竖向基础激励下圆弧拱面内振动失稳研究
Study on In-plane Vibration Instability of Circular Arches Under Vertical Base Excitation
钟子林 1黎剑华 1申富林 1徐晓斌 1董勤喜1
作者信息
- 1. 广州铁路职业技术学院,广东 广州 511300
- 折叠
摘要
基于能量原理,文中构建圆弧拱在基础竖向激励作用下平面内动力稳定性的能量方程.通过应用哈密顿原理,推导出描述拱面内径向与切向振动耦合行为的控制方程组.采用多尺度分析方法,解析得到圆弧拱在同时经历一阶反对称参数共振与二阶正对称共振条件下的动力不稳定区域解析表达式.此外,还探讨拱的圆心角及阻尼衰减率对动力不稳定区域的具体影响.为验证理论解析结果的准确性,进行有限元仿真分析,不仅证实了理论解析的有效性,而且揭示了圆弧拱在平面内发生动力失稳的内在机制.
Abstract
Based on the energy principle,this paper establishes an energy equation for the in-plane dynamic stability of a circular arch subjec-ted to vertical base excitation.By applying Hamilton's principle,a coupled system of governing equations describing the radial and tangential vibrations of the arch surface is derived.Furthermore,using the multiple scales method,an analytical expression for the dynamic instability re-gion of the circular arch under simultaneous first-order antisymmetric parametric resonance and second-order symmetric resonance conditions is obtained.Additionally,the paper delves into the specific impacts of the arch's central angle and damping decay rate on the dynamic instability region.To validate the accuracy of the theoretical analysis,finite element simulation analysis is conducted,which not only confirms the validity of the theoretical solutions but also reveals the underlying mechanism of in-plane dynamic instability in circular arches.
关键词
竖向基础激励/圆弧拱/动力不稳定域/振动失稳Key words
Vertical base excitation/Circular arch/Dynanic instability region/Vibration instability引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据