基于无网格点插值法的旋转悬臂梁的动力学分析  

A meshfree method based on point interpolation for dynamic analysis of rotating cantilever beams

作　　者：杜超凡 章定国[1] 

机构地区：[1]南京理工大学理学院,南京210094

出　　处：《物理学报》2015年第3期396-405,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11272155;11132007);江苏省"333"工程(批准号:BRA2011172);高校基本科研业务专项资金(批准号:30920130112009)资助的课题~~

摘　　要：将基于多项式点插值的无网格方法用于旋转悬臂梁的动力学分析.利用无网格点插值方法对柔性梁的变形场进行离散,考虑梁的纵向拉伸变形和横向弯曲变形,并计入横向弯曲变形引起的纵向缩短,即非线性耦合项,运用第二类Lagrange方程推导得到系统刚柔耦合动力学方程.与有限元法相比,该方法只需节点信息,无需定义单元,具有前处理简单的优势;构造的形函数采用更多的节点插值,具有高阶连续性.将无网格点插值方法的仿真结果与有限元和假设模态法进行比较分析,验证了该方法的正确性,并表明其作为一种柔性体离散方法在刚柔耦合多体系统动力学的研究中具有可推广性.A meshfree method based on polynominal point interpolation method（PIM） is proposed for dynamic analysis of a rotating cantilever beam; PIM is used to describe the deformation of the flexible beam. Its longitudinal and transverse deformations are both taken into consideration, and the coupling term of the deformation which is caused by the transverse deformation is included in the longitudinal deformation of the beam. The rigid-flexible coupling dynamic equations of the system are derived via employing Lagrange＇s equations of the second kind. Compared with the finite element method（FEM）, only individual nodal data are required in the current method so that its preprocessor is easier,and the shape functions constructed have high-order continuities due to more nodes to be interpolated. Simulation results of the meshfree method are compared with those obtained by using FEM and assumption of modes method. It is demonstrated that the meshfree method can be extended to the field of multibody system dynamics.

关 键 词：柔性梁 多项式点插值 无网格法 固有频率 

分 类 号：O342[理学—固体力学]