考虑不同边界条件悬臂梁的模态研究

刘建英, 王效岳,宫金良

振动与冲击 ›› 2017, Vol. 36 ›› Issue (19) : 221-226.

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (19) : 221-226.
论文

考虑不同边界条件悬臂梁的模态研究

  • 刘建英, 王效岳,宫金良
作者信息 +

Modal analysis of cantilever beams with different boundary conditions

  •   LIU Jianying   WANG Xiaoyue  GONG Jinliang
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摘要

为了提高假设模态法建立动力学模型的精确性,研究了将柔性机械臂简化为更精确的悬臂梁模型的问题。通过分析不同边界条件对Euler-Bernoulli悬臂梁横向振动的影响规律,将悬臂梁自由端的剪力边界条件具体化为集中质量和拉伸弹簧,弯矩边界条件具体化为扭转弹簧和转动惯性元件,得到了各种边界条件下悬臂梁的模态频率和模态振型的变化规律。结果表明添加边界条件的悬臂梁模型可以更好地表示柔性机械臂的模态振动,因此可以提高假设模态法建立的动力学模型的精确性。针对柔性机械臂之间模态振动耦合较强,添加边界条件无法表示柔性机械臂模态频率的变化规律,提出了修正当量密度的方法。最后给出了边界条件和修正当量密度的迭代计算方法,并用ANSYS和ADAMS联合仿真分析了由驱动关节和自由关节连接的二连杆柔性机械臂模型对应的模态振动,验证了计算方法的正确性。

Abstract

In order to improve the accuracy of the established dynamic model of the assumed mode method, the flexible manipulator is simplified as the cantilever beam model is more precise problem. By analyzing the influence of different boundary conditions on the lateral vibration of Euler-Bernoulli cantilever beam, the shear boundary condition of cantilever free end into a specific mass and tensile spring, bending moment boundary conditions specific for torsion springs and rotational inertia components, obtained various boundary conditions under the cantilever beam modal frequency and vibration modal. The results show that adding boundary conditions of the cantilever beam model can better describe the vibration of the flexible manipulator, it can improve the accuracy of the dynamic model of the assumed modal method. According to the mode coupling between the flexible manipulator is strong, variation of boundary conditions to add modal frequencies, and puts forward the method of equivalent density correction. Finally, boundary conditions and modify the equivalent density of iterative calculation method, and using ANSYS and Adams co simulation analysis by the driving joints and free joints connecting two link flexible manipulator model corresponding to the vibration mode to verify the correctness of the calculation method.
 
 

关键词

柔性机械臂 / 悬臂梁模型 / 边界条件 / 模态振动

Key words

 flexible manipulator / cantilever beam model / boundary condition / modal vibration

引用本文

导出引用
刘建英, 王效岳,宫金良. 考虑不同边界条件悬臂梁的模态研究[J]. 振动与冲击, 2017, 36(19): 221-226
LIU Jianying WANG Xiaoyue GONG Jinliang. Modal analysis of cantilever beams with different boundary conditions[J]. Journal of Vibration and Shock, 2017, 36(19): 221-226

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