cantilever beam-like structure. Subsequently, the cracked section of the beam was simulated by a torsional spring. The flexibility model of the torsional spring due to the crack was estimated by fracture mechanics and energy theory. Thereafter, a function model was proposed for crack identification by using the error between the measured natural frequencies and the predicted natural frequencies. In this manner, the crack depth and crack position can be determined when the total error reaches a minimum value. Finally, the accuracy of the natural frequency equation and the viabilty of the crack identification method were verified in the case studies by the measured natural frequencies from the literature. Results indicate that the first two predicted natural frequencies are in good agreement with the measured ones. However, the third predicted natural frequency is smaller than the measured natural frequency. In the case of small measured frequency errors, the predicted crack parameters are in good agreement with the measured crack parameters. However, in the case of large measured frequency errors, the predicted crack parameters only give roughly estimated results.     

Crack identification in a cantilever beam under uncertain end conditions

Crack identification in structures by changes of their dynamic behavior has been studied in the past, and various methods were developed enabling the calculation of crack location along a beam, by using the variations in the natural frequencies between the initial undamaged state and a later, cracked beam. Application of this procedure to cantilever beams may result in unacceptably large errors, due to changes in clamp rigidity between measurements in the two states. The present research studies the problem of crack identification in a cantilever when clamp rigidity is unknown, and may change with time. An identification method is developed, which requires monitoring of three natural bending frequencies. Crack location may then be found by using a universal curve, i.e. independent of any beam property (geometry or material). The proposed method was verified by numerical simulation and experiment.     

Crack detection in beams using experimental modal data and finite element model

In this paper, an analytical, as well as experimental approach to the crack detection in cantilever beams by vibration analysis is established. An experimental setup is designed in which a cracked cantilever beam is excited by a hammer and the response is obtained using an accelerometer attached to the beam. To avoid non-linearity, it is assumed that the crack is always open. To identify the crack, contours of the normalized frequency in terms of the normalized crack depth and location are plotted. The intersection of contours with the constant modal natural frequency planes is used to relate the crack location and depth. A minimization approach is employed for identifying the cracked element within the cantilever beam. The proposed method is based on measured frequencies and mode shapes of the beam.     

Three-steps-meshing based multiple crack identification for structures and its experimental studies

Multiple crack identification plays an important role in vibration-based crack identification of structures. Traditional crack detection method of single crack is difficult to be used in multiple crack diagnosis. A three-step-meshing method for the multiple cracks identification in structures is presented. Firstly, the changes in natural frequency of a structure with various crack locations and depth are accurately obtained by means of wavelet finite element method, and then the damage coefficient method is used to determine the number and the region of cracks. Secondly, different regions in the cracked structure are divided into meshes with different scales, and then the small unit containing cracks in the damaged area is gradually located by iterative computation. Lastly, by finding the points of intersection of three frequency contour lines in the small unit, the crack location and depth are identified. In order to verify the effectiveness of the presented method, a multiple cracks identification experiment is carried out. The diagnostic tests on a cantilever beam under two working conditions show the accuracy of the proposed method: with a maximum error of crack location identification 2.7% and of depth identification 5.2%. The method is able to detect multiple crack of beam with less subdivision and higher precision, and can be developed as a multiple crack detection approach for complicated structures.     

梁结构边界条件识别的行波法

基于Euler-Bernoulli梁模型，研究了梁结构的波动动力学方程以及结点散射关系，在此基础上提出了行波法识别梁结构边界条件的新方法。以系统固有频率值为已知量，从行波观点出发，建立起系统的特征方程，由特征方程反解识别得到结构的边界参数。通过对附加弹性支撑的悬臂梁进行振动实验，利用所测的低阶固有频率值，辨识出边界的横向和扭转刚度。实验结果表明，该方法具有良好的识别精度，是一种极有潜力的参数辨识方法。