基于一阶应变模态灵敏度的结构损伤定量研究

面向基于动态应变监测数据的结构损伤诊断问题,提出了一种仅利用一阶应变模态振型及其灵敏度分析的损伤定量诊断策略。该策略利用事先规定应变测量单元的变形体结构或构件应变响应数据,通过NExT-ERA方法提取进而筛选识别精度较高的某一阶应变模态振型向量,由该阶特征向量求导得到灵敏度矩阵的同时,提出对其进行参考点归一化以避免质量归一化过程,最后通过求解损伤方程组得到单元刚度参量的改变。分别以下承式钢桁梁桥主桁架和装配式T形简支梁桥主梁简化模型为例,验证了该策略的有效性,分析了识别精度、噪声干扰和损伤程度对诊断效果的影响。该研究可为基于实时监测的结构在线诊断提供一定的理论和技术支持。     

基于模态应变能法的弹性薄板损伤识别

针对薄板构件振动疲劳损伤问题,提出基于模态应变能结构损伤识别新方法。该方法以结构损伤会导致其模态性能变化为依据,通过比较弹性薄板结构单元损伤前后的模态应变能变化率构造损伤指针。在构建损伤指针之前,假定弹性板的刚度是由单元刚度组成,在定义单元刚度灵敏度公式基础上建立弹性薄板损伤前后模态应变能变化关系。最后,基于模态柔度曲率法验证模态应变能法在弹性薄板单损伤与多损伤识别方面的优劣性。     

基于遗传神经网络与模态应变能的斜裂缝两阶段诊断方法

基于遗传神经网络与模态应变能,提出了一种斜裂缝两阶段诊断方法,识别梁体中斜裂缝的位置、角度和深度。根据线弹性断裂力学与虚功原理,推导了斜裂缝梁的单元刚度矩阵,得到了其频率与振型。采用遗传算法对BP神经网络的拓扑结构、权值和阈值进行优化,从而建立了遗传神经网络,用于识别梁体中斜裂缝的位置和角度;结合斜裂缝单元的模态应变能,通过对斜裂缝应力强度因子的积分,得到斜裂缝深度的解析表达式,用于识别斜裂缝的深度。数值仿真表明:能够高精度地诊断出梁体中斜裂缝的损伤状态,包括位置、角度和深度;与BP神经网络相比,遗传神经网络具有更强的泛化能力,且对测量噪声具有较好的鲁棒性。     

基于缩聚模态应变能与频率的结构损伤识别

在结构损伤识别中,测试振型往往是不完整的,这阻碍了结构损伤识别技术的应用效率。提出了一种采用缩聚应变能与频率相结合的损伤识别定性与定量方法。采用基于Neumann 级数展开的方法对有限元模型进行缩聚,定义了单元缩聚模态应变能,并证明了缩聚模态应变能的变化对损伤的敏感性;将单元缩聚应变能变化率作为标识量来识别损伤的位置;在损伤位置初步判定的基础上,采用特征值灵敏度法求解损伤程度。以一简支钢梁为例证明了所提出的方法。结果表明:在测量模态数据有误差的情况下也能较好地给出损伤识别结果。     

基于CMSE理论和小生境遗传算法的结构多损伤检测方法研究

本文提供了一种基于交叉模态应变能简称CMSE（cross modal strain energy）和小生境遗传算法的结构多损伤位置和严重程度的有效检测方法。交叉模态应变能方法可以使用完好结构和损伤结构的任意一阶模态信息，并且可以使用极少量（例如只用一阶测量模态）的测量信息。不仅与传统的模态应变能方法相比有了很大的改进，而且对实际检测过程中的信息测量降低了要求。在损伤位置的检测中引入了小生境遗传算法，降低了计算量，提高了检测效率，有利于大型复杂结构的损伤位置检测。复合材料机翼盒段算例结果表明，CMSE方法与小生境遗传算法相结合是检测结构多损伤的有效方法之一。     

柱壳结构损伤识别方法

摘 要:对柱壳结构的损伤部位和程度进行识别是柱壳结构进行安全性评定的一个重要环节。本文对柱壳结构损伤前后动力特性进行了分析,采用摄动法推导了由于单元损伤引起的各阶模态振型改变系数;推导了模态应变能变化与单元损伤之间的关系;采用单元模态应变能的变化率作为柱壳结构损伤诊断的标识量,证明了单元模态应变化率对损伤的敏感性。对柱壳结构损伤识别方法进行了研究,所提出的方法仅需要量测的低阶模态信息和刚度矩阵就能完成结构的损伤识别。最后,以一混凝土柱壳结构为工程实例,对其在不同损伤情况下的损伤进行了分析,结果表明,所提出的损伤识别方法能够很好地识别不同损伤组合下的损伤部位和程度,同时能较好地识别结构小损伤,因而证明了本文所提出的方法的正确性和有效性。 关键词:柱壳结构;损伤识别;动力特性;损伤标识量;模态应变能     

利用模态应变能变化率的结构损伤识别优化方法

针对结构损伤识别过程中存在的定位精度和量化分析不足的问题，提出一种基于结构振动响应的模态应变能变化率与优化技术相结合的损伤识别方法。利用两步法确定可疑损伤单元及对其损伤程度进行量化分析。通过有限元法建立结构的损伤特征模型，且利用单元模态应变能变化率指标构建损伤指标优化分析的目标函数。数值分析过程中，利用粒子群优化算法与遗传算法对设计变量进行优化分析。同时比较模态应变能变化率与小波分析两种方法下的损伤定位的量化分析效果和识别效率。在实际算例中，利用梁结构进行损伤识别优化方法的结果验证。结果证明该方法能够显著提高结构振动损伤和定位的有效性。该方法不仅能够快速和精准地进行结构损伤量化分析，比小波方法具有更好的定位效果，而且能够提高量化分析的识别效率。但该方法在实施过程中的定位精度容易受到噪声的影响，通过优化目标函数可在一定程度上提高该结构损伤识别方法的抗噪能力。     

基于应变能耗散率的结构损伤识别方法研究

将损伤变量的概念从材料领域拓展到结构中,并用其作为损伤因子来表征结构的损伤程度。通过表示结构损伤时每一单元的模态应变能耗散率引起的单元模态应变能的变化,导出结构每一单元的损伤因子的表达式。考虑到所测的结构模态是不完备的,应用完备模态空间理论将未测的结构高阶模态用等效高阶模态来代替从而消除模态截断误差的影响。最后,通过对一悬臂六跨平面桁架结构的数值算例分析的结果说明,该方法简便、有效,可同时定位结构的损伤和识别损伤的程度。     

基于敏感性分析的周期结构损伤检测

介绍了一种基于敏感性分析的周期结构损伤检测方法的基本原理。首先得到了具有单一损伤的周期结构固有频率的一般表达式,并运用在不同单元出现损伤时的第一阶自振频率的近似值形成特征值敏感性矩阵;然后通过求解一组基于上述特征值敏感性矩阵的线性方程,识别出结构损伤位置和大小;针对大型结构可能出现多处损伤的特点,文章最后还介绍了一种方法,它不仅能改善计算精度,而且能提高计算效率。理论分析和数值结果表明周期结构自振频率对不同位置损伤的敏感性仅仅与结构单元数目和损伤位置有关,基于敏感性分析的方法能够准确识别出结构的损伤。     

比例损伤结构的两阶段损伤识别研究

为了提高结构的多损伤识别效率,提出一种先利用归一化条件下的模态应变能变化进行结构损伤定位,然后再利用改进的频率变化法进行损伤定量的两阶段损伤识别方法。该方法首先对损伤前后的单元模态应变能进行归一化处理,提出基于归一化条件下的模态应变能变化率的损伤定位指标并对结构进行准确的损伤定位识别;其次,在确定损伤位置的基础上,建立了只跟损伤单元数目相关的基于比例损伤模型的损伤定量方程,并用最小二乘技术进行损伤程度的求解。为了验证所提方法的有效性,以一个单跨6节平面桁架结构为例进行数值模拟。仿真结果表明,所提方法不但可以准确地识别出结构的损伤位置和程度,而且对测量噪声具有较强的鲁棒性。     

A method for scaling ballistic penetration phenomena

There are several established formulae for projectile penetration into semi-infinite concrete targets. Most of them include a term which indicates that regular scaling does not hold in this situation. Most of these formulae were derived using curve-fitting procedures, so that these terms do not represent any physical meaning. Non-scaling is also found in long rod penetrations, which cannot be attributed to strain rate effects. It is suggested here to differentiate the energy spent by the projectile during the penetration process into two parts, one—the energy expended for surface effects and the other—the energy expended for volume effects. By doing so, it is possible to derive expressions which account for the irregularity in scaling. These expressions are derived from the global, energy balance point of view, so they do not require the detailed characterization of the materials involved. They only require strict adherence to replica scaling procedures.

A similar approach is used to account for strain rate effects, but in that case, the results are not as general and can be applied only to a narrow span of configurations. Examples are cited from tests with concrete penetration and long rod penetration into different targets.     

Calculation of elasto-plastic strains and stresses in notches under multiaxial loading

A method for calculating elasto-plastic notch tip strains and stresses in bodies subjected to multiaxial loading has been presented. The method has been formulated in terms of strain energy density relationships. Two approximate formulae are derived based on the analysis of strain energy density in the notch tip region. The two formulae represent the lower and upper limits of the band within which the actual elasto-plastic notch tip strains can be found. All necessary relationships are derived for a general multiaxial stress state. The calculated notch tip strain and stress components are compared with experimental and finite element data obtained for a variety of loading conditions and materials. This method may be particularly useful for stress/strain analysis of notched components subjected to lengthy multiaxial cyclic loading histories.On leave from Warsaw University of Technology.     

Finite twist and extension of a cylindrical elastic membrane

Summary We consider a circular cylindrical membrane subjected to longitudinal extension and twist. The associated equilibrium deformation is considered to be axisymmetric and the analysis is based on a direct two-dimensional formulation. Wrinkling of the membrane is taken into account in an approximate way by introducing arelaxed strain energy function derived from the neo-Hookean strain energy for isotropic elastic solids. Analytical formulae for wrinkled parts of the membrane are used to corroborate the results of a numerical treatment of the full boundary value problem.Dedicated to the memory of A. C. Pipkin     

A note on bogie impact loads

Simple formulae are presented for the linear elastic and elasto-plastic response of a line of carriages or freight cars that are arrested suddenly. Starting with impact at the leading car, a wave of compression flows along the train during which, ideally, a quarter of a period passes until rest is momentarily achieved. Kinetic energy of the vehicles is changed into strain energy and heat in the couplers. The formulae are approximate but are, nonetheless, useful for design purposes, it being assumed that de-railing does not occur during this collision or buffer incident.     

Portable Power

In applications one must relate the probability constants α and β to differences of practical importance in the field of application. This paper states and proves a fundamental theorem which establishes this relationship and then derives elementary formulae for making power calculations in the most frequently encountered situations such as for main effects, interactions, regression coefficients and response surfaces. After an examination of the sensitivity of power calculations to ranges of α, β, and error degrees of freedom, modifications are made in the formulae which allow them to be used without reference to tables and charts: i.e., they are made portable.     

工字形截面悬臂钢梁的稳定性研究

在钢梁的稳定问题上近年来存在着两种不同的理论,对这两种理论应用于悬臂梁的情况进行了比较。应用非线性力学对稳定问题的变分原理,提出了考虑钢梁内各种应力的非线性应变能的新的总势能公式。对纯弯下单轴对称工字形截面的钢梁进行了研究,将以往两种理论及本文提出的理论在这个问题上存在的问题进行了讨论。对单轴对称截面悬臂梁作用于端部集中荷载的情况,从两种不同的总势能出发,编制了有限元程序,结果与文献的试验结果进行了比较。还提出了受横向荷载的双轴对称截面梁的新的临界弯矩计算公式,与文献公式和有限元结果进行了比较,结果说明本文的公式更精确,在形式上更加简单。     

研究单壁碳纳米管杨氏模量的一种能量方法

本文利用能量方法研究了单壁碳纳米管(single-walled carbon nanotubes, SWCNT)的杨氏模量.文中,首先采用分子力学理论得出了受轴向载荷作用下单壁碳纳米管的总势能;然后通过总势能与相应薄圆柱壳的应变能比较,推导出了单壁碳纳米管杨氏模量的计算公式.另外,从一系列碳纳米管杨氏模量的计算发现,本文研究结果与现有研究结果比较一致.     

SURFACE MICRO-CRACKS IN BLOCK AND RANDOM FATIGUE CYCLING OF 500 MPa STRENGTH STEEL AND WELD METAL

Abstract— Crack density, main crack length and the sum total length of micro-cracks, which initiated and extended on the surface of a 500 MPa strength steel and its weld metal, were investigated by a replica technique applied during fatigue tests. The base and weld metal specimens were subjected to constant amplitude, random and block strain cycling. The base metal specimens were further tested under 4 kinds of block cycling and 2 kinds of incremental strain cycling. All the cumulative cycling patterns in random and block modes followed the so-called p -distribution.
As a result of an analysis of micro-cracks, it was shown that the most useful parameter to estimate the accumulated fatigue damage was the sum total length of micro-cracks in a unit area, which increased exponentially with cycle ratio. Empirical formulae were obtained expressing the increasing tendency as a function of the cycle ratio for three groups of the equivalent strain amplitude. The formulae were applicable to all strain cycling patterns investigated in the present study.     

Statics of thin-walled pretwisted beams

The displacement and strain fields of thin-walled pretwisted beams are prescribed in terms of generalized displacements for extension, bending, torsion and warping. Differential equations and boundary conditions are obtained from the elastic potential energy functional without assuming coincidence of the beam axis with any of the structural axes. This procedure gives a unique consistent definition of sectional moments and generalized forces. Some simple explicit formulae are derived for homogeneous tension–torsion. For the general case a computer code is developed on the basis of discretized generalized displacements and a modified energy functional, devised to obtain consistent lengthwise variation of the stresses and a unique decomposition of the torsional moment. Examples show agreement with analytical results for cylindrical beams and illustrate the various coupling effects for beams with pretwist. They also demonstrate the usefulness of the explicit formulae for homogeneous tension–torsion.     

Measurement and prediction of compressive properties of polymers at high strain rate loading

Strain-rate effect is widely recognized as a crucial factor that influences the mechanical properties of material. Despite the acknowledge importance, the understanding of how such factor interact with the sensitivity of the polymers in terms of mechanical properties is still less reported. In this study, an experimental technique, based on the compression split Hopkinson pressure bar, was introduced to perform high strain rate testing, whereas, a conventional universal testing machine was used to perform static compression testing, to experimentally investigate the independent and interactive effects of strain rates towards mechanical properties of various polymers. Based on the experimental results, we parameterized two equation models, which were used to predict the yield behavior of tested polymer samplings. The experimental results indicate that, the yield stress, compression modulus, compressive strength, strain rate sensitivity and strain energy increased significantly with increasing strain rates for all tested polymers. Meanwhile, the yield strain and the thermal activation volume exhibit contrary trend to the increasing strain rates. Interestingly, the proposed constitutive models were almost agreed well with experimental results over a wide range of strain rate investigated. Of the three polymers, polypropylene shows the highest strain rate sensitivity at static and quasi-static region. On the other hand, at dynamic region, polycarbonate shows the highest strain rate sensitivity than that of polypropylene and polyethylene. Overall, both experimental and numerical models proved that the mechanical properties of polymer show significant sensitivity and dependency towards applied strain rates up to certain extent.