应用多刚体离散化方法对梁的动力屈曲和后屈曲分析

基于梁的多刚体离散化模型(有限段模型),建立了梁的链式多刚体_铰链_弹簧系统模型,利用坐标变换方法建立了相应的非线性多自由度系统的参数振动方程,并利用约束参数法对所得到的多度系统的Mathieu_Hill方程进行了梁的动力屈曲分析,得到系统的参数共振域.因为所用的离散化模型与动力方程对梁的变形并无限制,所以可以用所得到的数学模型在其失稳域对梁的动力后屈曲进行数值仿真分析.通过实例的数值仿真,证明了这种梁的参数振动模型与分析方法的正确性.

Analysis of Dynamical Buckling and Post Buckling for Beams by Finite Segment Method

Based on the multi-rigid body discretization model, namely finite segment model,a chain multi-rigid body-hinge-spring system model of a beam was presented, then a nonlinear parametrically exacted vibration equation of multi-degrees of freedom system was established using the coordination transformation method, and its resonance fields were derived by the restriction parameter method, that is the dynamical buckling analysis of the beam.Because the deformer of a beam isn't restricted by discrete model and dynamic equation, the post buckling analysis can be done in above math model. The numerical solutions of a few examples were obtained by direct integrated method, which shows that the mechanical and math model gotten is correct.