考虑轴力二阶效应的损伤梁弯曲摄动解

将损伤梁等效为阶梯型变刚度Euler-Bernoulli梁，利用Heaviside广义函数，给出了阶梯型变刚度梁抗弯刚度的统一表达式．在此基础上，考虑轴向压力二阶效应，并以损伤为摄动参数，得到了均布横向载荷作用下，简支损伤梁弯曲挠度的一阶和二阶摄动解析解，并数值分析了摄动解析解的精度和损伤梁的弯曲变形特性，结果表明：随着轴向压力和刚度损伤参数的增加，挠度一阶和二阶摄动解析解误差增加，挠度二阶摄动解析解误差通常小于其一阶摄动解析解误差，且二阶摄动解的误差很小，满足工程应用的精度．同时，损伤梁的挠度和转角分布与完整梁的挠度和转角分布差异较大，在刚度变化位置处损伤梁转角斜率存在突变．这些结果可为轴力作用下Euler-Bernoulli梁损伤识别提供理论支撑．     

多自由度复模态理论的摄动方法(二)——重特征值及高阶摄动

本文是《多自由度复模态理论的摄动方法(一)一阶摄动》[1]的继续,讨论重特征值及高阶摄动修正问题,对于有重特征值的实模态摄动修正已有论述,本文将论述复特征值的修正。一般而言,一阶摄动已有足够精度,但当参数变化范围稍大时,需要二阶或更高阶的摄动修正,Meirovitch等人讨论了无阻尼,非陀螺系统的二阶摄动修正,并用于响应计算。当阻尼系数增大时,复特征值的误差将随之增大。本文将给出二阶摄动修正及任意阶摄动修正,从而得到二阶及二阶以上的复特征值及复特征矢量的近似公式。Aubrun采用Jacobin公式讨论了有阻尼系统的摄动解,给出了一阶及二阶的阻尼,频率修正公式及一阶复模态,但是由于非按照正规的摄动方法来求解,其一阶阻尼系数与本文虽一致,但对频率则无修正,阻尼对复模态的修正也只有虚部而无实部。为了改善收敛速度,本文提出了将阻尼阵中可对角化部分作为与质量,刚度阵同量级列入方程,而不可对角化部分列入一阶摄动量。这种改进的摄动法以复特征值及实振型为零阶近似,从而可以提高精度改善收敛速度,使对阻尼阵作为一阶小量的限制放宽。作为复模态理论摄动法的应用,讨论了陀螺特征值问题。文末并给出了简单的算例。     

基于裂纹附加模态Timoshenko梁的裂纹损伤识别

将梁中横向裂纹等效为无质量扭转弹簧，并忽略其对梁剪切变形的影响，得到的具有任意裂纹数目Timoshenko 梁自振模态的统一显示解析表达式．将裂纹梁的自振模态分为基本模态和裂纹附加模态，利用最小二乘拟合，建立了利用裂纹附加模态函数的梁裂纹损伤识别方法．通过数值模拟开展了简支单裂纹梁以及悬臂和固支双裂纹梁等的裂纹损伤识别，考察了测量误差对损伤识别的影响，数值结果表明本文所提出的裂纹损伤识别方法对裂纹位置的识别精度高于对裂纹损伤程度的识别精度；随着测量误差的增加，裂纹位置及裂纹损伤程度的识别误差增加，但仍在可接受的范围内，故该裂纹损伤识别方法在实际工程中具有一定的应用价值．     

基于模态参数考虑边界条件变异的桥梁结构损伤识别

根据桥梁结构的实际工程特性,分析其边界条件变异、结构损伤及其参数变化,采用约束优化理论,建立以实测和理论模态参数误差平方和最小为目标函数的优化反演问题。基于矩阵摄动理论引入与结构动力方程对应的特征值和特征向量的一阶、二阶摄动量,将优化反演问题简化为非线性最小二乘法优化反演问题。针对桥梁结构边界条件对模态参数影响显著的实际情况,实施桥梁结构边界条件预识别,采用单元模态应变能方法预定位损伤,提出考虑边界条件变异的桥梁结构损伤识别具体流程。以一磁浮轨道梁方案为例,采用数值模拟进行边界条件变异及损伤的识别验证,结果表明:该方法能够有效识别边界条件的变异及构件损伤,识别参数的相对误差最大为12.48%,具有较高的识别精度。     

锅炉给水泵转子动力学参数的一、二阶摄动识别研究

锅炉给水泵的临界转速是非常重要的参数,与结构密切相关。为了准确地计算出给水泵的干临界转速(在空气中)和湿临界转速(在水中),必须知道转轴上的零部件对其弯曲刚度的加强作用。本文利用摄动传递矩阵法,结合实验室的试验数据,对某电站锅炉给水泵转子的动力学参数进行了一阶和二阶摄动识别。给出了给水泵转子上的热装叶轮、轴套对转子刚度产生加强作用的一、二阶摄动识别结果,得到了修正的给水泵转子系统动力学计算模型。由修正模型计算得到的转子系统固有频率与实测的转子系统固有频率吻合良好。指出一阶摄动识别的结果可以满足工程实际的精度要求。     

随机桁架结构几何非线性问题的混合摄动-伽辽金法求解

提出应用混合摄动-伽辽金法求解随机桁架结构的几何非线性问题.将含位移项的随机割线弹性模量以及随机响应表示为幂多项式展开,利用高阶摄动方法确定随机结构几何非线性响应的幂多项式展开的各项系数.将随机响应的各阶摄动项假定为伽辽金试函数,运用伽辽金投影对试函数系数进行求解,从而得到随机桁架结构几何非线性响应的显式表达式.同已有的随机伽辽金法相比,本文所给的试函数由摄动解的线性组合而成,在求解非线性问题时,试函数的获取具有自适应性.数值算例结果表明,对于具有不同概率分布的多随机变量问题,本文方法无需对随机变量的概率分布形式进行转换,避免了转换误差,因而比同阶的广义正交多项式方法 (generalized polynomial chaos, GPC)计算精度高.同时,在结果精度相当时,和GPC方法相比,本文方法得到的试函数系数的非线性方程维度不大,方程的求解工作量小且更易求解.当随机量涨落较大时,混合摄动-伽辽金法计算所得的结构响应的各阶统计矩比高阶摄动法所得结果更逼近于蒙特卡洛模拟结果,显示了该方法对几何非线性随机问题求解的有效性.     

基于改进残余力向量法的桁架结构损伤诊断

提出一种基于改进残余力向量法的桁架结构损伤诊断方法. 先由灵敏度分析, 求出结构刚度联系矩阵,再由刚度联系矩阵将损伤后的刚度摄动矩阵展开成对角矩阵,代入 残余力向量方程,得到由刚度联系矩阵表示的新的残余力向量方程,此方程可以直接求解, 即可诊断出桁架结构的损伤杆件及其损伤程度. 对于实测中难以获得完备振型的情况,采用 模态扩阶的方法来获得完备的测试振型. 最后以一桁架结构进行数值仿真分析,证实了该方 法的有效性.     

基于Rayleigh-Ritz算法的梁裂缝损伤识别及试验研究

结构动态特性的变化则预示结构出现损伤，基于Ritz线性近似，文中提出一种裂缝损伤识别的方法，用以识别结构裂缝损伤位置及损伤程度。该方法分两步：首先用模态子空间近似关系．消去模态应变能表达式中的整体刚度矩阵和整体质量矩阵，避免模型误差对识别结果的影响。再采用计算向量空间夹角的方法分离损伤位置与损伤程度的耦合影响，进而识别出单元裂缝损伤位置；其次，识别损伤程度采用二次线性规划方法，不再计算特征值灵敏度。线性约束条件保证了二次规划问题的解是唯一的。模拟筒支梁几种裂缝损伤情况进行数值计算与模态试验，利用所得模态参数对该算法程序进行了验证，识别出了裂缝损伤的确切位置及损伤程度，并进行了误差对比。结果表明，该算法由于不用整体结构的数值模型，从而避免了边界条件、连接条件及材料特性参数等因素对识别结果的干扰，识别精度得到提高，将其用于结构损伤识别是可行的。     

基于能量辨识的非线性静电-结构系统的自由度缩减建模方法

给出了一种基于系统能量函数辨识的静电致动微薄板系统自由度缩减建模方法.从Von Karman应变-位移关系式出发,推导出以广义模态坐标为变量的系统动能、应变能以及电容函数的函数表达式.为了将应变能以及电容函数写成广义模态坐标的多变量多项式形式,利用一系列经静态非线性结构有限元计算的结果,拟合得到多变量多项式的未知系数.由Lagrangian方程获得原系统的自由度缩减模型.利用该模型对器件的静/动态特性进行仿真,其计算费用很低.与有限元结果比较,验证了建模方法的正确性.     

计算特征向量摄动量的混合基展开法

在结构修改和模型校正中，模态展开法是计算特征向量摄动量的常用方法之一，但当高阶模态被截断时，它会带来很大的截断误差。本文利用已知的有限阶模态，构造了Ｎ维欧氏空间的一个新基－混合基，并将特征向量的摄动量在新基上展开来计算特征向量的一、二阶 摄动量。该方法使得不管截模态个数的多少，其精度总与全模态展开法相同，且计算量都远少于全模记展开法；与改进的部分民开法相比，本方法不要求所截留的模态边连续的低阶模态     

Crack detection in elastic beams by static measurements

This paper deals with the identification of a single crack in a beam based on the knowledge of the damage-induced variations in the static deflection of the beam. The crack is simulated by an equivalent linear spring connecting the two adjacent segments of the beam. Sufficient conditions on static measurements which allow for the unique identification of the crack are presented and discussed. The inverse analysis provides exact closed-form expressions of position and severity of the crack as functions of deflection measurements for different boundary conditions. The theoretical results are confirmed by a comparison with static measurements on steel beams with a crack. Extension of the presented analysis to multiple cracks is briefly discussed.     

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.      

A simple model of the double cantilever beam crack propagation specimen

A very simple model of the double cantilever beam (dcb) dynamic crack propagation specimen is studied. The main assumption on which the model is based is that the arms of the dcb specimen deform as shear beams. The particular problem studied is the dynamic growth of a sharp crack from a blunt pre-crack with the ends of the specimen arms held at a fixed separation distance. It is demonstrated that this simple model predicts crack motion which is qualitatively consistent with the results of more detailed numerical analyses of the problem and with experimental results. The analysis employs an energy balance crack propagation criterion and both constant specific fracture energy and a class of crack speed dependent fracture energies are considered. Among the features exhibited by the model is that, for constant specific fracture energy, the crack tip speed is constant from initiation up to arrest. On the other hand, for the same geometry and loading conditions, but a strongly crack speed dependent specific fracture energy, the crack speed decreases gradually between fracture initiation and crack arrest.     

Theoretical analysis of crack front instability in mode I+III

This paper focusses on the theoretical prediction of the widely observed crack front instability in mode I+III, that causes both the crack surface and crack front to deviate from planar and straight shapes, respectively. This problem is addressed within the classical framework of fracture mechanics, where the crack front evolution is governed by conditions of constant energy-release-rate (Griffith criterion) and vanishing stress intensity factor of mode II (principle of local symmetry) along the front. The formulation of the linear stability problem for the evolution of small perturbations of the crack front exploits previous results of Movchan et al. (1998) (suitably extended) and Gao and Rice (1986), which are used to derive expressions for the variations of the stress intensity factors along the front resulting from both in-plane and out-of-plane perturbations. We find exact eigenmode solutions to this problem, which correspond to perturbations of the crack front that are shaped as elliptic helices with their axis coinciding with the unperturbed straight front and an amplitude exponentially growing or decaying along the propagation direction. Exponential growth corresponding to unstable propagation occurs when the ratio of the unperturbed mode III to mode I stress intensity factors exceeds some “threshold” depending on Poisson's ratio. Moreover, the growth rate of helical perturbations is inversely proportional to their wavelength along the front. This growth rate therefore diverges when this wavelength goes to zero, which emphasizes the need for some “regularization” of crack propagation laws at very short scales. This divergence also reveals an interesting similarity between crack front instability in mode I+III and well-known growth front instabilities of interfaces governed by a Laplacian or diffusion field.     

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.     

Near tip quasi-static crack growth behavior in strain hardening and softening material

Analyzed in this work is a semi-infinite crack that grows slowly in a steady-state. The assumed constitutive relation for the material permits strain hardening and softening as it is damaged in time. Four distinct regions divided angularly are identified for the asymptotic expressions of the quasi-static crack-tip stress field. They refer to material degraded in front of the crack; undergone elastic unloading; reloading of degraded material; and material completely by exhausted in its load carrying capacity.     

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.     

基于裂纹诱导弦挠度的简支外伸梁裂纹损伤识别

基于梁横向开裂纹的线性扭转弹簧模型，给出了具有任意裂纹数目的简支外伸梁弯曲挠度的显式解析解，研究了集中载荷作用下简支外伸梁裂纹诱导弦挠度函数的性质，给出了裂纹位置和裂纹等效扭转弹簧柔度的近似表达式，从而实现了梁横向裂纹位置及裂纹损伤程度的识别．在此基础上，为利用裂纹梁的测量挠度识别裂纹损伤，提出了分段线性函数的最佳拟合法，实现了简支外伸梁裂纹的损伤参数识别．通过数值试验验证了该识别方法的适用性和可靠性，考察了识别结果对梁挠度测量误差和裂纹深度的敏感性，结果表明随着挠度测量误差的增大，裂纹损伤参数识别误差增大，但裂纹损伤识别方法具有较强的鲁棒性，在工程实际中具有一定的应用性．     

CRACK PROPAGATION IN STRUCTURES SUBJECTED TO PERIODIC EXCITATION

In the present paper,a simple mechanical model is developed to predict the dynamic response of a cracked structure subjected to periodic excitation,which has been used to identify the physical mechanisms in leading the growth or arrest of cracking.The structure under consideration consists of a beam with a crack along the axis,and thus,the crack may open in Mode I and in the axial direction propagate when the beam vibrates.In this paper,the system is modeled as a cantilever beam lying on a partial elastic foundation,where the portion of the beam on the foundation represents the intact portion of the beam.Modal analysis is employed to obtain a closed form solution for the structural response.Crack propagation is studied by allowing the elastic foundation to shorten(mimicking crack growth)if a displacement criterion,based on the material toughness,is met.As the crack propagates,the structural model is updated using the new foundation length and the response continues.From this work,two mechanisms for crack arrest are identified.It is also shown that the crack propagation is strongly influenced by the transient response of the structure.     

A new method for the non-linear deflection analysis of an infinite beam resting on a non-linear elastic foundation

The aim of this paper is to develop a new method of analyzing the non-linear deflection behavior of an infinite beam on a non-linear elastic foundation. Non-linear beam problems have traditionally been dealt with by semi-analytical approaches that involve small perturbations or by numerical methods, such as the non-linear finite element method. In this paper, in contrast, a transformed non-linear integral equation that governs non-linear beam deflection behavior is formulated to develop a new method for non-linear solutions. The proposed method requires an iteration to solve non-linear problems, but is fairly simple and straightforward to apply. It also converges quickly, whereas traditional non-linear solution procedures are generally quite complex in application. Mathematical analysis of the proposed method is performed. In addition, illustrative examples are presented to demonstrate the validity of the method developed in the present study.