中文摘要：

研究工字截面梁轨结构裂纹定量识别中的正反问题,即通过裂纹位置和深度求解结构的固有频率以及利用结构的固有频率,识别裂纹位置和深度。裂纹被看作为一扭转线弹簧,利用工字梁裂纹应力强度因子推导出线弹簧刚度,构造出结构的小波有限元刚度矩阵和质量矩阵,从而获得裂纹结构的前3阶固有频率。通过行列式变换,将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题,分别做出以不同固有频率作为输入值时裂纹位置与裂纹深度之间的解曲线,曲线交点预测出裂纹的位置与深度,试验结果验证算法的有效性。

英文摘要：

The forward and inverse problems in crack identification of I-beams are studied.The forward problem is to determine the first three natural frequencies of the cracked beam given the location and size of the crack and the inverse problem is to determine the location and size of the crack given the first few natural frequencies of the cracked I-beam.By taking the cracked rail with I cross-section as an example,the model of the beam based on wavelet finite element methods is constructed and the first three natural frequencies are obtained.The crack is modeled as a rotational spring.A fast algorithm of inverse problem is presented which transforms the vibration frequency equation into the quadratic equation with only one unknown parameter,the rotational spring stiffness,by the determinant transformation method.Then the graphs of crack depth versus crack location are plotted for each natural frequency.The point of intersection of the curves gives the location and size of the crack.The experimental example indicates that the current method is effective and accurate.This study provides a new method for the prognosis and diagnosis of cracks in I-beam structures.