旋转薄板的一种高次动力学模型与频率转向

对固结于转动刚体上柔性薄板的刚柔耦合动力学和频率转向特性进行了深入研究,建立了系统的高次刚柔耦合动力学模型,该动力学模型计入了由于横向变形而引起的面内纵向缩短项,即非线性耦合变形量,并且完整保留了与非线性耦合变形量相关的所有项. 研究表明,高次耦合模型不仅适用于小变形问题,而且还适用于大变形问题,弥补了一次近似耦合模型在处理大变形问题上的不足. 旋转悬臂薄板相邻两阶模态间既有柔和的频率转向现象也有剧烈的频率转向现象. 柔和的频率转向伴随着的振型转换的过程是连续的,而剧烈的频率转向伴随着的振型转换的过程则是不连续的. 相隔多阶模态间存在传递性频率转向,并伴随着振型转移. 

A HIGH-ORDER RIGID-FLEXIBLE COUPLING MODEL AND FREQUENCY VEERING OF A ROTATING CANTILEVER THIN PLATE

The rigid-flexible coupling dynamics and frequency veering of a thin flexible plate on a rotating rigid body are further studied. The high-order coupling (HOC) dynamic model is derived by Lagrange's equations. The in-plane longitudinal shortening terms caused by lateral deformation, generally called non-linear coupling deformation terms, are considered here. Furthermore, all derived items associated with the non-linear coupling terms are retained completely in the HOC model. The HOC model can not only be applied in the small deformation case, but also in the large deformation case, and makes up the deficiency of the first-order approximation coupling (FOAC) model in the large deformation case. In addition, the frequency veering phenomena along with the corresponding mode shape variations are exhibited and discussed in detail. When two frequency loci veer, the nodal line patterns of the mode shapes switch their shapes each other, and the changes of the nodal line patterns are continuous in the mild veering region, while those in the abrupt veering region are discontinuous. The transitive frequency veerings among the multiple modes accompanied by mode shape transfer are also exhibited.