大跨圆拱屋盖结构的风致响应分析

大跨屋盖特征值问题的求解是结构动力响应分析中最繁琐的一个环节，而且一些对结构响应贡献较大的高阶模态容易在传统的模态叠加法中被忽略。本文以典型的大跨圆拱屋盖为例，将里兹向量直接叠加法应用于屋盖系统特征值问题计算和风致响应分析，其特点是在误差逼近的基础上自动生成一组正交的里兹向量并用于缩减系统自由度数。与传统模态叠加法算得的结果相比，里兹向量直接叠加法只用很少数目的向量就可以得到较精确的结果，而且高阶模态的贡献不会被忽略。该方法不仅大幅度地减少了机时，而且提供了动力分析的误差估计。     

基于改进Ritz法的耗能减震高层建筑结构地震响应分析

用改进Ritz法计算耗能减震高层建筑结构的地震响应。改进Ritz法采用基于外荷载空间分布的Ritz向量和基于外荷载频率的Ritz向量。其中,基于外荷载空间分布的Ritz向量用Lanczos法形成。基于外荷载频率的Ritz向量则用外荷载主频的平方进行特征值平移后再用Lanczos法形成。文中还给出上述两种Ritz向量的截断标准。之后用改进Ritz法的Ritz向量对结构动力方程进行线性变换。由于耗能减震高层建筑结构的阻尼是非比例阻尼,广义阻尼矩阵是非对角矩阵,所以文中采用拟力实模态法对线性变换后的耦联动力方程进行求解。最后的算例说明该方法用于耗能减震高层建筑结构的地震响应分析是有效可行的。     

一种粘性阻尼系统频域响应灵敏度计算方法

给出了一种粘性阻尼系统频域响应灵敏度分析的双模态展开方法，引入与响应相对应的虚拟载荷，由两次模态展开得出频域响应灵敏度公式，为了减少模态截断误差，本文基于幂级数展开原理，又导出了一种双模态加速方法。数值示例表明，双模态加速法可大大提高模态截断时频域响应灵敏度分析的精度。     

EXPLOITING DESIGN LENGTH SCALES IN STRUCTURAL OPTIMIZATION

Many structural optimization methods use geometric length scales as well as artificially imposed lengths such as finite element dimensions. One considers functions defined over these dimensions in characterizing and solving the problem. The natural length scales involved in the proposed design change are generally overlooked. When one proposes an optimization based on change of certain panels in a sheet metal structure, for instance, it might be helpful to use the dimensions of the redesign areas as characteristic lengths. In the present study, a Rayleigh–Ritz approach is taken where the responses of a structure to pseudo-loads (acting only over specified design-change regions) are employed as basis vectors. It is found that convergence of the optimization process is improved. The method is demonstrated for moderate-sized problems, and as with other modal methods, should become even more helpful for large problems. The new complexity involved is the requirement for a type of problem-dependent linking, in parallel with the conventional design variable linking. This can be automated. © 1997 by John Wiley & Sons, Ltd.     

An iterated IRS technique for cross-sectional damage modelling and identification in beams using limited sensors measurement

This paper presents an effective method for cross-sectional damage localization and quantification in beams. First, a new strategy is suggested for cross-sectional damage modelling by means of Iterated Improved Reduction System (IIRS) approach. Then, a novel damage localization index is proposed employing Grey System Theory (GST) as a geometrical criterion for quantifying the amount of correlation between vectors of the calculated curvatures for the diagonal members of the flexibility matrices in the damaged and undamaged states. Since the method employs only the modal data of the translational degrees of freedom, it can be interpreted as damage identification method by utilizing incomplete modal data or installing a limited number of sensors. After detecting the damage location, to estimate the exact parameters of the cross-sectional damage, the problem is defined as a finite element model-updating problem which is solved with a new evolutionary optimization approach named Imperialist Competitive Algorithm (ICA). The applicability of the method is demonstrated by studying different damage patterns on two numerical examples of beams. In addition, its robustness is investigated in the presence of random noises and modelling errors. Obtained results emphasize the high accuracy and promising performance of the method, especially when noisy incomplete modal data are used.     

强震下网壳结构性能的多模态整体损伤演化

在已有宏观地震整体损伤模型基础上,借助线性模态置信准则(英文简称LMAC)来考虑强震作用下网壳结构体系中普遍存在的模态跃迁现象,并结合网壳结构振动特性,给出了模态损伤贡献因子取值为1.0的简化模态损伤计算模型,结构整体损伤则由各阶模态损伤依据模态损伤独立性假设来进行组合得到。在将该模型应用于强震作用下某一算例施威德勒单层网壳结构的损伤演化规律分析与数值验证中发现,当认真处理好模态匹配和高阶模态对损伤的贡献度时,得到的损伤指数更符合通用正S型损伤发展规律,且与三条地震波作用下网壳结构增量动力分析(IDA)得到的特征响应,尤其是最大节点位移曲线吻合较好。此外,简化H2损伤模型不仅能够量化初始缺陷对结构整体初始损伤的影响,而且能够揭示初始缺陷对结构损伤影响的多模态特性。尽管计算结果与地震波的选择存在较大的关联,但是对应于各个特征点损伤数值却显示出较好的一致性。     

斜拉桥桥面结构损伤位置识别的指标比较

以香港汲水门大桥为背景,应用高精度三维有限元模型,对斜拉桥桥面结构损伤位置识别的模态曲率指标、模态柔度指标和斜拉索张力指标进行了比较研究.主要比较了(1)在无噪声情况下,三损伤指标对各种不同损伤情况的识别效果;(2)三损伤指标对损伤程度的敏感性;(3)三损伤指标的抗噪声能力.获得以下结论:(1)曲率和柔度指标在损伤定位上对不同类型的损伤情况显现一定的互补性;(2)同曲率和柔度指标比较,索张力指标对不同的损伤程度呈现较好的稳定性;(3)对大多数损伤情况,柔度指标的抗噪性最好,曲率指标最差.     

Incompressible and locking-free finite elements from Rayleigh mode vectors: quadratic polynomial displacement fields

Under pure bending, with an arbitrary patch of plane four-node finite elements, the exact analytical algebraic expressions of deformation, strain and stress fields are numerically captured by a computer algebra program for both compressible and incompressible continua. Linear combinations of Rayleigh displacement vectors yield the Ritz test functions. These coupled fields model pure bending of an Euler-Bernoulli beam with appropriate linearly varying axial strains devoid of shear. Such Courant admissible functions allow an undeformed straight side to curve in flexure. Since these displacement vectors satisfy equilibrium conditions, they are necessarily functions of the Poisson’s ratio. Applications in bio-, micro- and nano-mechanics motivated this formulation that blurs the frontier between the finite and the boundary element methods. Exact integration yields the element stiffness matrix of a compressible convex or concave quadrilateral, or a triangular element with a side node. For the generic energy density integral, the paper furnishes an analytical expression that can be incorporated in Fortran or C ⁺⁺. In isochoric plane strain problems, the Rayleigh kinematic mode of dilatation is replaced by a constant element pressure. The equivalent nodal loadings are calculated according to the Ritz variational statement. Subsequently, without assembling the global stiffness matrix, nodal compatibility and equilibrium equations are solved in terms of Rayleigh modal participation factors.     

基于叠加曲率模态改变率的梁结构损伤诊断

通过理论分析证明曲率模态差指标存在两个不足：一是对曲率模态节点处损伤不够敏感,二是不能有效反映损伤程度。对曲率模态差指标进行改进,提出叠加曲率模态改变率指标,理论上克服了原指标的不足。采用连续梁算例进行对比验证,结果表明新指标能够同时反映损伤位置和损伤程度,较曲率模态差指标更加优越。最后提出了基于新指标的单元损伤因子估算方法并验证了有效性。     

Reduction methods based on eigenvectors and Ritz vectors for nonlinear transient analysis

Reduction methods using eigenvectors and Ritz vectors as basis vectors are empolyed to reduce the finite element nonlinear system of equations using a 48 D.O.F. doubly curved thin plate/shell element. With and without basis updating, the solutions obtained by reduction methods are compared with the direct solutions. It is observed that basis updating is essential to obtain accurate solutions. The present reduction methods need a large number of basis vectors (eigenvectors and Ritz vectors) to account for the impact load which has high frequency characteristics. Furthermore, for nonlinear analysis, the reduction achieved in the CPU time are only marginal since most of the CPU time was spent in the calculation of the internal nodal force vector. These considerations indicate that reduction methods may not be efficient for the impact response analysis.     

单层网壳结构风振响应的主要贡献模态识别

网壳结构具有频谱分布密集、振型复杂的动力特性，在对该类结构进行风振响应分析时，通常存在着一些对响应贡献较大的高阶振型，但由于其频率较高而容易被忽略。因此，研究网壳结构风振响应的主要贡献模态分布规律有利于提高结构风振响应计算的精度和效率。本文利用Ritz-POD法，分析了单层球面网壳和单层柱面网壳结构风振响应的主要贡献模态，着重考察了主要贡献模态的自身参振能力。及其与脉动风压空间分布模式之间的关系。在此基础上，初步给出了网壳结构风振响应的主要贡献模态识别准则。     

模态曲率差法对梁结构的损伤诊断

首先在理论上证明模态曲率差法,对结构损伤识别的可行性,提出了用损伤前后的模态矢量差,来计算结构损伤因子矩阵的计算公式。为验证方法的正确性,采用一个标准梁算例给予验证,算例表明该方法对结构的损伤位置和损伤程度具有准确的识别能力。并在此基础上,根据两个线性假设,提出了一种可用于评价结构寿命的简易、有效的计算方法。     

单层球面网壳结构风致响应计算的块里兹向量法

单层球面网壳结构自振频率密集，且高阶模态可能对结构的风致响应有较大贡献。利用传统模态叠加法计算结构风致响应时需截取较多的模态，导致计算效率较低。本文提出的块里兹向量法所生成的向量都是被荷载所激发的，因此仅使用少数向量即可获得准确的响应结果。块里兹向量迭代所需的多荷载模式可以利用本征正交分解（POD）技术获得，这种技术将脉动风压场分解为与时间无关的协方差模态以及与空间位置无关的主坐标。根据风洞实验同步测量的风压数据，利用本文计算了0．1和0．2矢跨比的单层球面网壳的风致响应。通过与传统模态叠加法计算结果的对比分析说明了本文方法的有效性。     

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     

损伤定位向量法原理及应用

该文中证明了损伤定位向量存在的条件,推导了梁、柱和支撑单元的特征应力计算公式,改进了损伤后振型质量归一化系数的简化求解。完成了一个空间钢支撑框架模型损伤定位的数值模拟分析,模拟了包括支撑损伤和连接损伤的7种损伤模式。分别采用力锤激励和环境激励两种激励方式;使用自然激励技术和特征系统实现算法进行模态参数识别,得到了模态频率和振型;使用损伤定位向量法判定损伤单元,并对两种损伤模式进行了误差分析。结果表明:当损伤达到一定程度时,损伤定位向量法能有效判定损伤单元。     

基于加速度二次协方差矩阵参数变化比法的环境振动下结构损伤识别

在白噪声环境激励下,结构加速度响应的自相关/互相关函数构成一个新的二次协方差（CoC）矩阵,组成这一协方差矩阵的元素经证明是结构模态参数（频率、振型、阻尼）的函数;与提取模态参数的一般损伤识别方法相比,二次协方差矩阵包含结构振动的更多和更高阶模态信息。本文利用结构损伤前和损伤后的二次协方差（CoC）矩阵参数的变化比,对只基于振动输出的、环境振动下的结构进行损伤识别。对一个七层框架结构模型进行了数值模拟,首先对不同噪声程度、不同损伤位置和程度的损伤结构进行损伤定位,再结合模型修正法,对结构损伤程度进行识别,展示了该方法的有效性。     

Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam

This paper presents a detailed investigation on the modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam with hollow circular cross-section. To consider multiple crack effects, a cantilever beam including cracks is considered for six damage scenarios. Finite element models are constituted in ANSYS software for numerical solutions. The results are validated by experimental measurements. Ambient vibration tests are performed to extract the dynamic characteristics using Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) methods. Calculated and measured natural frequencies and mode shapes for undamaged and damaged beams are compared with each other. Automated model updating is carried out using the modal sensitivity method based on Bayesian parameter estimation to minimize the differences for damage detection. In addition, modal assurance criterion (MAC) and coordinated modal assurance criterion (COMAC) factors are obtained from the mode shapes and two set of measurements to establish the correlation between the measured and calculated values for damage location identification.     

Ritz analysis of vibrating rectangular and skew multilayered plates based on advanced variable-kinematic models

A variable-kinematic Ritz formulation based on two-dimensional higher-order layerwise and equivalent single-layer theories is described in this paper to accurately predict free vibration of thick and thin, rectangular and skew multilayered plates with clamped, free and simply-supported boundary conditions. The main result is the derivation at a layer level of so-called Ritz fundamental nuclei for the stiffness and mass matrices which are invariant with respect to both the assumed kinematic model and the type of Ritz functions. In this work, products of Chebyshev polynomials and boundary-compliant functions are chosen as admissible trial set. After studying the convergence of the method, its accuracy is evaluated, in terms of frequency parameters and through-the-thickness distribution of modal displacements, by comparison with some reference results available in the literature. Results for sandwich plates with soft core are given for the first time, which may serve as benchmark values for future research.     

Evaluation of structural joints in composites with modal parameters

The paper examines if modal parameters can be used in non-destructive test (NDT) methods for the control of the structural integrity of joints in large glass fiber reinforced polyester structures. Therefore, an attempt is made to look for a correlation between modal parameters and the accumulated damage of the joints of a stiffened plate structure that is subjected to several underwater explosions with successively higher shock loadings, until debonding of rib and panel is obtained. Attention is paid to the method used for the determination of the modal parameters. The evolution of the modal parameters in relation to the accumulated damage is discussed, after which it is concluded that modal frequency measurements are more appropriate as parameters in NDT of large structures than modal damping measurements.     

高层建筑结构之非线性地震响应分析

将高层建筑结构近似地等效成非线性弹性支承梁，以悬臂梁，柱之本征函数作为Ｒｉｔｚ矢量，用能量法推导出结构的运动方程，其自由度数及计算量均比用有限元法时大为减小，用本文的方法可以计算具弹塑性铰或弹塑性耗能器之剪切墙及框架式高层建筑结构，计算结果表明，采用非线性耗能器并引起高阻尼，可以显著地降低结构之地震响应。