中文摘要：

以等效弹簧模拟裂纹引起的局部软化效应，应用Bernoulli-Euler梁理论建立双裂纹阶梯悬臂梁的振动特征方程。鉴于方程含有较多的未知量，提出联合小波变换和结构测量频率的裂纹参数识别两步法。首先，含裂纹悬臂梁的一阶模态作为信号用于连续小波变换，通过小波系数的局部极值可以清楚地确定结构的裂纹位置。其次，将识别得到的裂纹位置代入双裂纹阶梯悬臂梁的特征方程，最后通过绘制两个裂纹的等效柔度的等值线图，通过交点确定满足特征方程的两个裂纹的等效柔度，并进一步确定裂纹深度。最后利用数值算例验证该方法的有效性。

英文摘要：

A two-step method is suggested to identify separately the location and the depth of cracks in a stepped cantilever beam, which incorporates the merit of wavelet transform with the merit of natural frequency measurement. Firstly, the wavelet analysis is apphed to the fundamental vibration mode of the stepped beam, The crack location is found by the peak value of the wavelet coefficients. Secondly, based on the identified crack locations, a frequency-based method requiring the first two tested natural frequencies only is used to further identify the crack depths. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.