基于时间谱元法的动态响应优化

Dynamic Response Optimization Based on Time Spectral Element Method

机械系统动态响应优化设计有很好的应用前景。动态响应必须满足依赖于时间的微分方程。为了获得最优解且满足与时间有关的约束,要求获得整个时间上的响应。研究基于时间谱元法的系统动态响应设计。深入探讨在时间域内离散动态响应,将运动微分方程组转化成代数方程组,精确解出瞬态响应,用高斯罗巴托勒让德(Gauss-Lobatto-Legendre,GLL)点法和关键点法处理时间约束。以最简单的多自由度动力学设计问题——2自由度弹簧减振器设计为例,引入人工设计变量,详细分析两种处理约束方法的优缺点,也说明此方法的正确性。这些内容可为进一步研究机械零部件的动态优化设计问题以及动载荷弹性分布参数系统的优化设计奠定基础,比如在固定端承受振动输入的矩形变截面梁的动态优化设计,在不同边界条件下承受垂直平面均布瞬态动载荷作用的弹性梁的动态优化设计等。

Dynamic response optimization of mechanical system design has good application prospects.Dynamic response must meet the time-dependent differential equations.In order to obtain the optimal solution and satisfy the time-related constraints,the responses over the entire time should be obtained.The system dynamic response design based on time spectral element method is studied.The discrete dynamic response in time domain is discussed in depth.Motion differential equations are converted into algebraic equations,so as to accurately solve out the transient response.GLL（Gauss-Lobatto-Legendre） point method and key point method are used to deal with time constraints.The most simple multi-degree of freedom dynamic design problem─two degrees of freedom spring shock absorber,is taken as an example,artificial design variables are introduced,the advantages and disadvantages of the two methods of dealing with constraints are analyzed in detail,and the correctness of this method is also shown.These contents lay a foundation for further study of the dynamic optimization design of mechanical parts as well as the optimization design of dynamic load elasticity distribution parameter system,such as the dynamic optimization design of rectangular variable cross-section beam which bears vibration input at the fixed end,and the dynamical optimization design of elastic beam which bears vertical plane uniform transient dynamic loads under different boundary conditions.