空间大挠度梁的有限元动力学响应分析

Finite Element Method for Dynamics Response Analysis of Large Deflection of Three-Dimensional Beam

何欢(Huan He)；陈国平(Guo-Ping Chen)

大挠度 ； 空间梁 ； 几何非线性 ； 非线性惯性 ； 弯扭耦合 ； 动响应 ； large deflection ； three-dimensional beam ； geometric nonlinearity ； nonlinear inertia ； coupled deformation of bending and torsion ； dynamic response

南京航空航天大學學報

37卷2期（2005 / 04 / 01）

198 - 202

簡體中文

从弹性梁的非线性应变位移关系出发，结合Hamilton变分原理推导出了作大挠度振动的空间梁的动力学有限元方程。方程中考虑了与变形相耦合的非线性惯性项。计算表明，作大挠度振动的悬臂梁的响应是由不同的谐波成分组成；在相同结构阻尼影响下，大挠度梁的稳态振幅比线性情况下的稳态振幅要低；非线性惯性项与弯扭耦合项对系统的动力学特性有比较明显的影响。

Based on the nonlinear relationship between strains and displacements, the finite element formulation for large deflection of three-dimensional beam is developed through Hamilton's variational principle. The formulation can describe the nonlinear vibration of the three-dimensional beam. Nonlinear inertia term coupled with the displacement of torsion is concerned. Calculational results show that the nonlinear response of a cantilever beam consists of a series of different harmonic waves; the stable amplitude plitude of the nonlinear vibration is smaller than that of the linear systems under the same structure damping; the dynamics characteristic can be significantly influenced by the nonlinear inertia term and the coupling terms of bending and torsion.