摘要
基于有限变形原理,采用微分几何的方法推导了不考虑剪切、转动惯量和翘曲影响的曲梁的三维变形的应力应变关系.然后利用Hamilton变分原理推导了三维空间曲梁在考虑三个位移自由度和三个转动自由度下的非线性动力学方程.把得到的非线性动力学方程退化为面内圆弧拱的线性动力学方程,并与已有结果进行了对比.非线性动力学方程的建立为曲梁的非线性动力学分析做好了必要的准备.
Based on the theory of large deformation and using the differential geometry. The paper derived the relationship of strain and displacement for spatial curved beams, taking into account the longitudinal strains and torsion strains, but neglecting the effects of shear, moment of inertia and warping. The Hamilton variation principle was used to derive the nonlinear dynamics equations of spatial curved beam under three-displacement- freedom and three-rotation-freedom, which can be degenerated to linear dynamics equations of planar circular arch, and their results were compared with the results in literatures. The nonlinear dynamics equations provide a reliable foundation for analysis of the nonlinear dynamics of curved beam.
出处
《动力学与控制学报》
2005年第4期34-38,共5页
Journal of Dynamics and Control
关键词
空间曲梁
动力学方程
微分几何
变分原理
spatial curved beam, nonlinear kinematic equation, differential geometry, variation principle
