基于时滞惯性流形的浅拱动力屈曲研究

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振动与冲击 ›› 2009, Vol. 28 ›› Issue (6) : 100-103,.

论文

基于时滞惯性流形的浅拱动力屈曲研究

张家忠陈丽莺梅冠华周志宏苏哲

作者信息 +

Dynamic Bucking Analysis of Shallow Arch under Impact using Inertial Manifolds with Time Delay

Jia-Zhong Zhang, Li-Ying Chen, Guan-Hua Mei, Zhi-Hong Zhou, Zhe Su

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文章历史 +

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，论文针对抛物线浅拱，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。

Abstract

From viewpoint of nonlinear dynamics, the shallow arch under impact can be considered as a continuous dynamic system or dynamic system with infinite dimension. The governing equation for the shallow parabolic arch under impact is derived following the nonlinear shell theory. Then, a new nonlinear Galerkin method, namely, Inertial Manifolds with Time Delay, is developed and applied to the dynamic buckling analysis of shallow arch, which is governed by a set of nonlinear partial differential equations. By this method, the solutions of the governing equations are projected onto the complete space spanned by the eigenfunctions of the linear operator of the governing equations. In comparison with traditional Approximate Inertial Manifolds(AIMs), the relationship between the high and low modes is improved by Approximate Inertial Manifolds with Time Delay (AIMTDs), that is, not only the instantaneous relationship is considered, but also the past behaviors. Finally, the method is applied to the dynamics buckling analysis of the shallow arch under impact, and the comparisons between traditional Galerkin's procedure, traditional AIMs, and AIMTDs are given. It can be concluded that the methods presented are effective for the dynamic buckling analysis of continuous dynamic system.

导出引用

张家忠陈丽莺梅冠华周志宏苏哲. 基于时滞惯性流形的浅拱动力屈曲研究[J]. 振动与冲击, 2009, 28(6): 100-103,

Jia-Zhong Zhang;Li-Ying Chen;Guan-Hua Mei;Zhi-Hong Zhou;Zhe Su. Dynamic Bucking Analysis of Shallow Arch under Impact using Inertial Manifolds with Time Delay[J]. Journal of Vibration and Shock, 2009, 28(6): 100-103,

中图分类号： O322 TBZ23