疲劳裂纹叶片振动的非线性特性研究

On Non Linear Vibration Characteristics of Blade with Fatigue Crack

以带疲劳裂纹悬臂梁为例研究疲劳裂纹对叶片固有频率及强迫振动响应的影响。应用传递矩阵法求解裂纹叶片振动响应，选用余弦函数模拟疲劳裂纹的开合过程，理论分析了裂纹叶片的非线性振动特性，并进行裂纹试件实验。理论分析及实验结果都表明疲劳裂纹不仅使悬臂梁的固有频率下降，而且引起强迫振动响应的非线性特征。最后，就叶片裂纹故障监测特征量的选取做了分析、讨论。

Aiming at effective on line monitoring of blade crack fault, we studied the natural frequency and forced vibration of a cracked cantilever beam (Fig.1). We used transfer matrix method to calculate the natural frequency (Fig.3) and non linear characteristics (Figs.4 and 5), with the fatigue cracks open close process being simulated by a cosine function. We also determined experimentally the natural frequency as well as the damping coefficient (Fig.6) and non linear characteristics (Fig.7). Calculated results are in good agreement with test data. Fatigue crack decreases natural frequency as is to be expected. As crack depth increases, there is increasing non symmetry very important for on line monitoring for vibration amplitude and half period (Fig.7). In Figs.5 and 7, D a and D p are the coefficients of non symmetry for amplitude and half period respectively. As non symmetry appears, the frequency spectrum exhibits not only the excitation frequency but also its multiples. The multiples are also useful for on line monitoring.