含双裂纹圆截面悬臂梁的损伤识别研究

裂纹的萌生和扩展直接影响构件的振动响应，对构件的安全可靠性具有重要影响．本文以圆截面悬臂梁为对象，结合转角模态振型和模态频率等高线，研究了一种双裂纹识别技术．首先，基于应力强度因子和卡氏定理推导了无裂纹梁单元和含裂纹梁单元的刚度矩阵；在此基础上，建立了含裂纹圆截面悬臂梁的有限元动力学方程；然后，结合裂纹对梁转角模态振型和模态频率的影响，提出了双裂纹识别策略．最后，通过算例讨论了双裂纹识别策略的可行性．结果表明，圆截面悬臂梁的模态转角在裂纹位置出现突变，裂纹深度越大转角突变值越大；将识别出的裂纹位置作为已知参数，通过模态频率等高线法，可以准确地识别出双裂纹的深度．     

含裂纹梁非线性静动力特性及简化动力学建模Static and dynamic behaviour of cracked beam and simplified dynamic model

主要研究裂纹对梁结构动力特性的影响规律,进而为含裂纹梁结构状态监测提供理论依据。首先,对裂纹影响区域进行分析,建立含裂纹梁二维接触非线性有限元模型,阐明含裂纹梁具有拉压不同刚度的静力特性;其次,通过对机理模型的分析,指出拉压不同刚度会引起轴向与弯曲的耦合振动;然后,通过非线性动力学分析方法研究其动力特性,观察到含裂纹梁在冲击荷载下会产生轴向与弯曲的耦合振动现象,并指出这种轴向与弯曲耦合振动的一个重要特征是轴向振动频谱图中含有弯曲振动基频的两倍频成分;最后,通过引入非线性弹簧建立一种新颖的含裂纹梁简化动力学模型,通过与精细有限元分析对比,验证了模型的合理性。该简化动力学模型将接触非线性问题转换为材料非线性问题,避免了费时的接触非线性动力学求解过程。     

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.     

Six degrees of freedom coupled dynamic response of rotor with a transverse breathing crack

More coupling mechanisms between the six degrees of freedom (DOFs) are introduced by considering the contribution of the general transverse forces to stress intensity factor of mode I crack in predicting the crack additional flexibility matrix of the cracked rotor. And the obtained flexibility elements show a good agreement with the experiment result for a wide range of the crack depth ratio. Six DOFs coupled dynamic equations for cracked rotor are formulated by introducing three rotational DOFs. A response-dependent non-linear breathing crack model is applied to simulate the breathing behavior during operation in this paper. Numerical investigations are carried out to simulate the various parametric conditions on the dynamic characteristics of cracked rotor, including the crack depth, shaft slenderness ratio, and rotating speed ratio. A perturbation frequency component and its combinations with harmonic components are observed in the dynamic response obtained by six DOFs coupled models (SDCM). Some differences in evolution of whirling orbit obtained by SDCM and three DOFs coupled models are found, when the cracked rotor passes through the sub-critical speeds.     

基于压电振动能量俘获的弯曲结构损伤监测研究

建立了含裂纹损伤的曲梁压电能量俘获系统在强迫振动下的动力学模型. 基于Prescott型压电曲梁力电耦合振动方程的解析解和裂纹截面处的连续性条件, 求解了含裂纹损伤的压电曲梁的格林函数. 根据线性叠加原理, 对含裂纹的力电耦合模型的系统方程解耦, 得到强迫振动下含裂纹损伤的曲梁压电俘能器的输出电压. 在得到模型的强迫振动解析解后, 提出逆方法检测结构中的裂纹损伤, 这一检测方法适用于处于振动状态下的结构. 在数值计算中, 令裂纹深度为零, 通过对比本文的解析解与现有文献中的解析解, 验证了本文解的有效性. 分别分析了含裂纹损伤的压电曲梁的电压响应与裂纹深度、裂纹位置、材料的几何参数以及阻尼之间的关系. 研究结果表明: 裂纹的存在对曲梁式压电俘能器的影响比直梁式更加复杂; 裂纹出现时, 损伤曲梁在健康曲梁的一阶频率值处一定会出现波动并被激励出二阶频率, 此时的二阶频率是开路中健康压电曲梁的一阶频率值; 通过对电压响应的检测可以确定的损伤裂纹的深度和在结构中出现的位置范围; 利用振动问题的解来检测压电曲梁的健康状况是可行且准确的.      

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。     

Effects of a crack on the stability of a non-linear rotor system

The stability of a rotor system presenting a transverse breathing crack is studied by considering the effects of crack depth, crack location and the shaft's rotational speed. The harmonic balance method, in combination with a path-following continuation procedure, is used to calculate the periodic response of a non-linear model of a cracked rotor system. The stability of the rotor's periodic movements is studied in the frequency domain by introducing the effects of a perturbation on the periodic solution for the cracked rotor system.It is shown that the areas of instability increase considerably when the crack deepens, and that the crack's position and depth are the main factors affecting not only the non-linear behaviour of the rotor system but also the different zones of dynamic instability in the periodic solution for the cracked rotor. The effects of some other system parameters (including the disk position and the stiffness of the supports) on the dynamic stability of the non-linear periodic response of the cracked rotor system are also investigated.     

Detection of crack location using cracked beam element method for structural analysis

The local flexibility introduced by cracks changes the dynamic behavior of the structure and, by examining this change, crack position and magnitude can be identified. In order to model the structure for FEM analysis, a special finite element for a cracked Timoshenko beam is developed. Shape functions for rotational and translational displacements are used to obtain the consistent mass matrix for the cracked beam element. Effect of the crack on the stiffness matrix and consistent mass matrix is investigated. Proposed is a procedure for identifying cracks in structures using modal test data.     

小波分析在悬臂梁裂纹识别中的应用

基于空间信号的小波分析理论,将含裂纹悬臂梁前四阶振型信息直接用于小波变换,小波系数在空间域上的突变反映了裂纹的存在并指出了裂纹的位置.本文分析了前四阶振型对小波识别结果的敏感性,利用小波系数模极大值在尺度上的表现与Lipschitz指数之闻的关系建立了集中因子和裂纹深度之间的关系,以此来估计裂纹深度.鉴于实测信号往往是含噪声信号,分析了噪声对识别结果的影响规律.数值算例表明利用sym4小波对含裂纹梁的四阶振型信息进行小波分析可以准确地识别出裂纹的位置和深度;高阶振型对结构损伤较为敏感,高阶振型更适合于微裂纹和含噪声信息的处理,但高阶振型的非线性也会给裂纹识别带来一定的困难.使用本文方法进行结构裂纹参数识别,噪声对裂纹位置的影响只是指示清晰度的影响,基本不会产生错误的识别,而对裂纹深度的影响远比对位置的影响复杂,由于小波系数混入了噪声成分,从而增加了集中因子的取值,致使识别结果总是比真实结果偏大.     

基于小波分析的梁裂缝识别研究

利用小波分析对筒支梁的裂缝进行识别。将带裂缝筒支梁的基本振型用Mexican Hat小波进行连续小波变换，从小波系数在裂缝处出现模极大值可以识别出裂缝位置，利用由小波系数计算得到的Lipschitz指数来识别裂缝深度，Lipschitz指数随着裂缝深度的增加而减小。通过分析和仿真计算获得满意结果，在仿真算例中分析了裂缝位置对Lipschitz指数的影响很小，可以忽略；振型的测点距离越大，Lipschitz指数越大。同时指出噪声对Lipschitz指数有影响但在噪声不很大时仍能较好地识别裂缝。该方法同样适用于多条裂缝的识别和其他构件的裂缝识别。     

锻压操作机夹持长棒料随动过程动态受力分析

研究了锻压操作机夹持长棒料锻件锻压随动过程中夹钳的受力状态。利用拉格朗日方程及有限元方法建立了包含操作机及其锻件的总体动力学方程。操作机系统建立为端部悬挂质量弹簧的Euler-Bernoulli梁模型,随动过程中因为梁上节点位移激励引起操作机系统的瞬态振动。计算结果与LS-DYNA显式有限元模型结果进行了比对,吻合良好。结果表明,对于长棒料锻件,液压机锻压的位置对操作机的动态受力有着十分显著的影响。     

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.     

Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on onedimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either the Timoshenko or Euler-Bernoulli beam theory. Then, Hamilton's principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam's natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.     

Mechanics and fracture of crack tip deformable bi-material interface

Novel interface deformable bi-layer beam theory is developed to account for local effects at crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable sub-layers with consideration of crack tip deformation. Unlike the sub-layer model in the literature in which the crack tip deformations under the interface peel and shear stresses are ignored and thus a “rigid” joint is used, the present study introduces two interface compliances to account for the effect of interface stresses on the crack tip deformation which is referred to as the elastic foundation effect; thus a flexible condition along the interface is considered. Closed-form solutions of resultant forces, deformations, and interface stresses are obtained for each sub-layer in the bi-layer beam, of which the local effects at the crack tip are demonstrated. In this study, an elastic deformable crack tip model is presented for the first time which can improve the split beam solution. The present model is in excellent agreements with analytical 2-D continuum solutions and finite element analyses. The resulting crack tip rotation is then used to calculate the energy release rate (ERR) and stress intensity factor (SIF) of interface fracture in bi-layer materials. Explicit closed-form solutions for ERR and SIF are obtained for which both the transverse shear and crack tip deformation effects are accounted. Compared to the full continuum elasticity analysis, such as finite element analysis, the present solutions are much explicit, more applicable, while comparable in accuracy. Further, the concept of deformable crack tip model can be applied to other bi-layer beam analyses (e.g., delamination buckling and vibration, etc.).     

含裂纹梁参数的谐响应识别

主要研究含裂纹梁在简谐激励作用下的动力特性,提出一种依据幅值变化对裂纹参数进行识别的新方法。首先,在振动过程中考虑裂纹的呼吸特性,以悬臂梁为例建立含裂纹梁的二维有限元模型,指出在一般激励频率下,其对应的幅值均是明显信号,可用来描述裂纹梁的动力特性。其次,当激励频率分别取无裂纹梁一阶频率的1/4和二阶频率的1/4时,幅值随裂纹参数的变化明显不同,可依据响应幅值的变化对裂纹参数进行识别。然后,利用曲面拟合技术绘出幅值变化曲面,对未知参数的裂纹进行识别,验证了该方法的有效性,并归纳出利用幅值变化对任意裂纹参数进行识别的基本步骤。最后,针对无裂纹梁频率计算可能存在误差的情况,分析识别方法的鲁棒性,结果显示即使最大误差为10%,该方法也能对裂纹参数进行准确识别。     

大跨度斜拉桥环境振动试验与分析

桥梁环境振动试验具有简单方便和花费少等优点。以青洲闽江大跨度斜拉桥为背景,介绍了通车前全桥环境激励动力试验,采用频域峰值法和时域随机子空间识别得到了该桥的基准的动力学特性,并与三维有限元模型计算结果进行了比较,二者吻合良好。结果表明环境振动响应足以识别出该桥所感兴趣的模态,结果可作为该桥的有限元模型修正、损伤检测、使用状态评估和健康监测的基础。     

力-压电混合弹性超材料梁的带隙调节特性

为实现宽带低频减振,本文将力振子和串联负电容的压电分流振子分别置于基体上下两侧,设计了混合弹性超材料梁。基于传递矩阵法建立了理论模型,用于计算混合弹性超材料梁的频散关系和动态有效参数,通过有限元法进行了验证。分别采用理论方法和数值方法研究了电路元件参数对混合弹性超材料梁的带隙和振动衰减特性的调节机理,通过与单振子超材料的带隙对比,分析了两种振子间的相互影响。结果表明：电路元件参数主要影响压电分流振子产生的带隙的位置、宽度及带隙内的振动衰减程度;两种振子的带隙重叠区域不一定为通带;两种振子会因为负动态有效刚度范围靠近而相互影响。本研究将为此类超材料的设计提供参考依据。     

Kinematics of layered reinforced-concrete planar beam finite elements with embedded transversal cracking

In this work crack formation and development is addressed and implemented in a planar layered reinforced-concrete beam element. The crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the crack position reaching the tensile strength will trigger a crack to open. Since the element is multi-layered, in this way the crack is allowed to propagate through the depth of the beam. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle, as well as a discontinuity in the position vector of the layer’s reference line. A bond–slip relationship is superimposed onto this model in a kinematically consistent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in the multi-layered beam element.     

A new efficient procedure to solve the nonlinear dynamics of a cracked rotor

The dynamic analysis of a cracked rotor with a breathing crack leads to the formulation of a nonlinear time-dependent problem. For the simple Jeffcott rotor model, this problem has been addressed using numerical integration methods that are very time consuming. A first simplification can be done assuming that the stiffness is a time-dependent function obtained with the quasi-static displacements of the shaft. In this study, we propose a new procedure to analyze the nonlinear dynamic of such a kind of cracked rotors using an iterative technique that transforms the full nonlinear problem in a succession of time-dependent linear ones. We show with different examples that this technique virtually gives the same results as the classical integration methods, but being much more efficient and achieving a significant saving of computation time. The calculations using the proposed method are over a 100 times faster than the corresponding to integrate the full nonlinear problem, being very helpful in on-line crack identification procedures. Also, this analysis shows that, in cases for which the vertical whirl amplitude is greater than the shaft weight static deflection, the use of simplified methods based on the quasi-static stiffness matrix could not be adequate.     

青洲斜拉桥的基准动力有限元模型

讨论了斜拉桥有限元动力分析模型,给出了基于环境振动试验结果建立大跨度斜拉桥基准有限元模型的步骤;讨论了桥面初始平衡构型、几何非线性、桥面板、混凝土桥面板与钢梁的剪力连接和端部纵向约束对模型的影响。经通车前现场环境振动试验结果验证的青洲闽江斜拉桥三维有限元模型,反映了桥梁在运营前的真实动力行为,可作为该桥各种复杂响应分析和长期健康监测、使用状态评估的基准。