梁结构中裂纹参数识别方法研究

以等效弹簧模型来模拟裂纹引起的局部软化效应,将该模型同Bernoulli-Euler梁理论、模态分析方法以及断裂力学原理等结合起来,利用传递矩阵法导出含裂纹梁振动的各种边界条件下的特征方程通解。借助于特征方程,提出两种识别裂纹深度和位置参数的数值方法,最后,通过对含裂纹悬臂梁的分析说明文中方法的有效性。     

不确定边界条件下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和由非完全固支边界条件引起的转角效应。推导了悬臂梁在不确定边界条件下确定其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,通过计算测量频率和理论频率之间的误差目标函数最小化即可识别裂纹参数-裂纹位置和深度。最后,应用两个实例-理想固支边界条件下和非完全固支边界条件下的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。对于理想边界条件下的裂纹参数识别,在测量频率存在小误差情况下,该方法仍能给出比较满意的结果,对于非完全固支边界条件下的裂纹参数识别,利用本文方法能得到比Narkis的方法更精确的裂纹位置识别结果。同时本文方法还能给出比较满意的裂纹深度识别结果。     

CRACK IDENTIFICATION IN STEPPED CANTILEVER BEAM COMBINING WAVELET ANALYSIS WITH TRANSFORM MATRIX

This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.     

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 %．     

Longitudinal vibrations of a bar with incipient transverse cracks

The simplest model of longitudinal vibrations of a bar with incipient transverse cracks is considered under the essential assumption that the crack size is small compared with the bar cross-section area and the difference between the mode shapes of the bar with incipient cracks and the undamaged bar is small. The different manifestation of cracks in the phases of extension and compression strains is taken into account. The natural vibration frequencies and the crack coordinates and dimensions are determined from experimental values of natural frequencies.     

A NEW APPROACH TO FREE VIBRATION ANALYSIS OF A BEAM WITH A BREATHING CRACK BASED ON MECHANICAL ENERGY BALANCE METHOD

In this paper, a new approach to free vibration analysis of a cracked cantilever beam is proposed. By considering the effect of opening and closing the crack during the beam vibration, it is modeled as a fatigue crack. Also, local stiffness changes at the crack location are considered to be a nonlinear amplitude-dependent function and it is assumed that during one half a cycle, the frequencies and mode shapes of the beam vary continuously with time. In addition, by using the experimental tests, it is shown that the local stiffness at the crack location varies continuously between the two extreme values corresponding to the fully closed and the fully open cases of the crack. Then, by using the mechanical energy balance the dynamic response of the cracked beam is obtained at every time instant. The results show that for a specific crack depth, by approaching the crack location to the fixed end of the beam, more reduction in the fundamental frequency occurs. Furthermore, for a specific crack location, the fundamental frequency diminishes and the nonlinearity of the system increases by increasing the crack depth. In order to validate the results, the variations of the fundamental frequency ratio against the crack location are compared with experimental results.     

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.     

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.     

含裂纹圆柱薄壳的动态特性试验研究

 利用时间平均法分别拍摄了含轴向和环向裂纹圆柱薄壳的激光 全息振型图，讨论了裂纹对圆柱薄壳振型及固有频率的影响，把含裂 纹壳体的振型分为三个区，即：裂纹周围的局部振动区，壳体原振动 区和过渡区. 并着重分析了局部振动的特征，得出了局部振动有着自 己的独有振形和固有频率的结论，从而很好解释了含裂纹圆柱薄壳的 复杂振型图及固有频率的反常变化.     

混凝土空心板动力损伤诊断研究

利用4块预应力混凝土空心板的动力测试数据,对板的支承条件和损伤参数进行了识别。识别板的支承条件时,引入弹性支座－质量体系,利用实测的前四阶固有频率作为已知信息,直接采用牛顿法求解,根据板的损伤特征,以线弹性断裂力学为基础,推导了混凝土构件裂缝截面转动刚度表达式。然后利用特征值灵敏度分析和实测的固有频率变化率对单条裂缝的位置及裂缝程度进行了识别。     

含多处裂纹梁的振动分析

基于传递矩阵方法,提出了一种计算含有任意处裂纹梁固有频率的新方法。将梁内裂纹模拟为无质量的弯曲弹簧,得到了梁的解析特征方程。通过数值模拟计算,讨论了裂纹数量,以及裂纹位置和裂纹深度对梁的固有频率的影响。通过与文献[4]的计算结果比较,验证了本文方法的有效性。     

Fatigue cracking and its influence on dynamic response characteristics of spot welded specimens

X-ray imaging has been used to determine the fatigue crack growth behavior and failure mechanisms of spot welded specimens. Cracks critical to final failure of the tensileshear specimens studied are through-thickness plate cracks, which are usually initiated about 0.2–1.0 mm away from the edge of the nugget. In addition, frequency response functions (FRFs), obtained by impact hammer-accelerometer experiments throughout the fatigue process, show that the natural frequencies of these joints nonlinearly decrease with the growth of fatigue cracks. The three-dimensional finite-element analysis results for FRFs of uncracked and cracked spot welded joints are shown to be in good agreement with the experimental data. It is also shown that the fatigue cracks have different degrees of influence on different natural frequencies because of the location of cracks and vibrating modes. The results by both experiment and finite element analysis indicate that analysis of the variation of natural frequencies and vibrating modes may be used to study the fatigue crack propagating shape and the location of the fatigue crack.     

含裂纹纳米板振动问题的哈密顿体系方法

基于裂纹处范德华力效应,采用非局部弹性理论构造纳米板模型,并通过导入哈密顿体系建立含裂纹纳米板振动问题的对偶正则控制方程组。在全状态向量表示的哈密顿体系下,将含裂纹纳米板的固有频率和振型问题归结为广义辛本征值和本征解问题。利用哈密顿体系具有的辛共轭正交关系,得到问题解的级数解析表达式。结合边界条件,得到固有频率与辛本征值的代数方程关系式,进而直接给出固有频率的表达式。数值结果表明,非局部尺寸参数和裂纹长度对纳米板振动的各阶固有频率有直接的影响。对比表明,辛方法是准确且可靠的,可为工程应用提供依据。     

Identification of an open crack in a beam using an a posteriori error estimator of the frequency response functions with noisy measurements

This paper presents a robust damage assessment technique for the nondestructive detection and size estimation of open cracks in beams. The damage detection, based on the constitutive relation error updating method, is used for the identification of the crack's location and size in a simply-supported beam. The transverse open crack is modeled through the introduction of the flexibility due to the presence of the crack, i.e. by reducing the second moment of area of the element at the crack's location.This identification algorithm is illustrated through numerical examples involving different positions and sizes of a transverse open crack. We show that the detection of damage and the identification of the crack's size and position can be achieved with satisfactory precision, even if 20% noise has been added to the simulations and less than 5% of all displacements have been measured.     

含45°斜裂纹圆柱薄壳动态特性试验研究

测量了含45°斜裂纹圆柱薄壳的固有频率并拍摄了相应的激光全息振型图．实验表明斜裂纹比轴向和环向裂纹对壳体动态特性的影响更大,致使振型图发生了严重畸变而显得相当复杂,利用传统思路难以找到裂纹长度对壳体动态特性的影响规律．为此,把裂纹周围的振动看作为一种独立的局部振动,从而把含斜裂纹壳体的各种复杂振型划分为3类:纯局部振动振型、纯原振动振型、局部振动和原振动耦合振型．其中前两种振型的固有频率皆随裂纹的加长而降低,但对于耦合振型有时会出现“随裂纹加长频率反而升高的现象”, 这是由于把壳体原振动的频率和局部振动的频率相混淆而产生的错觉．     

含45度斜裂纹圆柱薄壳动态特性试验研究

测量了含45度斜裂纹圆柱薄壳的固有频率并拍摄了相应的激光全息振型图. 实验 表明斜裂纹比轴向和环向裂纹对壳体动态特性的影响更大，致使振型图发生了严重 畸变而显得相当复杂，利用传统思路难以找到裂纹长度对壳体动态特性的影响规律. 为此， 把裂纹周围的振动看作为一种独立的局部振动，从而把含斜裂纹壳体的各种复杂振型划 分为3类：纯局部振动振型、纯原振动振型、局部振动和原振动耦合振型. 其中前两种振型 的固有频率皆随裂纹的加长而降低，但对于耦合振型有时会出现``随裂纹加长频率反而升高 的现象'，这是由于把壳体原振动的频率和局部振动的频率相混淆而产生的错觉.     

Variational formulation of a rod under torsional vibration for crack identification

A variational formulation is developed for the torsional vibration of a cylindrical shaft with a circumferential crack. The work is compared with existing methods. The Hu–Washizu–Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked rod. The general variational principle and the independent assumptions about the displacement, the momentum, the strain and the stress fields of the cracked rod, and the equations of motion for a uniform rod in torsional vibration, are derived. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. Rayleigh quotient was used to approximate the natural frequencies of the cracked rod. Independent evaluations of crack identification methods in rotating shafts are reported and compared with methods using the continuous crack flexibility theory.     

Thermo-mechanical nonlinear vibration analysis of a spring-mass-beam system

Thermo-mechanical vibrations of a simply supported spring-mass-beam system are investigated analytically in this paper. Taking into account the thermal effects, the nonlinear equations of motion and internal/external boundary conditions are derived through Hamilton’s principle and constitutive relations. Under quasi-static assumptions, the equations governing the longitudinal motion are transformed into functions of transverse displacements, which results in three integro-partial differential equations with coupling terms. These are solved using the direct multiple-scale method, leading to closed-form solutions for the mode functions, nonlinear natural frequencies and frequency–response curves of the system. The influence of system parameters on the linear and nonlinear natural frequencies, mode functions, and frequency–response curves is studied through numerical parametric analysis. It is shown that the vibration characteristics depend on the mid-plane stretching, intra-span spring, point mass, and temperature change.     

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.     

Non-linear dynamics of a cracked cantilever beam under harmonic excitation

The presence of cracks in a structure is usually detected by adopting a linear approach through the monitoring of changes in its dynamic response features, such as natural frequencies and mode shapes. But these linear vibration procedures do not always come up to practical results because of their inherently low sensitivity to defects. Since a crack introduces non-linearities in the system, their use in damage detection merits to be investigated. With this aim the present paper is devoted to analysing the peculiar features of the non-linear response of a cracked beam.The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite elements; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, and quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics, strictly due to the presence of a crack, can be used in non-linear techniques of crack identification.