模态平均曲率在悬臂挡墙损伤检测中的应用

Application of Modal Mean Curvature in Damage Detection for Cantilever Retaining Wall

目前曲率方法主要应用于一维梁结构损伤位置的确定,如模态曲率和柔度曲率,因此本文提出一种适用于二维悬臂挡墙的损伤识别方法——模态平均曲率差法,该方法仅需挡墙完好和损伤状态下前几阶模态振型。首先引入微分几何理论中曲面上一点的平均曲率概念,通过该点上2个主曲率求其平均曲率,利用中心差分法计算挡墙损伤前、后的模态平均曲率值,再利用其差值的绝对值作为损伤识别新指标;然后通过损伤指标识别挡墙的损伤位置,建立损伤位置处的损伤程度和指标值的拟合曲线,进而确定其损伤程度;最后通过悬臂挡墙数值算例,验证不同损伤位置和损伤程度下所提出方法的有效性和敏感性。研究结果表明,模态平均曲率差法的损伤识别精度令人满意。因此,该方法可为挡墙损伤检测提供理论参考依据,并具有工程应用价值。

At present,curvature method,e. g.,mode shape curvature and flexibility curvature methods have been mainly applied to localize damage in 1D beam structures,so a new damage identification method for 2D cantilever retaining wall,i. e.,modal mean curvature difference method,is proposed. The method requires only the mode shapes of the first few modes of both the intact and damaged states. First,the concept of surface mean curvature in differential geometry theory,which is introduced and obtained through 2 principal curvatures on the point,the modal mean curvatures of the retaining wall before and after damage are calculated by using the central difference method,and the absolute value of the modal mean curvature difference is presented as a new index of damage identification. Then,the damage location of retaining wall is identified by the index,the fitting curve between damage extent and index is established to evaluate the damage extent. Finally,numerical simulations of cantilever retaining wall considering different damage locations and damage extents are conducted to verify the effectiveness and sensitivity of the proposed method.The result indicates that the damage identification accuracy of the proposed method is satisfactory. Therefore,the method can provide a theoretical reference basis for damage detection of retaining wall and owns engineering value.