用摄动方法进行受损悬臂梁的模态分析

将结构的裂纹损伤用δ函数进行表达，建立了损伤条件下悬臂梁的自由振动方程。利用一阶摄动方法给出了摄动项的一般表达式，并结合δ函数的性质，获得了受损悬臂梁的特征值和模态振型的解析表达式。以一个受损悬臂梁为数值算例，计算了不同损伤条件下其模态参数的变化。分析了损伤条件对模态参数的影响，为利用动力学特性对悬臂梁的损伤监控和检测提供了理论依据。     

受损悬臂梁的模态分析研究

基于Euler-Bernoulli梁的自由振动方程,利用一阶摄动方法,对受损悬臂梁进行了模态分析计算,并利用Pro/MECHANICA有限元结构分析软件对悬臂梁受损前后的模态进行分析,与摄动数值计算方法进行比较,验证摄动理论分析的正确性。通过具体算例,得出悬臂梁在受损前后前四阶固有频率,以及在各个固有频率下的位移、应力云图,从而验证了基于摄动法理论分析的正确性,为利用动力学特性对悬臂梁的损伤监控和检测提供了理论依据。     

基于BFGS摄动法的固定梁损伤检测

运用损伤结构的特征值问题,建立拟牛顿法的BFGS优化摄动方法来检测固定梁的损伤情况。多单元两端固定梁的损伤位置与程度,可以从首几对振动模态在数次迭代內准確获取。首先,摄动展开损伤结构的刚度矩阵、特征值和特征向量,并代入损伤结构的特征值方程;然后,集合p阶的弹性模量摄动项,以显式直接推导特征参数的p阶摄动系数;最后,把系数代入摄动方程,对于多个弹性模量进行BFGS拟牛顿优化迭代,其目标函数由摄动方程剩余项的总和产生。使用两端固定梁的有限元模型,五单元至九单元梁的损伤检测验证了该方法在有限模态参数与减少自由度模型的有效性。在终止准则方面,使用了d-模与t-模比较不同迭代阶段的收敛性,并精确地在0.06~0.001弹性模量误差內检测了小至大损伤的各个单元号及其损伤程度。     

基于小波方法的板结构损伤识别研究

进行不同边界条件下板结构损伤位置和大小的评估以及传感器布置和噪音对损伤识别影响研究。主要内容包括:首先,通过薄板结构的有限元模态分析,获取有无损伤板结构点的固有特性参数的分布状况,利用离散小波变换将矩形薄板的模态节点位移数据进行分解计算,获得损伤位置数据的高频信息和奇异值。其次,进行不同边界条件下的板结构损伤识别分析,利用小波系数的最大值变化率进行板结构损伤程度的定量化评估。最后,分析了传感器布置以及噪音情况下小波变换方法对板结构损伤识别的有效性。研究结果表明,四边固支约束下的小波系数比四边简支约束的小波系数大0.5%,比两边固支约束的小波系数大0.88%;在网格g=40 mm且通过小波变换对信号进行去噪处理之后都能够有效识别板结构损伤。说明该方法针对二维板结构损伤位置及程度的识别问题具有一定的有效性,能够为车辆结构损伤识别问题提供技术思路和参考价值。     

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。     

大修改结构特征向量重分析的混合基展开法

为拓展基于矩阵摄动理论的结构重分析方法在实际工程中的适用范围,提高重分析计算精度,针对结构模态空间不完备和参数大修改提出了结构动力重分析的混合基展开法。利用已知的少数几个可能不连续的低阶模态构造出整个模态空间的一个混合基,同时将反映结构参数改变的质量矩阵和刚度矩阵的增量表示为高次增量形式,保留了经典摄动法简单易行的特点。数值算例表明,所提出方法适用范围广,极大提高了结构大修改下的动力重分析计算精度。     

一种钢管焊接结构焊缝损伤识别方法

提出了一种基于模型修正的钢管焊接结构焊缝损伤识别方法.利用从发射台骨架试验模型获取的模态参数,选择识别结果中精度较好的模态参数作为模型修正的基准参数.提出基于柔度的最小二乘目标函数,极小化结构实测模态柔度与分析模态柔度之间的误差,将损伤识别问题转化为二次优化问题,并采用信赖域方法求解该问题.以有限元模型焊接结点单元组弹性模量的降低模拟焊缝损伤,并假定两种损伤工况,通过对发射台骨架模型的数值仿真及试验研究,表明所提出的损伤识别方法识别效果较为理想,为解决这种复杂焊接结构焊缝损伤识别问题提供了新的思路.     

基于曲率模态与柔度曲率的损伤识别

以含两条裂纹的两端固定梁为例,采用曲率模态差和模态柔度曲率差来检测结构的损伤。首先将梁的裂纹模拟为无质量的等效扭转弹簧,推导了裂纹梁的特征微分方程,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的振形函数解析表达式。然后用中心差分法分别求解裂纹梁损伤前后的曲率模态值和模态柔度曲率值,利用其差值确定梁的损伤位置,进而确定损伤程度。最后讨论了曲率模态和柔度曲率对结构损伤识别的敏感性。     

一种基于经验模式分解的结构损伤预警方法

提出了一种基于经验模式分解的结构损伤预警方法。首先,将结构反应信号用经验模式分解方法分解成一系列固有模态函数;然后,利用固有模态函数在结构损伤前后的能量分布变化来表征结构因损伤引起的动力特性改变;最后,计算结构的损伤预警指标。应用该方法对健康监测Benchmark模型结构进行分析,采集模型在锤击激励下结构损伤前后的动力响应,计算了结构损伤预警参数及其损伤预警指标。试验数据分析表明,基于经验模式分解的结构损伤预警指标具有良好的损伤预警能力,能够准确地判断结构初期损伤的发生。     

热弹耦合运动斜板振动特性研究

分析无量纲运动速度、边长比、斜角,无量纲热弹耦合因子等参数对热弹耦合运动斜薄板振动特性的影响。以运动热弹耦合运动斜薄板为研究对象,基于弹性薄板小挠度弯曲理论,建立运动微分方程,采用微分求积法进行离散建立热弹耦合运动斜板的特征方程。得到了热弹耦合运动斜板前3阶模态的无量纲复频率与运动速度之间的关系曲线。结果表明,相同条件下,第1阶模态发散失稳的临界速度随着斜板角度的增加而减小,第1阶模态的发散失稳临界速度随着无量纲热弹耦合因子的增大而增大。     

Development of scanning damage index for the damage detection of plate structures using modal strain energy method

This work presents a novel approach of nondestructive detection of damage in plate structures by using experimental modal analysis (EMA) and modal strain energy method (MSEM). An aluminum alloy 6061 thin plate with a surface crack is investigated in this study. EMA is conducted on the plate to obtain the mode shapes before and after damage. The modal displacements of each mode shape are then used to compute the modal strain energy. For all measured mode shapes, a damage index is defined by using the ratio of modal strain energies of the plate before and after damage. In fact, small damage causes very little change in system response, but it is an essential early warning of structure damage. As the second-order derivatives, modal strain energy is much more sensitive to the small change of structural response than frequencies and mode shapes. It is therefore feasible to approach the small damage by using a damage index defined by fractional MSE of the structure before and after damage. In this study, a scanning damage index (SDI) is developed by moving damage indices obtained from the local area throughout the structure as if a scanning sensor is used to inspect the structure. The damage indices in overlap areas are added up and the summation may intensify the signals of damage in the plate. Limited by the numbers of measured point, a differential quadrature method is employed to calculate the partial differential terms in strain energy formula. Experimental results show that SDI well identifies a surface crack location by using only few measured mode shapes of the aluminum plate. This novel approach provides a flexible, cost-effective, and nondestructive damage evaluation in either local or global structure. Its applicability to different types of structures and different sizes of damage is to be experimentally validated in the future work.     

振型曲率在板类结构动力检测中的应用

以四边简支方形弹性薄板为研究对象，通过数值计算得到板损伤前后的多阶模态参数，进而得到板面内两个方向的位移振型曲率并用于板的损伤检测研究。结果表明：当布置有足够数量的振型测点时，振型曲率及板损伤前后的振型曲率差均可用于板损伤的探测与定位，并能大致判断损伤的程度；当振型测点间距过大，或测点偏离损伤区域时，均可能导致检测的失败。     

薄板组合结构动力学特性解析研究

研究薄板组合结构的动力学特性。基于薄板自由振动问题的动态基本解,运用边界元法建立薄板在横向和面内方向的边界控制方程式,为了提高解析建模的精度和效率,根据耦合的思想推导出薄板组合结构的动力学方程,采用频率扫描的方法,准确、快速地求解出薄板组合结构的频率,并得到其相应的振型。数值算例表明本建模方法的可行性和良好的解析计算精度。     

钢筋混凝土简支梁超载后动力特性试验研究

基于采用动态法评估桥梁结构构件超载后损伤的目的,设计和开展了试验研究和相应理论分析。通过对钢筋混凝土简支梁进行反复超载试验,测出构件从完整到破损,以及不同超载幅值和次数对应损伤状态下的频率和阻尼比等模态参数,考查了其与构件承载力的关系,为采用结构动力参数评估结构损伤分析了频率和阻尼比随损伤状态不同的变化规律,根据试验结果得到频率和荷载等级关系的经验公式,为采用动态法评估既有桥梁提供了理论依据     

一种基于模型修改的结构多点损伤识别方法

可用于结构损伤识别的方法很多。一般来讲正向方法直接利用结构模态参数的变化，逆向方法则利用模态参数变化反演结构物理参数变化，还有些方法利用了神经网络和模式识别技术。文中利用模型修改的思想，通过逆向方法计算结构单元刚度变化系数来对结构的多点损伤进行识别。以一个七自由度弹簧阻尼质量系统作为研究对象，用数值模拟方法及特征系统实现算法计算系统的模态参数，并用这些模态参数验证所提出方法的可行性，结果表明该方法对多点损伤的识别是简单而可行的。     

An experimental study on damage detection of structures using a timber beam

Using vibration methods for the damage detection and structural health monitoring in bridge structures is rapidly developing. However, very little work has so far been reported on timber bridges. This paper intends to address such shortcomings by experimental investigation on a timber beam using a vibration based method to detect damage. A promising damage detection algorithm based on modal strain energy was adopted and modified to locate/evaluate damage. A laboratory investigation was conducted on a timber beam inflicted with various damage scenarios using modal tests. The modal parameters obtained from the undamaged and damaged state of the test beam were used in the computation of damage index, were then applied using a damage detection algorithm utilising modal strain energy and a statistical approach to detect location of damage. A mode shape reconstruction technique was used to enhance the capability of the damage detection algorithm with limited number of sensors. The test results and analysis show that location of damage can be accurately identified with limited sensors. The modified method is less dependent on the number of modes selected and can detect damage with a higher degree of confidence.     

A frequency response function-based damage identification method for cylindrical shell structures

In this paper, a structural damage identification method (SDIM) is developed for cylindrical shells and the numerically simulated damage identification tests are conducted to study the feasibility of the proposed SDIM. The SDIM is derived from the frequency response function solved from the structural dynamic equations of damaged cylindrical shells. A damage distribution function is used to represent the distribution and magnitudes of the local damages within a cylindrical shell. In contrast with most existing modal parameters-based SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM requires only the FRF-data measured in the damaged state. By virtue of utilizing FRF-data, one is able to make the inverse problem of damage identification well-posed by choosing as many sets of excitation frequency and FRF measurement point as needed to obtain a sufficient number of equations.     

Dynamic characteristics of a damaged plate

It is very important to well understand the dynamic characteristics of damaged structures to successfully develop or to choose a most appropriate structural damage identification method (SDIM) as the means of non-destructive testing. In this paper, the dynamic equation of motion for damaged plates is derived by introducing a damage distribution function, which may characterize the effective state of structural damages. It is found that structural damages may induce the coupling between modal coordinates. The effects of damages on the vibration characteristics of a plate depending on their locations, sizes, and magnitudes are numerically investigated in a systematic way. The numerical investigations are also given to the effects of damage-induced modal coupling on the changes in vibration characteristics and to the minimum number of natural modes required to predict sufficiently accurate vibration characteristics of damaged plates.     

运用拓扑优化的结构损伤定位

以结构共振频率和结构某点的反共振频率为基础,对拓扑优化中的渐进结构优化法应用于结构损伤定位的可行性进行了研究。基于结构共振频率和反共振频率的灵敏度分析,建立了损伤定位的数学模型,提出了利用渐进结构优化法进行损伤定位的策略。针对单一和多处损伤结构,分别给出了损伤定位的数值算例,对不同的损伤结构予以讨论,并准确识别出了损伤位置。结果表明,在已经测得结构损伤前后共振频率和反共振频率的基础上,渐进结构优化法能够在整个结构区域内寻找损伤点,有较好的搜寻效果。