应变能中耦合项对旋转悬臂梁振动频率的影响

大范围运动悬臂梁的动力学建模问题对动力学特性分析及控制系统设计具有极其重要的作用. 当前研究多采用一次近似模型,其忽略了由轴向和横向变形所产生的应变能中的耦合项,然而这些项对动力学特性会产生影响. 通过讨论应变能的选取方式,计入了应变能中的耦合项;利用哈密尔顿原理建立结构的耦合振动模型;再借助瑞利—里兹法,以无大范围运动时的振型函数作为基本解组,得到了结构振动广义特征方程并求解. 通过数值算例对比分析,指出考虑应变能耦合项得到的频率与不考虑应变能耦合项得到的频率存在明显差别. 

EFFECTS OF COUPLING TERMS IN STRAIN ENERGY ON FREQUENCY OF A ROTATING CANTILEVER BEAM

Dynamic modeling of a rotating cantilever beam is very important for dynamic characteristics analysis and controller design. In literature, the coupling terms between axial and transverse deformation in strain energy are ignored in first order approximate model. However, as shown by this paper, these terms have a significant impact on the dynamic characteristics. By discussing how to select the strain energy, this paper takes into account the coupling terms. Based on Hamilton's principle, the coupling vibration equations of the rotating cantilever beam are obtained. Using Rayleigh- Ritz method, the bending mode shapes of the beam without rotational motion are selected as basic functions to derive characteristic equation. A numerical example is presented to show that the evident difference of bending frequencies between the models with and without the coupling terms in strain energy.