基础竖向激励下复合材料圆弧拱的面内参数共振失稳研究  

STUDY ON IN-PLANE PARAMETRIC RESONANCE OF COMPOSITE LAMINATED CIRCULAR ARCH UNDER A VERTICAL BASE EXCITATION

作　　者：刘圆圆 刘爱荣[1] LIU Yuan-yuan;LIU Ai-rong(Research Centre for Wind Engineering and Engineering Vibration,Guangzhou University,Guangzhou,Guangdong 510006,China)

机构地区：[1]广州大学风工程与工程振动研究中心,广东广州510006

出　　处：《工程力学》2022年第S01期15-20,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(51878188);高等学校学科创新引智计划项目(111计划D21021);广州市科技计划项目(20212200004);中国工程院战略咨询重点项目(2021-XZ-37)。

摘　　要：该文研究了基础竖向激励作用下复合材料圆弧层合拱的平面内参数共振失稳。基于Hamilton原理推导了拱的动力稳定平衡微分方程和Mathieu-Hill方程,获得了层合拱周期2T和周期T对应的动力不稳定域。探明了矢跨比以及铺层角度对动力不稳定域的影响规律。研究结果表明:参数共振主要出现在两倍的结构自振频率附近;随着矢跨比的减小,动力不稳定域的域宽逐渐增大,临界激励频率逐渐增大;同斜交铺层相比,正交铺层拱的动力不稳定域的域宽较小;对于斜交铺层,随着铺层角度增大,动力不稳定域的域宽逐渐增加,临界激振频率向低频方向移动。The in-plane parametric resonance instability of composite laminated circular arches under a vertical base excitation is investigated.The equilibrium differential equations of dynamic stability and the Mathieu-Hill equation of an arch are derived based on the Hamiltonian principle.The dynamic instability regions corresponding to period 2T and period T are obtained.The effects of rise-span ratios and ply-angle on the dynamic instability region are researched.It is found that the dynamic instability region where the parametric resonance mainly appears near twice the natural frequency of the structure.With a decrease of rise-to-span ratio,the bandwidth of the dynamic instability region increases,and the critical excitation frequency increases accordingly.Compared to the angle-ply laminated arch,the cross-ply arch shows a smaller bandwidth of the instability region and a larger critical excitation frequency.For an angle-ply laminated arch,the bandwidth of the dynamic instability region increases and the critical excitation frequency deceases with the increasing ply-angles.

关 键 词：复合材料层合拱 竖向周期荷载 矢跨比 铺层角度 参数共振失稳 

分 类 号：TU311.2[建筑科学—结构工程]