一种长悬臂梁结构动力学建模方法

为了有效抑制长悬臂梁结构在受到固定端持续传来的周期性振动时在远端连接处产生的疲劳破坏，保护悬臂梁结构，需要对其远端连接处保持的辅助支撑机构施加一定的主动抑振控制算法。为此提出悬臂梁结构动力学建模，为控制算法分析、参数设计和研究提供模型基础。在对欧拉-伯努利梁振动模型和柔性基础简化模型的分析基础上，根据固定端输入的周期性振动信号推导出辅助支撑点处的含柔性基础悬臂梁振动微分方程，并结合梁的结构推导出符合实际的结构动力学模型。通过计算仿真，获得柔性基础悬臂梁的动态响应并确认了模型的准确性。因此为长悬臂梁结构提供了一种有效的建模方案并对具有柔性基础的机械臂的振动抑制具有一定的借鉴意义。

A Structural-Dynamic-Modeling Method for Long Cantilever Beam

The long cantilever beam structure connected by multiple sections is often designed as a multi-point support.It is easy to generate fatigue and breakage at the distal joint when it is subjected to periodic vibration continuously transmitted from the fixed end,resulting in a significant reduction in fatigue life.In order to achieve effective vibration suppression and protect the structure,it is necessary to apply a certain active control algorithm to the auxiliary support manipulator holding the beam.The cantilever beam structure dynamics modeling proposed is intended for providing a model basis for parameter-designation of the control algorithm.Based on the analysis of the Euler-Bernoulli beam vibration model,the vibration differential equations of the beam are derived,and the actual structural dynamics model is established based on the structure of the beam.Finally,through the calculation and simulation,the dynamic response of the cantilever beam is obtained and the accuracy of the model is confirmed.It provides an effective modeling solution for the long cantilever beam structure and has certain reference significance for the vibration suppression of the manipulator with flexible foundation.