高柔悬臂结构的弯曲型集中质量模型研究

Bending Lumped Mass Model of High Flexibility Cantilever Structure

基于质量集中和刚度等效的原则,提出了一种将高柔悬臂结构简化为弯曲型集中质量模型的新方法。首先,根据集中质量法确定简化模型节点处的集中质量。然后,基于振动特征方程和悬臂结构柔度矩阵中各元素与抗弯刚度的倒数之间具有线性关系的特点,推导出固有频率与层间等效抗弯刚度之间的非线性关系式;通过有限元软件对结构进行模态分析,提取其固有频率,将提取的固有频率代入关系式即可计算出等效抗弯刚度。最后,用数值算例对比验证了该模型简化方法的有效性和精确性。

According to the principles of mass lumped and stiffness equivalent, a new method is proposed to simplify the high flexibility cantilever structure to bending lumped mass model. Firstly, the lumped mass at the node Of simplified model is deter- mined by the lumped mass method. Secondly, based on the vibration characteristic equation and the characteristics of linear rela- tionship between each element of the cantilever structure＇ s flexibility matrix and the reciprocal of bending stiffness, the nonlinear relationship between the natural frequency and the interlayer equivalent bending stiffness is deduced. By finite element modal analy- sis of the cantilever structure, the natural frequency of the structure is extracted, and it can be prepared into the relative equation to calculate the equivalent bending stiffness. Finally, a numerical example is used to contrast with above calculation and to verify the validity and accuracy of the model-simplified method.