离散侧向平移支撑圆弧拱的自由振动分析  

Free vibration analysis of circular arches with discrete lateral translational braces

作　　者：陈隆凯 蔡勇[1] 吕晓勇 谢金[3] CHEN Longkai;CAI Yong;LÜXiaoyong;XIE Jin(School of Civil Engineering,Central South University,Changsha 410075,China;School of Civil Engineering,Central South University of Forestry and Technology,Changsha 410004,China;School of Civil Engineering,Hunan City University,Yiyang 413000,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075 [2]中南林业科技大学土木工程学院,湖南长沙410004 [3]湖南城市学院土木工程学院,湖南益阳413000

出　　处：《铁道科学与工程学报》2024年第1期275-285,共11页Journal of Railway Science and Engineering

基　　金：国家自然科学基金资助项目(51078354)。

摘　　要：拱通常采用离散侧向平移支撑增加其面外稳定性,而离散侧向平移支撑会产生振型耦合效应,显著影响拱的振动特性。为研究等间距离散侧向平移支撑对两铰圆弧拱自由振动的影响,通过假定拱的耦合振型,基于Hamilton原理求解离散侧向平移支撑圆弧拱的自振频率,并与有限元数值结果比较。同时,还探究了拱的面外长细比、圆心角以及侧向支撑的数量和位置对拱的临界刚度及最大基频的影响。研究结果表明:假定的耦合振型可以描述复杂的离散侧向平移支撑拱的弯扭振型,并能准确预测拱的自振频率和支撑临界刚度。侧向平移支撑拱的基频随支撑刚度的增加呈现多种增长模式,根据振型变化情况将其划分为第1类、过渡和第2类增长模式,不同增长模式之间的转换取决于拱的面外长细比、拱的圆心角、支撑数量以及支撑位置。当拱的面外长细比和拱的圆心角的组合靠近第1类增长模式和其他增长模式的分界线时,拱的支撑临界刚度和最大基频显著增大。支撑位置靠近两端翼缘时可能会改变拱的基频振型,但支撑位置在剪切中心附近时,拱的基频最大。拱基频在第1类增长模式时,支撑数量的增加显著提高拱的最大基频,在过渡增长模式时,支撑数量的增加对最大基频的影响减弱,而在第2类增长模式下,拱的最大基频随支撑数量的增加基本不发生变化。Discrete lateral translational braces are commonly employed to enhance the out-of-plane stability of arches,while it will cause the coupling effect of the vibration modes,which significantly affects the vibration characteristics of arches.To investigate the effects of equally-spaced discrete lateral translational braces on the free vibration of two-hinged circular arches,the coupling vibration modes were assumed.Based on Hamilton’s principle,the natural frequencies of the arches with lateral translational braces were carried out.Compared with the results from the finite element method,the analytical solutions of natural frequency of braced arches were reasonably accurate.Moreover,the effects of out-of-plane slenderness,subtended angle and number and position of braces on the threshold bracing stiffness and maximum fundamental frequency were also explored.The main conclusions are drawn as follows.The assumed coupling vibration mode can describe the complex flexuraltorsional vibration mode shapes of arches with translational braces and can provide an accurate prediction about the natural frequency of the arches and threshold bracing stiffness.The fundamental frequency of the arches with lateral translational braces exhibits multiple increasing modes with increasing bracing stiffness,categorized into the first,transitional,and second increasing mode based on mode shape changes,with the conversion between different increasing modes depending on out-of-plane slenderness,subtended angle of the arch,number of braces and bracing position.The threshold stiffness and maximum fundamental frequencies of the arches with lateral translational braces significantly increase when the out-of-plane slenderness and subtended angle of the arches near the boundary between the first and other type of increasing modes.When bracing position is close to the two flanges,it may alter the fundamental vibration mode of the arch.However,when the braces are positioned near the shear center,the fundamental frequency of the arch is maximized.Wh

关 键 词：圆弧拱 自由振动 侧向支撑 临界刚度 振型 

分 类 号：TU323.3[建筑科学—结构工程]