开口裂纹梁振动特性参数分析

开展仿真分析探究梁边界条件、裂纹位置、裂纹程度、梁几何尺寸对开口裂纹矩形梁振动特性的影响．采用等效刚度模型建立裂纹梁结构振动方程，并与试验比较完成验证．预报梁在简支、悬臂、固支三种边界下，在不同位置发生不同程度裂纹损伤时的固有频率．研究发现，裂纹梁固有频率特性与完好无损梁曲率模态相关．裂纹可使固有频率降低，且降低程度随损伤程度增加而愈显著．裂纹位置接近完好梁某阶曲率模态零点（无效位置）/极点时，该阶固有频率受到影响将会减弱/增强．开展悬臂裂纹梁在不同几何尺寸下曲率模态分析．研究发现，曲率模态在裂纹处发生尖角突变现象，且尖角峰值随着损伤程度的增加而增大．裂纹位置接近某阶曲率模态极点/零点时，该阶模态受裂纹影响更显著/不明显．在裂纹相对位置和损伤程度相同时，增加梁长度使裂纹处尖角峰值减小，改变梁宽度不影响曲率模态，增加梁高度可使尖角峰值增加．研究成果可为试验提供基础，为扩建数据库，探索一种在线检测方法，基于实时大数据和人工智能技术开展各项振动参数综合分析，为实现梁裂纹智能识别与定位提供依据．     

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.     

基于连续抗弯刚度模型的裂纹梁动力指纹损伤识别

基于断裂力学的应变能概念,建立裂纹简支梁连续抗弯刚度模型,提出基于连续抗弯刚度模型的裂纹梁动力指纹损伤识别方法。借助有限差分方法、Mathematica软件编程求解裂纹梁动力指纹(固有频率、振型、振型曲率),通过与铰接法及FEM法对不同裂纹工况下裂纹梁固有频率的数值计算比较及误差分析,成功验证了方法的有效性,并探讨了裂纹参数对动力指纹的影响。算例分析表明:连续抗弯刚度模型对裂纹参数变化敏感,裂纹梁抗弯刚度在裂纹处呈现最小值,邻近区域抗弯刚度受裂纹影响明显;裂纹简支梁的动力指纹随裂纹参数的变化呈跨中对称变化;裂纹梁结构的固有频率与振型曲率耦合的识别方法可以较好地识别出梁结构裂纹参数,识别误差为2.23%,证实了基于动力指纹检测裂纹损伤的可行性。本文结果为梁结构裂纹的检测提供了重要的理论依据,有广泛的实用与理论研究前景。     

基于均匀荷载面曲率的简支裂纹梁损伤识别

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。     

裂纹对两端固定的圆柱薄壳振动特性影响的试验研究

裂纹使弹性体产生新的自由边界,引起刚度降低,从而导致固有频率和屈曲临界载荷等力学特性发生变化。冈村弘之在分析裂纹对梁的固有频率影响时采用了弹性铰的力学模型,计算结果与试验较符合。等用Ritz法研究了悬臂板上不同位置的裂纹对固有频率与振型的影响,由沙型确定节线位置,发现随裂纹增长固有频率不断地降低。本文进一步研究不同方向的裂纹对两端固定的圆柱薄壳弯曲振动固有频率及振型的影响,采用全息摄影记录振型。     

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.     

局部裂纹损伤简支梁的曲率模态特性

将裂缝损伤简化成矩形凹槽,采用delta函数表示简支梁的裂纹损伤位置,得到了全梁范围内截面转动惯量和单位长度质量的表达式,建立了局部裂缝损伤简支梁的横向自由振动方程.利用摄动方法给出了裂纹摄动项的一般表达式,根据摄动项和完整梁都同时满足边界条件的特点,将一阶和二阶摄动项都表示成完整梁模态的线性组合,结合delta函数的性质,最终获得了受损简支梁的特征值和模态振型的解析表达式.最后,通过数值计算得到结构模态参数,对比了一阶摄动和二阶摄动对计算结果的影响,分析了不同阶固有频率和模态曲率的变动量,为简支梁的损伤监控和检测提供了理论依据.     

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.     

Crack propagation in wedged double cantilevered beam specimens

A closed form analytical solution of crack propagation in double cantilevered beam specimens opened at a constant rate has been found. Hamilton's principle for non-conservative systems was applied to describe the crack motion, under the assumption of a Bernoulli-Euler beam. The criterion of crack propagation is a critical bending moment at the crack tip. The calculations of beam motion take into account wave effects in the Bernoulli-Euler theory of elastic beams. The beam shape during the crack motion is found with a similarity transformation and expressed by Fresnel integrals. The boundary conditions satisfied are the fixed ones of zero bending moment and constant beam opening rate at the load end of the specimen and the moving ones of zero deflection and zero slope of the deflected beam at the tip of the moving crack. The fracture represents a moving critical bending moment. The analytical results show that the specific fracture surface energy is a unique function of the ratio of the crack length squared to the time subsequent to loading and this is computed from the recorded time-dependence of the crack length.     

K III -Deformation modes in internal oblique cracks under plane-stress conditions

The exact shape of the deformed internal oblique crack in an infinite elastic plate under conditions of plane stress was studied. The Muskhelishvili potential function yielded the exact stress and displacement field around the crack. While in previous papers by the author the study was mainly concerned with the definition of the in-plane shape of the deformed crack and important properties were disclosed concerning especially the contribution of the shear loading of the crack, in this paper the out-of-plane component of displacements is determined and its influence on the exact shape of the deformed crack in space is presented. It is shown that, as soon as shear displacements appear in the cracked plate under plane stress, out-of-plane shear displacements are a compulsory consequence for plane-stress conditions of the plate. The elliptic form of the deformed internal crack was twisted out of the plane of the plate with its zero twisting displacement near the new crack tip of its deformed shape corresponding to the vertex of the ellipse. The points of maximum and minimum out-of-plane displacements were placed close to the vertices of the ellipse at polar angles, θ, depending only on the eccentricity of the ellipse and displaced always on both sides of the vertices. The compulsory coexistence of mode II and mode III deformations makes the internal crack in plane stress to present a complicated pattern of deformation at its deformed crack tips. All of these results are amply supported by experimental evidence with caustics, which always show either a simple mode I pattern or a complex mode II and III pattern as soon as shear interferes in the mode of deformation of the plate.     

On irregularity-based damage detection method for cracked beams

A new damage detection technique using irregularity profile of a structural mode shape is proposed in this paper. The mode-shape of a cracked beam is first obtained analytically by using a general function. Its irregularity profile is then extracted from the mode shape by a numerical filter. The location and size of the crack in the beam can be determined by the peak value appearing on the irregularity profile. Two types of numerical filters, i.e., triangular and Gaussian, are examined. It has been found that the former filter is more effective in damage detection than the latter one. Numerical simulations suggest that the irregularity-based method requires a relatively low measurement resolution. Noise stress tests are carried out to demonstrate the effectiveness and robustness of this method under the influence of noise. As a validation, the proposed method is applied to detect crack damage in an E-glass/epoxy laminated composite beam. The successful detection of the crack in the composite beam demonstrates that the irregularity-based method is capable of assessing both the location and size of the crack and can be used efficiently and effectively in damage identification and health monitoring of beam-type structures.     

Nonlinear dynamic response of a functionally graded plate with a through-width surface crack

A nonlinear vibration analysis of a simply supported functionally graded rectangular plate with a through-width surface crack is presented in this paper. The plate is subjected to a transverse excitation force. Material properties are graded in the thickness direction according to exponential distributions. The cracked plate is treated as an assembly of two sub-plates connected by a rotational spring at the cracked section whose stiffness is calculated through stress intensity factor. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the FGM plate are derived by using the Hamilton’s principle. The deflection of each sub-plate is assumed to be a combination of the first two mode shape functions with unknown constants to be determined from boundary and compatibility conditions. The Galerkin’s method is then utilized to convert the governing equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms under the external excitation, which is numerically solved to obtain the nonlinear responses of cracked FGM rectangular plates. The influences of material property gradient, crack depth, crack location and plate thickness ratio on the vibration frequencies and transient response of the surface-racked FGM plate are discussed in detail through a parametric study.     

Shaping a thin-walled cylindrical shell on a three-roll bending machine

We use the Bernoulli-Euler kinematic hypothesis to model the steady-state process of shaping a thin-walled cylindrical shell by bending an elastoplastic strengthening parent sheet on a three-roll bending machine. We determine the curvilinear shape of the moving parent sheet in the bending area and the displacement of the central roll axis needed to obtain the prescribed curvature of the cylindrical shell when leaving the bending area. One- and multitransition shell shaping processes are considered. The computational model is in satisfactory agreement with experiments.     

中心直裂纹平台巴西圆盘复合型动态应力强度因子

为了指导用中心直裂纹平台巴西圆盘(CSTFBD)试样进行岩石复合型动态断裂 试验,利用有限元法首先验证了文献中对中心直裂纹巴西圆盘(CSTBD)得到的有关结果,分析 比较了不同无量纲裂纹长度(即裂纹半长和圆盘半径之比)时两种圆盘的I, II型动态应力 强度因子的时间历程,发现两者的差异大部分在10{\%}以内,同时验证了该文数值方法的可 靠性. 然后讨论了CSTFBD试样I, II型动态应力强度因子的复合比、起裂角以及纯II型加 载角. 研究成果可为复合型动态断裂试验中CSTFBD试样的加工、试样上应变片的粘贴、起裂 方向和起裂时间的估计等提供参考.     

求解三维裂纹前缘SIF分布时间历程的通用权函数法和有限变分法

将三维热权函数法扩展为适用于表面力、体积力和温度载荷的通用权函数法(UWF).推导出以变分型积分方程表达的UWF法基本方程,从变分的角度,将求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE)改造为可以适用于一般的变分型积分方程的一类新型数值方法--有限变分法(FVM).在FVM中可以引入无穷多种线性无关的局部变分模式,可以根据计算要求在求解域中插入任意多个计算节点,单一型裂纹问题FVM所得到的最终方程组的系数矩阵总是一个对称的窄带矩阵,而且对角元总是大数,具有良好的数值计算性能.FVM对于SIF沿裂纹前缘急剧变化的复杂情况具有较好的数值模拟能力和较高的计算精度,利用自身一致性,可以求得三维裂纹前缘SIF的高精度解.     

Waveform fractal dimension for mode shape-based damage identification of beam-type structures

Mode shape-based structural damage identification has been a research focus during the last couple of decades. Most of the existing methods need a numerical or measured baseline mode shape serving as a reference to identify damage, and this requirement extremely limits the practicability of the methods. Recently, waveform fractal dimension such as Katz’s waveform fractal dimension (KWD) has been explored and applied to mode shape for crack identification without a baseline requirement. In this study, different from the popular KWD, an approximate waveform capacity dimension (AWCD) is formulated first, from which an AWCD-based modal abnormality algorithm (AWCD-MAA) is systematically established. Then, the basic characteristics of AWCD-MAA on abnormality detection of mode shapes, e.g., crack localization, crack quantification, noise immunity, etc., are investigated based on an analytical crack model of cantilever beams using linear elastic fracture mechanics. In particular, from the perspective of isomorphism, a mathematical solution on the use of applying waveform fractal dimension to higher mode shapes for crack identification is originally proposed, from which the inherent deficiency of waveform fractal dimension to identify crack when implemented to higher mode shapes is overcome. The applicability and effectiveness of the AWCD-MAA is validated by an experimental program on damage identification of a cracked composite cantilever beam using smart piezoelectric sensors/actuators (i.e., Piezoelectric lead–zirconate–titanate (PZT) and polyvinylidene fluoride (PVDF)). The proposed AWCD-MAA provides a novel, viable method for crack identification of beam-type structures without baseline requirement, and it largely expands the scope of fractal in structural health monitoring applications.     

Fracture mechanics analysis of curved stiffened panels using BEM

A dual boundary element method is developed for a analysis of reinforced cracked shallow shells. Boundary integral equations are derived from the Betti’s reciprocal theorem for a cracked shallow shell with transverse frames and longitudinal stiffeners. The effect of frames and stiffeners are treated as a distribution of line body forces. The radial basis function is used to transform domain integrals to boundary integrals. Stress intensity factors are evaluated from crack opening displacements. The effect of curvature on the stress intensity factors is illustrated by numerical examples. Three examples are presented to demonstrate the accuracy of this method compared with solutions obtained using the finite element method.