基于时滞惯性流形的浅拱动力屈曲研究  

Dynamic bucking analysis of shallow parabolic arch based on the method of inertial manifolds with time delay

作　　者：张家忠[1] 陈丽莺[1] 梅冠华[1] 周志宏[1] 苏哲[1] 

机构地区：[1]西安交通大学能源与动力工程学院,西安710049

出　　处：《振动与冲击》2009年第6期100-103,167,共5页Journal of Vibration and Shock

基　　金：新世纪优秀人才支持计划(NCET-07-0685);自然科学基金项目(10471110)

摘　　要：从动力学观点,浅拱受冲击是一种无穷维或者连续的动力系统,针对抛物线浅拱,应用有关薄壁结构的基本理论和非线性几何关系推导并建立其控制微分方程。然后,利用时滞惯性流形的新思想,提出一种求解这类强非线性偏微分方程的新方法,即基于时滞惯性流形的非线性Galerkin方法。通过这种方法,把原始方程的解投影到由控制方程中线性算子的特征函数所张成的完备空间内,并构造出无限维子空间内的动力行为与有限维子空间内的动力行为之间的耦合作用,该耦合作用认为高低阶分量间的相互作用并不是一种简单的瞬时行为,而是与模态发展的历史有关。通过数值分析得到:系统存在两个稳定平衡位置,与传统的Galerkin方法相比,所提出的基于时滞惯性流形的非线性Galerkin方法可以大幅度地降低方程的维数,提高计算速度,有效地降低对计算机内存的需求和减少计算时间。某种程度上,时滞惯性流形为系统的非线性动力行为如屈曲、分岔、突跳等动态模拟和数值分析提供了一个新的更为合理的研究手段。The governing equations for the shallow parabolic arch under impact were derived following the nonlinear shell theory. A new nonlinear Galerkin method, namely, inertial manifolds with time delay, was developed and applied to the dynamic buckling analysis of shallow arch, which is governed by a set of nonlinear partial differential equations. By the method, the solutions of the governing equations were projected onto the complete space spanned by the eigenfunctions of the linear operator of the governing equations. In comparison with the traditional approximate inertial manifolds (AIMs),the relationship between the high and low modes was improved by the approximate inertial manifolds with time delay (AIMTDs), that is, not only the instantaneous relationship was considered, but also the past behaviors. Finally, the method was applied to the dynamics buckling analysis of the shallow arch under impact, and the comparisons between traditional Galerkin's procedure, traditional AIMs, and AIMTDs were given. It can be concluded that the method presented is effective for the dynamic buckling analysis of continuous dynamic system.

关 键 词：时滞惯性流形 特征函数 动力屈曲 屈曲模态 

分 类 号：O322[理学—一般力学与力学基础]