非惯性系下考虑剪切变形的柔性梁的动力学建模  

Dynamic modeling of flexible beam with considering shear deformation in non-inertial reference frame

作　　者：和兴锁[1] 宋明[1] 邓峰岩[1] 

机构地区：[1]西北工业大学工程力学系,西安710072

出　　处：《物理学报》2011年第4期316-321,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10672133)资助的课题~~

摘　　要：研究非惯性坐标系下考虑剪切变形的柔性梁的动力学建模.首先借鉴Euler-Bernoulli梁的几何非线性变形模式,考虑了Timoshenko梁弯曲以及剪切变形产生的几何非线性效应对纵向、横向变形位移的影响,在考虑两个方向的变形耦合项后,利用有限元法对柔性梁进行了离散,采用Lagrange方程建立了柔性梁的动力学模型,首次建立了包含变形二次耦合量的Timoshenko梁的动力学方程.In this paper,the effect of shear deformation is considered into flexural deflection of the geometrically nonlinear deformation of a flexible beam.Then,considering the coupling effect of deformation in to the extensional and flexural deflection,the second-order coupling terms of deformation in two displacement fields are developed and the axial inertial force and transverse distributed force are considered.The finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange＇s equations.In this way,the new governing differential equations of the beam in the geometrically non-linear kinematics of deformation are derived.Numerical examples of a flexible beam are studied to analyze the effect of shear deformation on the dynamic character and to investigate the coupling effect.Furthermore,from this present method,a moving Timoshenko beam can also produce the dynamic stiffening phenomenon and some new properties can be shown.

关 键 词：非惯性坐标系 剪切变形 柔性梁 动力学建模 

分 类 号：O302[理学—力学]