柔度差曲率,损伤识别

第26卷第2期 V ol.26 No.2 工 程 力 学 2009年 2 月 Feb. 2009 ENGINEERING MECHANICS

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收稿日期：2007-10-26；修改日期：2008-04-21

基金项目：国家自然科学基金项目(50678013)；中国博士后科学基金项目(20060390387)

作者简介：*李永梅(1971―)，女，河北邢台人，副教授，博士后，主要从事结构工程研究(E-mail: liym@)； 周锡元(1938―)，男，江苏无锡人，研究员，主要从事地震工程研究(E-mail: zhouxy@)； 高向宇(1959―)，男，北京人，教授，博士，主要从事结构工程减震研究(E-mail: gaoxy@)

文章编号：1000-4750(2009)02-0188-08

基于柔度差曲率矩阵的结构损伤识别方法

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李永梅1,2，周锡元1,3，高向宇1

(1. 北京工业大学建筑工程学院，北京 100124；2. 北京工业大学城市与工程安全减灾省部共建教育部重点实验室，北京 100124；

3. 工程抗震与结构诊治北京市重点实验室，北京 100124)

摘 要：柔度是较频率和位移模态更敏感的结构损伤标示量。提出利用结构损伤前、后的柔度矩阵，先后对柔度矩阵差的列、行进行两次差分，求得柔度差曲率矩阵(δ Flexibility Curvature Matrix)，并以其对角元素作为检测结构损伤指标(δ FCMD)的新方法。该方法仅需低阶模态参数即可进行损伤检测，不论对简支梁、悬臂梁、固支梁，或多跨连续梁，单一位置损伤、支撑处损伤、轻微损伤，还是多种损伤共存，均具有损伤定位的能力、并能定性反映损伤程度。通过与已有的柔度差、柔度变化率、均匀荷载面曲率差等柔度指标的数值模拟分析研究，显示了该指标检测损伤的有效性和优越性。

关键词：结构；损伤识别；柔度；曲率；柔度差曲率矩阵 中图分类号：O327; TU311.3; TB123 文献标识码：A

DETECTION INDICTOR OF STRUCTURAL NONDESTRUCTIVE

DAMAGE BASED ON CURVATURE-FLEXIBILITY-DIFFERENCE MATRIX

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LI Yong-mei 1,2 , ZHOU Xi-yuan 1,3 , GAO Xiang-yu 1

(1. College of Civil Engineering and Architecture, Beijing University of Technology, Beijing 100124, China;

2. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education of China, Beijing University of Technology, Beijing 100124, China;

3. Beijing Key Laboratory of Earthquake Engineering Structural Retrofit, Beijing 100124, China)

Abstract: For structural damage, the flexibility is more sensitive than its frequency or mode. The curvature difference matrix in flexibility is presented as a new index of nondestructive damage detection, derived from the change in structural flexibilities calculated before damaging and after damaging by means of difference calculation twice, firstly to columns, and then to rows. Therefore a new indicator called δFlexibility Curvature Matrix Diagonal (δ FCMD) is constructed through principal diagonal elements based on the curvature difference matrix in flexibility. Numerical simulation examples indicate that the damage location and severity in structures, with single damage, multiple ones, lighter ones and ones at the supports, can be detected efficiently for cantilever beams, fixed supported beams, simply supported beams, continuous beams and so on by δFCMD through only a few of the lower order modes. Compared to the aforementioned flexibility indicators and δ FCMD, such as the change in flexibility, the rate in flexibility, the curvature change in uniform load surface (ULSC), the effectiveness and advantage of δ FCMD, etc are shown.

Key words: structure; nondestructive damage detection; flexibility; curvature; δ flexibility curvature matrix

近年来，各类结构的无损探伤检测一直是土木工程研究的热门课题。由于结构的高阶模态往往难

以获得，这就使得基于刚度矩阵的方法难以应用于工程实践中。与之相反，由于柔度矩阵可以比较精