基于柔度差曲率矩阵的结构损伤识别方法

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(δFlexibility Curvature Matrix),并以其对角元素作为检测结构损伤指标(δFCMD)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。

DETECTION INDICTOR OF STRUCTURAL NONDESTRUCTIVE DAMAGE BASED ON CURVATURE-FLEXIBILITY-DIFFERENCE MATRIX

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.