A novel spectral transfer matrix for a cracked beam element is developed in this article and the same is used to identify the crack parameters on the beam structures. Spectral transfer matrix is developed from trigonometric functions based on the theory of fracture mechanics. This matrix determines the natural frequencies of a structure with crack with better accuracy than any other transfer matrices in the literature. The state vector at a node on the structure is formed which includes the displacement, rotation, internal and external forces, and moments at that node. When the state vector is multiplied with the transfer matrix, the state vector at the adjacent node is obtained. Each element is assumed to have a single open breathing crack with unknown depth and location. Initially, the developed spectral transfer matrix is used to determine the natural frequencies of a known cantilever, and after successful validation, the same is used for crack damage detection. By an inverse approach, crack parameters in each element are identified. The state vector at one node on the structure is obtained by measurement of input and out responses which is known as the initial state vector. Acceleration responses at selected nodes on the structure are measured and the state vectors at those nodes are predicted using spectral transfer matrices. The mean square error between measured and simulated responses is minimized using a heuristic optimization algorithm, with crack depth and location in each element as the optimization variables. Spectral transfer matrix method is applied to two numerical problems with single crack in each element; later, this method is successfully validated experimentally with structures having different boundary conditions. The accuracy in identified crack parameters and the applicability to sub-structures of a large structure are the important aspects of this method.

本文开发了一种新的裂纹梁单元的谱传递矩阵，并将其用于识别梁结构上的裂纹参数。光谱传递矩阵是基于断裂力学理论的三角函数开发的。该矩阵确定具有裂纹的结构的固有频率，其精度要比文献中的任何其他传递矩阵更好。形成了结构上一个节点的状态向量，该状态向量包括位移，旋转，内外力以及该节点上的力矩。当状态向量与传输矩阵相乘时，将获得相邻节点的状态向量。假定每个元素都有一个未知深度和位置的开放式呼吸裂缝。原来，所开发的光谱传输矩阵用于确定已知悬臂的固有频率，并在成功验证后将其用于裂纹损伤检测。通过反向方法，可以识别每个元素中的裂纹参数。结构的一个节点上的状态向量是通过测量输入和输出响应获得的，称为初始状态向量。测量结构上选定节点处的加速度响应，并使用频谱转移矩阵预测这些节点处的状态向量。使用启发式优化算法将实测响应与模拟响应之间的均方误差最小化，并将裂纹深度和每个元素中的位置作为优化变量。光谱传递矩阵法应用于两个数值问题，每个元素中都有一个裂纹。后来，该方法已成功通过实验验证了具有不同边界条件的结构。确定裂纹参数的准确性以及对大型结构子结构的适用性是该方法的重要方面。