圆截面梁结构中裂纹局部柔度的测量

作为梁类结构动力学特性分析和损伤识别的重要参数之一,裂纹局部柔度可以有效地反映结构的损伤程度和特征。通过对梁结构进行动力学建模和振动测试,给出了一种基于固有频率的圆截面梁结构中裂纹局部柔度的测量方法。首先为了获得裂纹梁故障数据库,建立了圆形截面裂纹梁结构的有限元模型,进而绘制结构的前两阶固有频率影响曲面。然后对裂纹梁结构进行振动测试,采用测试所得的结构前两阶固有频率去截取结构的前两阶固有频率影响曲面,绘制出裂纹位置和裂纹局部柔度所对应的结构前两阶固有频率影响曲线,利用其交点测量出裂纹局部柔度。这种方法可以被用于圆截面梁中不同类型和形状裂纹的局部柔度测量。     

工字截面梁轨结构裂纹损伤的小波有限元定量诊断

研究工字截面梁轨结构裂纹定量识别中的正反问题,即通过裂纹位置和深度求解结构的固有频率以及利用结构的固有频率,识别裂纹位置和深度.裂纹被看作为一扭转线弹簧,利用工字梁裂纹应力强度因子推导出线弹簧刚度,构造出结构的小波有限元刚度矩阵和质量矩阵,从而获得裂纹结构的前3阶固有频率.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,分别做出以不同固有频率作为输入值时裂纹位置与裂纹深度之间的解曲线,曲线交点预测出裂纹的位置与深度,试验结果验证算法的有效性.     

含垂直裂纹的简支梁自由振动分析

裂纹将改变梁结构局部刚度,导致其结构模态参数变化,影响结构工作特性。针对这个问题,以简支梁为研究对象,采用有限元分析方法,建立含垂直内部裂纹的简支梁有限元模型,研究垂直内部裂纹的长度和位置对简支梁的固有频率和振型的影响规律。讨论垂直内部裂纹简支梁振动曲率与裂纹长度和位置的关系。结果表明,随着裂纹长度的增加,简支梁的固有频率减小,裂纹简支梁与健康简支梁之间的差异逐渐增加;垂直内部裂纹将导致简支梁在裂纹所在截面附件的局部刚度发生变化,且裂纹的影响区域随着裂纹长度的增加而增加;振型的曲率可以用于识别简支梁垂直内部裂纹位置。     

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。     

考虑翘曲影响的Bernoulli-Euler薄壁梁的弯扭耦合振动

通过直接求解均匀薄壁梁单元弯扭耦合振动的运动偏微分方程，推导其自由振动时的精确动态传递矩阵。采用考虑翘曲影响的Bernoulli-Euler梁理论，且假定薄壁梁单元的横截面是单对称的。动态传递矩阵可以用于计算薄壁梁集合体的精确固有频率和模态形状。针对两个薄壁梁算例，采用自动Muller法和结合频率扫描法的二分法求解频率特征方程，并讨论翘曲刚度对弯扭耦合：Bernoulli-Euler薄壁梁固有频率的影响。数值结果验证了本文方法的精确性和有效性，并指出翘曲刚度可以显著改变薄壁开口截面梁的固有频率。     

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。     

激振频率对裂纹梁系统振动特性的影响

用ZK-4VIC型振动与控制实验台和ZK-1型电动式激振器分别对相同的Q235裂纹梁系统加载大小相同频率不同的简谐激振力(F=1.12N,w=17Hz、19Hz、21Hz、23Hz),对裂纹梁的振动疲劳过程进行模拟。记录实验过程中裂纹梁的振动幅值随时间变化的趋势,分析在不同激振频率的激振力作用下,疲劳裂纹对裂纹梁振动特性的影响。结果表明:加载简谐激振力的激振频率与固有频率的关系对裂纹梁系统的振幅变化影响显著;裂纹产生后,刚性系统受裂纹的影响大于柔性系统受裂纹的影响,寿命较短;刚性系统比柔性系统更容易从振动变化上发现裂纹故障的存在。     

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。     

呼吸式裂纹梁的振动疲劳裂纹扩展耦合分析

为提高结构振动疲劳分析的精度,提出一种呼吸式裂纹梁的振动疲劳裂纹扩展耦合分析方法。分析过程中,采用双线性弹簧描述呼吸式裂纹,广义的Forman方程模拟疲劳裂纹扩展;运用Galerkin法把裂纹梁简化为单自由度系统,振动分析与疲劳裂纹扩展计算交替进行,并考虑了振动疲劳裂纹扩展耦合行为。结果表明,对于含裂纹结构的振动疲劳裂纹扩展,采用呼吸式裂纹可以更客观地描述振动过程和裂纹扩展现象;激励频率和阻尼效应对疲劳寿命具有重要影响,尤其对共振疲劳裂纹扩展而言,阻尼效应特别明显。     

Nonlinear vibrational response of a single edge cracked beam

The nonlinear vibrational response of a breathing cracked beam was investigated. The study was done by using a new crack stiffness model to examine some of the nonlinear behaviors of a cantilever beam with a breathing crack. The quadratic polynomial stiffness equation of the cracked beam was derived based on the hypothesis that the breathing process of a crack depends on the vibration magnitude. The Galerkin method combined with the stiffness equation was used to simplify the cracked beam into a Single-degree-of-freedom (SDOF) lumped system with nonlinear terms. The multi scale method was adopted to analyze the nonlinear amplitude frequency response of the beam. The applicability of the stiffness model was discussed and parameter sensitivity studies on the dynamic response were carried out by the SDOF model for a cantilever beam. Results indicate that the new stiffness model provides an efficient tool to study the vibrational nonlinearities introuduced by the breathing crack. Therefore, it might be used to develop a nonlinear identification method of a crack in a beam.     

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.     

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.     

含多条裂纹梁的模态与振动疲劳寿命分析

基于Paris公式,提出了一种含多条裂纹梁疲劳寿命预估的方法。在模态分析中,基于传递矩阵方法,利用无质量的弯曲弹簧等效裂纹,提出一种求解含有多条裂纹梁固有振型的方法,分析裂纹数目、裂纹位置、裂纹深度对裂纹梁固有频率的影响。在振动疲劳分析中,研究了在简谐激励作用下裂纹数目对裂纹尖端应力强度因子的影响。通过Paris疲劳裂纹扩展方程和同步分析法,考虑裂纹梁振动与裂纹扩展的相互作用,分析了裂纹数目和裂纹位置对裂纹梁疲劳寿命的影响。结果表明,裂纹数量、裂纹位置和深度对梁的模态参数和疲劳寿命有重要影响。     

基于裂缝梁动力特性和自振频率的参数敏感性

基于Bernoulli-Euler理论,将开口裂缝梁视为变截面梁,利用模态摄动方法建立了一种求解带任意数量开口裂缝简支梁和连续梁动力特性的半解析分析方法。在等截面无损梁的模态子空间内将裂缝梁的变系数微分方程的求解转化为非线性代数方程组的求解;利用无损梁的自振频率和振型函数摄动求解裂缝梁的模态参数;通过矩形开口裂缝简支梁和两跨连续梁的动力试验验证了笔者方法的准确性;最后,利用开口裂缝梁动力特性的半解析解研究了简支梁和两跨连续梁的自振频率对裂缝尺寸和位置的敏感性。     

Second Generation Wavelet Finite Element and Rotor Cracks Quantitative Identification Method

The presence of cracks in the rotor is one of the most dangerous and critical defects for rotating machinery. Defect of fatigue cracks may lead to long out-of-service periods, heavy damages of machines and severe economic consequences. With the method of finite element, vibration behavior of cracked rotors and crack detection was received considerable attention in the academic and engineering field. Various researchers studied the response of a cracked rotor and most of them are focused on the crack detection based on vibration behavior of cracked rotors. But it is often difficult to identify the crack parameters quantitatively. Second generation wavelets (SGW) finite element has good ability in modal analysis for singularity problems like a cracked rotor. Based on the fact that the feature of SGW could be designed depending on applications, a multiresolution finite element method is presented. The new model of SGW beam element is constructed. The first three natural frequencies of the rotor with different crack location and size were solved with SGW beam elements, and the database for crack diagnosis is obtained. The first three metrical natural frequencies are employed as inputs of the database and the intersection of the three frequencies contour lines predicted the normalized crack location and size. With the Bently RK4 rotor test rig, rotors with different crack location and size are tested and diagnosed. The experimental results denote the cracks quantitative identification method has higher identification precision. With SGW finite element method, a novel method is presented that has higher precision and faster computing speed to identify the crack location and size.     

基于有限元位移模式的含裂纹梁结构动力学模型

针对裂纹的存在将降低梁的刚度的实际情形,首先根据断裂力学理论,引入裂纹梁因裂纹扩展而释放的应变能表达式,然后根据金属材料的特点,运用有限元位移法建立裂纹梁单元的动力学模型,再在梁单元模型的基础上应用有限元位移法建立裂纹梁结构的动力学方程。研究表明：基于有限元位移模式所建立的动力学方程较好地体现了裂纹梁动态性能与其结构参数和裂纹参数之间的内在关系,反映了裂纹的位置及长度对含裂纹梁结构动态性能的影响,为建立含裂纹梁结构动力学模型提供了一种新的有效方法。最后通过实例对理论分析结果进行了验证。     

利用传递矩阵法对阶梯悬臂梁的裂纹参数识别

基于Bernoulli-Euler梁振动理论,以等效弹簧模拟裂纹引起的局部软化效应,利用传递矩阵法推导阶梯悬臂梁振动频率的特征方程,对于含多个裂纹以及复杂边界条件的阶梯梁,仅需求解4×4的行列式即可获得相应的频率特征方程。直接利用该特征方程,提出两种有效估计裂纹参数的方法———等值线法和目标函数最小化法,并应用两段阶梯悬臂梁的数值算例说明方法的有效性。算例结果表明,只需结构前三阶频率即可识别裂纹位置和深度。应用“零设置”可减小计算频率与理论频率不相等对识别结果的影响。等值线法可以直观给出裂纹位置和裂纹深度参数,目标函数最小化法可给出最优的裂纹参数结果,并且该方法可推广应用到含多个裂纹复杂梁(如非完全固支、弹性支撑等)结构的裂纹参数识别中。     

Modified breathing mechanism model and phase waterfall plot diagnostic method for cracked rotors

Transverse breathing cracks are a primary damage mode in rotor systems and seriously influence the safety and reliability of equipment operation. The vibration characteristics exhibited by cracked rotors when passing through critical speeds serve as important evidence in the diagnosis of cracks, and a breathing mechanism model without weight dominance is needed to study these resonant characteristics. In this work, a restoring force modified model is proposed for studying the breathing mechanism of cracked Jeffcott rotors without weight dominance. Furthermore, a novel phase waterfall plot method that can identify frequency components with weak amplitudes is proposed to analyze the vibration response characteristics of cracked Jeffcott rotors. Numerical and experimental studies indicate that the phase waterfall plots effectively recognize the weak characteristic frequencies of cracked rotors. This study can also provide references for the crack monitoring of rotor systems.