弹性浅拱的非线性动力屈曲  

Nonlinear Dynamic Buckling of Shallow Elastic Arch

作　　者：韩强[1,2] 黄怀纬[1] 樊学军[1] 

机构地区：[1]华南理工大学土木与交通学院,广东广州510640 [2]新疆大学建筑工程学院,新疆乌鲁木齐830046

出　　处：《华南理工大学学报（自然科学版）》2010年第3期1-7,共7页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10672059);广东省自然科学基金资助项目(8151064101000002)

摘　　要：采用非线性动力学方法探索了跌落冲击弹性浅拱的动力跳跃屈曲问题.由哈密顿原理得到结构的非线性动力平衡方程,同时采用单模态和双模态两种模态形式进行分析,并通过伽辽金方法得到结构响应的控制方程.文中讨论了系统平衡点的特性,研究了系统的吸引子及其吸引域等稳定性问题.数值结果表明:双模态分析法较单模态分析法精确;在某些情况下,单模态分析无法给出正确的屈曲临界条件和系统动力响应.另外,拱的初始位形变化对跳跃屈曲的临界条件影响显著,高拱具有更高的屈曲承载力.This paper deals with the snap-through buckling of a shallow elastic arch under dropping impacts by means of the nonlinear dynamic method. In the investigation, a nonlinear dynamic equilibrium equation is deduced based on the Hamilton principle and is then analyzed using both the single-mode and the double-mode methods. Then, the governing equation of structure responses is obtained via Galerkin＇s approach. Moreover, the charactcristics of equilibrium points of the system are discussed and the stability of system attracters and their attraction domains is analyzed. Numerical results show that the double-mode method is more accurate than the single-mode one. The single-mode method may give incorrect critical buckling conditions and dynamic responses in some conditions. In addition, the initial shape of the shallow arch greatly affects the critical conditions of snap-through buckling, and that higher arch may possess greater buckling bearing capacity.

关 键 词：非线性动力学 动力屈曲 跳跃屈曲 浅拱 

分 类 号：O317[理学—一般力学与力学基础]