变截面旋转裂纹梁横向振动特性的研究

对损伤结构进行动力特性分析是进行无损检测的重要基础,而对于旋转梁结构的裂纹损伤动力特性研究,却鲜有文献涉及。以变截面旋转裂纹梁为研究对象,对其横向振动特性进行研究,提出一种求解变截面旋转裂纹梁横向振动特性的新方法。首先利用扭转弹簧模拟裂纹效应,建立含裂纹梁局部柔度模型,然后采用Frobenius方法求解振动方程,得到方程的级数解析解,并研究裂纹位置和深度对振动频率的影响,分析不同损伤程度、不同转速工况下梁的前两阶固有频率变化情况。结果表明:本文方法是有效的,转速和损伤程度的变化并非独立影响梁的固有频率,两者间具有耦合作用机理,对于变截面梁同样成立。

Research on Transverse Vibration of Rotating Beams with Crack

The analysis of dynamic characteristics of damage structures is an important basis for non-destructive testing. However, there are few literatures concerning the study of dynamic characteristics of rotating beams with crack. In this paper, the transverse vibration characteristics of rotating beams with crack are investigated. Firstly, the crack effect was simulated using a torsion spring, and the lumped crack model of the beam was established. Then the Frobenius method was used to solve the vibration equation, and the series solution of the equation was obtained. The natural frequency of the damage structure was calculated, and the first two natural frequency variations of beams under different damage degree and rotating speeds was analyzed. Numerical simulation results verified the effectiveness of the proposed method. At the same time, it is found that the change of rotating speed and damage degree do not affect the natural frequency of the beam independently, there is a coupling mechanism between the two sides.