摘要
为精确描述面内端部激励下拉索非线性振动机制,构建抽象端部激励下的拉索力学描述模型,分别推导了拉索拟静态振动和模态振动控制方程,基于有限差分法给出了拉索模态振动的数值求解方法。由于垂度效应的影响,在轴向、竖向以及轴向和竖向共同激励下拉索的拟静态索力与端部位移采用一个非线性方程予以表征。拉索拟静态振动可视作外部激励施加在拉索上,引起拉索的非线性模态振动,通过理论推导分别求得模态振动的控制方程和变形协调方程。在模态振动过程中,拉索的动力特性(如刚度和周期)不断变化,索力和拉索变形相互耦合,使得其求解非常复杂。采用有限差分法进行数值求解,并基于有限元方法验证了数值求解方法的准确性。重点讨论了拉索模态振动共振机制,结果表明,在轴向、竖向以及轴向和竖向激励下,拉索模态振动存在多个共振区域,包括小周期、0.5 T 1、T 1和2T 1等(T 1为成桥状态下拉索基本振动周期);在共振区域内,拉索振动索力幅度较大,模态振动对总索力的贡献系数较高,超过0.4,在实际工程中不容忽视;拉索阻尼对模态振动的影响较大,增加拉索阻尼比将改变拉索模态振动的幅频特征,模态振动索力及其贡献系数均有所降低,但降低程度受激励幅度的影响较大。
This study aims to accurately reproduce the nonlinear vibration mechanism of stayed cables under in-plane end excitation.The mechanical description model of the cable is established under end excitation and the quasi-static vibration and modal vibration equations of the cable are derived respectively.The numerical solution method of cable parametric vibration is illustrated using the finite difference method.Due to the sag effect,there exists a highly nonlinear relationship between the quasi-static cable force and end displacement under axial,vertical and axial-vertical excitations,under which the nonlinearity can be characterized by a nonlinear equation respectively.The quasi-static vibration of the cable can be regarded as an external force applied to the cable,which causes the nonlinear modal vibration of the cable.Through theoretical derivation,both the governing equation of motion and the compatibility can be obtained.In the process of modal vibration,the dynamic characteristics of the cable(such as stiffness and period)are continuously varying,and the cable force and deformation are highly coupled,which makes the solution of the modal vibration equations extremely complicated.The finite difference method is suggested to obtain the numerical solution,whose accuracy is verified by the finite element method.This study focuses on the resonant mechanism of modal vibration.The results show that under axial,vertical and axial and vertical excitation,there are many resonance regions of cable parametric vibration,including very small periods,periods near 0.5 T 1,T 1 and 2T 1.In the resonance region,the cable vibration amplitude is quite large.The contribution of modal vibration to the total cable force is high,more than 0.4,which can not be ignored in practical engineering.Cable damping plays an important role in the modal vibration.Increasing the cable damping ratio will alter the amplitude and frequency characteristics of cable modal vibration,reduce the cable force and the contribution coefficient of modal vibration,but the degree of reduction is greatly affected by the excitation amplitude.
作者
朱付祥
易江
ZHU Fuxiang;YI Jiang(College of Civil Engineering,Guangzhou University,Guangzhou 510006,China)
出处
《地震工程与工程振动》
CSCD
北大核心
2023年第3期150-160,共11页
Earthquake Engineering and Engineering Dynamics
基金
国家青年科学基金项目(5210080018)
广东省教育厅(2021KQNCX069)
广州市教育局(202032797)
广州市科技计划(202102020594)。
关键词
桥梁工程
参数振动
振动方程
斜拉索
面内端部激励
共振周期
bridge engineering
parametric vibration
vibration equations
stay cables
in-plan support excitation
resonant period
