薄板损伤检测的高斯曲率模态差方法

Damage detection for an elastic thin plate based on Gauss curvature modal difference

采用结构损伤前后振动的曲率模态差来检测薄板结构的损伤,引入微分几何理论中曲面上一点的高斯曲率概念,通过该点上两个主曲率求其高斯曲率,同时用中心差分求解薄板结构损伤前后的曲率模态值,利用其差值确定薄板的损伤位置,进而确定损伤程度。数值仿真的损伤检测算例表明,曲率模态检测方法的损伤识别精度令人满意。

The feasibility of damage detection for plate structures using curvature modal difference was explored.The concept of Gauss curvature in differential geometry was introduced to calculate the curvature modes from the deflection modes of a plate.A simply supported rectangular plate was adopted in the verification of the proposed damage detection method.In the simulation of damage detection,the curvature modal differences between an intact plate and a damaged plate were calculated,and the location of damage could be identified from the variation of the curvature modal differences.Furthermore,an index was also proposed to evaluate damage level using curvature modal differences together with natural frequencies of the damaged plate and the intact one.Numerical simulations for the detection of damage location and damage level were performed and the results showed that the presented method is feasible and effective for damage detection of plate-like structures.