摘要
采用连续模型研究了设置中央扣悬索桥的扭转自振特性,建立了考虑跨中位移的分段主缆相容方程,以及跨中断面主缆纵向位移和中央扣、加劲梁变形的协调关系;应用哈密顿原理推导了扭转振动微分方程,求得振动频率方程和振型表达式,提取了决定自振特征的量纲一化参数,并作了参数分析;最后用里兹法推导了扭转基频的估算公式。研究结果表明:在反对称扭转振动时,主缆在中央扣前、后会产生反对称的附加缆力,从而提高该振型的频率;主缆弹性刚度与主缆重力刚度、加劲梁刚度之和的比值是悬索桥扭转特征的主导参数,决定了第1阶对称和反对称扭转振型的形态和排列次序;中央扣自身变形,以及加劲梁的侧向挠曲变形和扭翘变形都会减弱中央扣对主缆纵向位移的约束,在缆梁体系总体参数不变的前提下,中央扣刚度和跨中缆梁间距是影响反对称扭转基频大小的主要因素;2座属性各异的悬索桥基频计算结果验证了频率方程解、估算公式值与有限元结果吻合良好。
An improved continuum-model based analytical solution was developed for the free torsional vibration of suspension bridges with center ties. For each half bridge, the compatibility equations were established for cables with the longitudinal displacement of the cable at mid-span considered. The relationship between the longitudinal displacement of cables and the deformation of both stiffening girder and center ties at mid-span was analyzed. The differential equation for free torsional vibration was derived theoretically under Hamilton＇s principle. The general expressions of mode shapes and the implicit equations of frequencies were presented. The dimensionless parameters controlling the vibration characteristics were defined and analyzed. Finally, the estimation formulas for symmetric and antisymmetric fundamental frequencies were obtained with the Ritz approach. The results indicate that, upon antisymmetric torsional vibration, the center tie＇s restriction on the cable＇s longitudinal movement causes the particular additional cable tension being antisymmetric at mid-span, which will enhance the frequency as a result. The dimensionless parameter that accounts for the ratio of cables＇ elastic stiffness to the sum of cables＇ gravity stiffness and girder＇s stiffness is critical in governing the torsional vibration behaviors, such as the shapes and the relative order of the first symmetric and asymmetric mode. The constraint on cable＇s longitudinal movement will be weakened in consideration of the deformation of center ties, and the lateral flexural and warping deformation of stiffening girder. Given that the cable and stiffening girder have no change, the stiffness of center tie and the vertical distance between cable and girder at mid-span are the key parameters in affecting the fundamental antisymmetric torsional frequency. Investigations on two specific bridge examples with different properties indicate that the results of frequency equations and estimation formulas are in good agreement with those with finite element method.
出处
《中国公路学报》
EI
CAS
CSCD
北大核心
2013年第5期76-87,共12页
China Journal of Highway and Transport
基金
国家自然科学基金项目(50908083)
关键词
桥梁工程
悬索桥
连续模型
中央扣
反对称扭转振动
基频
估算公式
bridge engineering
suspension bridge
continuum model
center tie
antisymmetrictorsional vibration
fundamental frequency
estimation formula
作者简介
彭旺虎（1975-），男，湖南长沙人，工学博士研究生，Email：onehoo@163．com。
