梁类结构多裂纹微弱损伤的小波有限元定量检测方法

提出了一种定量检测梁类结构多裂纹参数的方法。利用适宜求解奇异性问题的小波有限元法，从动力学正问题入手，对裂纹梁进行有限元建模，获得裂纹故障在结构固有频率上反映的本质征兆，并利用曲面拟合技术绘制出以裂纹位置和深度作为变量的固有频率变化率曲面，然后对整个裂纹梁进行剖分，迭代求解出每个剖分单元上的结构损伤系数。损伤系数为正的单元诊断为裂纹单元，在每个裂纹单元上求出裂纹对应的前三阶固有频率变化率，并分别将其作为输入参数代入固有频率变化率曲面，做出前三阶模态的频率变化率等高线，最后通过三条等高线的交点预测出裂纹存在的位置和深度，算例分析验证了该算法的有效性。

MULTIPLE INFANT CRACKS DETECTION FOR BEAM-TYPE STRUCTURES BY WAVELET FINITE ELEMENT METHOD

A method for identification of multiple cracks in beam-type structures is presented. The changes in nature frequency of the structure with various crack locations and depths are accurately obtained by means of wavelet finite element methods, and then the surface-fitting technique is employed to plot the surfaces of nature frequency shifts. The global cracked beam is divided into coarse mesh and the expressions relating changes in natural frequency and damage index matrix are formulated via an influence matrix. Damage index matrix can be solved by the resulting system of linear algebraic equations. The elements corresponding to the damage indexes with positive values are predicted to contain the crack. In each damage element, the corresponding natural frequency shifts are used as input in multiple cracks detection process and the crack locations and depths can be identified through finding the points of intersection of three frequency contour lines. Numerical example is employed to demonstrate the effectiveness of the presented method.