刚柔耦合运动对起重机吊臂振动固有频率的影响

分析了大型起重机吊臂在变幅过程中存在的刚柔耦合的运动特点对吊臂在标称运动附近振动固有频率的影响，考虑了吊钩和滑轮组质量对吊臂振动固有频率产生的附加效应。基于柔性多体系统动力学理论，采用拉格朗日方程建立了吊臂在标称运动附近的微振动方程，用复模态分析中的状态矢量法对机构振动方程进行了解耦。计算结果表明，在非线性惯性系下，吊臂在标称运动附近的微振动有3对共轭复频率。与采用传统结构动力学方法相比，考虑刚柔耦合运动的因素时，吊臂在三个方向振动的固有频率都有所降低，同时固有频率还受吊臂绕定点转动角速度、吊钩和滑轮组质量的影响，但影响程度较小。

INFLUENCE OF RIGID BODY AND DEFORMATION COUPLING ON THE VIBRATING NATURAL FREQUENCIES OF THE BOOM IN A CRANE

Influence on the natural vibrating frequencies of the boom is analyzed, which is brought by rigid body and deformation coupling of the boom in a large crane when luffing. Additional influence on natural frequencies of the boom brought by mass of hook and pulley block is also taken into account. Based on theory of flexible multi-body system, equation describing vibration by the nominal motion is created by Lagrange method. And it is uncoupled by state vector approach in complex modal analysis. The results are three pairs of conjugate complex numbers and smaller than those worked out by the structure dynamics method. And the natural vibratioing frequencies are also influenced by rotary speed surrounding the given point and mass of hook and pulley block, but the effects are small.