基于契贝雪夫多项式曲率模态在结构损伤检测中的应用

Application of curvature mode in damage detection of plate-like structure based on Chebyshev polynomial

曲率模态在结构损伤检测中具有对结构损伤部位非常敏感的特性,从而曲率模态计算的准确度是影响检测结果的重要因素。传统方法主要是运用中心差分法求解曲率模态,由于中心差分法的计算精度依赖于测点分布的紧密程度,这样就使结构检测结果具有很大的误差。函数按契贝雪夫多项式展开式具有很高的逼近特性。本文运用这种特性提出板类结构损伤检测的曲率模态算法——契贝雪夫多项式逼近算法,构造板类结构振型的契贝雪夫多项式函数,对该函数进行求二阶偏导得到x和y方向的曲率模态,进而求出结构损伤前后的曲率模态差,为结构损伤检测提供可靠的数据,从而达到良好的检测效果。

Curvature mode is very sensitive to the local damage of a structure in damage detection, therefore the accuracy of the curvature mode computation is of significance for the results of damage detections. The traditional method for curvature mode computation is the central difference method, but its accuracy is well known depended on the density of the measurement grid, which may induce a very large error in dynamic damage detection. On the basis of a good approximation of the Chebyshev polynomial, in the present paper the authors defines a Chebyshev polynomial function of the mode shape, the sectond derivatives of which then leads to the corresponding curvature mode. This method provides a reliable data for dynamic damage detection.