时间谱元法在动态响应优化中的应用

摘要

研究用时间谱元法求解运动微分方程,从Bubnov-Galerkin方法出发,深入探讨在时间域内离散动态响应,将整体运动微分方程组转化成代数方程组,精确高效解出瞬态响应；提出了关键点及其相邻GLL(Gauss-Lobatto-Legendre)点法处理与时间相关的约束,并且提出了时间谱元法的单元划分和插值次数为动态载荷变化程度的函数.以弹簧减振器设计以及汽车悬挂系统设计为例,引人人工设计变量,分析了处理约束方法的优缺点,也说明了此方法的正确性.为进一步研究动态响应优化提供参考.%The temporal spectral element method is adopted to solve the dynamic differential equations.After the discrete dynamic response in time domain is deeply considered,the second order differential equations are transformed into first order ones by using Bubnov-Galerkin method and the transient responses can be calculated accurately and efficiently.The critical point and its adjacent GLL point method is developed to deal with the constraints related to the time.Furthermore,it is proposed that spectral element division and interpolation number are function of dynamic load variation.Two optimization examples of spring shock absorber and the five DOFs vehicle suspension system are given.The artificial design variable is introduced.A detailed analysis of the advantages and disadvantages for the proposed method is finished.Results show the correctness of the method,thus providing a reference for further study of dynamic response optimization.