空间网格结构动力分析的非线性模态方法

Nonlinear Mode Method for Dynamic Analysis of Spatial Latticed Structures

空间网格结构因自由度数多且无简化的力学模型,非线性动力分析通常要耗费大量时间.传统的非线性模态方法用于求解多高层结构的局部非线性问题已获得良好的效果,但对系统非线性问题的应用尚缺少研究.对比分析多高层结构和空间网格结构动力性能差异,指出网格结构动力非线性分析存在的问题.以主振型理论和切线刚度分离法为基础,将非线性模态方法用于几何非线性效应显著的空间网格结构动力分析.通过对运动方程的非线性恢复力进行拆分,形成线性表达形式,然后解耦到主振型所在的广义坐标系,以达到缩减自由度数量的目的.并通过实例验证非线性模态方法的高效性与适用性.

Nonlinear dynamic analysis of spatial latticed structures will spend much time because of its un-simplified model with large degree of freedoms（DOFs）. It turns out to be satisfied that traditional nonlinear mode dynamic method is applied on solving local nonlinearity of multi-storey structures, however, few researchers try to use the method to analyze systematical nonlinearity of spatial latticed structures. Dynamics characteristics of multi-storey and spatial latticed structure were discussed by comparison, then some problems encountered by nonlinear dynamic analysis of spatial latticed structure were listed. Based on dominant vibration theory and tangent stiffness separation method, nonlinear mode method was updated to be suit for dynamic analysis of spatial latticed structure with significant geometrical nonlinearity. The method aims at reducing number of DOFs and solving differential equation efficiently by such a series of manipulations, where they are splitting up restoring force vector into linear and nonlinear parts, changing equation of motion to be linear formally, decomposing the converted equation of motion by the generalized coordination consisting of dominant vibration mode vector and time-stepping integral so on. In the end, the efficiency and applicablity of nonlinear mode method was verified by Gedesike shell.