基于敏感性分析的周期结构损伤检测

DAMAGE DETECTION IN PERIODIC STRUCTURES BASED ON A SENSITIVITY METHOD

介绍了一种基于敏感性分析的周期结构损伤检测方法的基本原理。首先得到了具有单一损伤的周期结构固有频率的一般表达式,并运用在不同单元出现损伤时的第一阶自振频率的近似值形成特征值敏感性矩阵;然后通过求解一组基于上述特征值敏感性矩阵的线性方程,识别出结构损伤位置和大小;针对大型结构可能出现多处损伤的特点,文章最后还介绍了一种方法,它不仅能改善计算精度,而且能提高计算效率。理论分析和数值结果表明周期结构自振频率对不同位置损伤的敏感性仅仅与结构单元数目和损伤位置有关,基于敏感性分析的方法能够准确识别出结构的损伤。

A damage detection procedure applied to mono-coupled periodic systems using a sensitivity-based method is presented in this paper. The first order approximation of the natural frequencies with respect to one single damage in different elements is obtained and then used to form the sensitivity matrix. Consequently, the stiffness changes due to damage can be identified by solving a set of underdetermined equations based on the sensitivity matrix. For complex structures, there are many possible damage locations, a means of improving the computational efficiency of damage detection while maintaining the accuracy for large periodic structures with limited available measured natural frequencies is introduced. The theoretical analysis and numerical results show that the sensitivity of natural frequencies to damage in different locations depends only on the mode number and the location of damage, and the proposed method can locate correctly single or multiple damages in a large periodic structure.