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。     

含有裂纹的齿轮轴动力特性分析与模拟

将裂纹梁理论应用于齿轮轴的动力学研究当中，以轴开放裂纹作为研究对象，对齿轮轴出现裂纹后的动力特性进行了分析模拟，并对裂纹位置和裂纹尺寸等对轴特性的影响进行了深入探讨，指出裂纹发生位置对齿轮轴的振型有着直接的影响，在裂纹发生处振型发生突变，而裂纹尺寸对轴的振型和固有频率都有影响，当出现裂纹后齿轮轴的固有频率发生下降，越是大尺寸的裂纹，轴固有频率越是下落显著。这对齿轮轴的损伤监测和诊断具有重要价值。     

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。     

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.     

基于固有频率的呼吸式裂纹梁损伤识别方法

将呼吸裂纹梁简化为由扭转弹簧连接的两段弹性梁,在假定振动响应随振幅变化的基础上推导出呼吸裂纹梁的固有频率方程;考虑振动过程中呼吸裂纹的开合情况,假定裂纹梁的刚度是振幅的非线性函数,建立了呼吸裂纹梁的多项式刚度模型;结合等高线裂纹识别理论和方法,提出了一种基于固有频率的呼吸裂纹梁损伤识别方法,算例验证了方法的可行性与有效性。研究表明,该方法的识别精度取决于实验固有频率的精度。     

基于模态分析的裂纹齿轮特征识别

为辨别裂纹齿轮的故障位置,通过有限元技术和模态曲率对比分析,获得了裂纹齿轮的动力学特性。建立了正常齿轮和裂纹齿轮的精确模型,利用ANSYS软件计算了齿轮的固有频率和振型,并通过差分法获得振型的模态曲率。分析结果表明,裂纹齿轮的弯曲振动模式发生频率分裂现象,固有频率和振型的变化不明显,而模态曲率的变化可明显指出裂纹的位置。     

裂纹齿轮动力特性分析与模拟

建立了齿轮的动力学模型 ,分析了齿轮轮齿发生裂纹后的动力特性 (固有频率、振型等 ) ,并对裂纹出现位置和裂纹尺寸等对齿轮动力特性的影响进行了深入探讨和计算机模拟 ,指出裂纹发生位置对齿轮轮齿振型影响较大 ,在裂纹发生处振型发生突变 ;而裂纹尺寸对其振型和固有频率影响都较大 ,当出现裂纹后固有频率发生下降 ,振型也发生变化 ,随着裂纹尺寸增加 ,固有频率下降更加显著 ,各阶幅值下降大小不一 ,振型也与无裂纹的情况完全不同。这对齿轮的损伤监测和诊断具有重要价值     

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。     

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。     

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。     

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。     

轴结构件的裂纹参数识别

在带有裂纹的轴结构件中 ,当裂纹较小时轴的裂纹参数与其固有频率的变化率相关联。为此计算轴结构件固有频率的变化率去识别裂纹位置和深度 ,从而为轴结构件的改进设计及带裂纹的轴结构件剩余寿命的估算提供理论依据     

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.     

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     

Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms

In this paper, a crack detection approach is presented for detecting depth and location of cracks in beam-like structures. For this purpose, a new beam element with an arbitrary number of embedded transverse edge cracks, in arbitrary positions of beam element with any depth, is derived. The components of the stiffness matrix for the cracked element are computed using the conjugate beam concept and Betti’s theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain precise natural frequencies and mode shapes of the beam knowing the cracks’ characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results and available experimental measurements. Moreover, by knowing the natural frequencies and mode shapes, an inverse problem is established in which the location and depth of cracks are determined. In the inverse approach, an optimization problem based on the new finite element and genetic algorithms (GAs) is solved to search the solution. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam. The proposed approach is verified through a cracked beam containing various cracks with different depths.     

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.     

基于压电增益特性进行梁中缺陷的识别

驱动元件PZT片和传感元件PVDF膜粘贴于自由梁表面,通过测试压电增益,试验获取梁中不同缺陷尺寸下的固有频率,根据固有频率的变化,实现缺陷的识别,梁中的缺陷采用等效线性弹簧模拟,描绘出不同模态下刚度与缺陷可能位置曲线,根据曲线的交点,得出缺陷位置与尺寸,相比于实际的缺陷位置与尺寸,自由梁弯曲激振下识别的结果满足一定的精度。     

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。     

基于区间B样条小波有限元的裂纹故障定量诊断

研究基于模型的结构裂纹故障诊断中的正反问题,即求解含裂纹参数结构的固有频率以及利用实测固有频率,定量识别裂纹参数。构造用于求解正问题的一维区间B样条小波裂纹单元,通过求解裂纹结构有限元模型,绘制以裂纹等效刚度与裂纹位置为变量的三阶频响函数解曲线,将实际测出的系统前三阶固有频率作为输入,根据曲线的交点定量预示出裂纹的位置和深度。实验研究表明,文中构造的区间B样条小波裂纹单元有效克服了传统有限元分析在求解裂纹奇异性问题时存在的效率低、精度差甚至难以收敛到正确解的缺陷,同时具有足够的辨识精度,为早期裂纹故障定量诊断提供新方法。