索拱组合结构1:1内共振及其参数影响  

One-to-one internal resonance and parameter analysis of cable-stayed arch

作　　者：吕建根[1] 康厚军[2] 

机构地区：[1]仲恺农业工程学院城市建设学院,广州510225 [2]湖南大学土木工程学院,长沙410082

出　　处：《应用力学学报》2017年第3期450-455,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11572117)

摘　　要：研究土木工程中索拱组合结构的1:1内共振及其参数影响,可为拱桥施工中振动控制提供依据。利用索拱连接条件和边界条件,忽略索拱纵向振动,考虑索拱的几何非线性,运用Hamilton变分原理研究了拱出现主共振情形下索拱的1:1内共振问题,并建立了索拱的面内耦合非线性振动方程。运用Galerkin和多尺度摄动,以某拱桥施工中的结构为例,研究了索拱相互作用时的能量转换过程,数值模拟分析了索、拱主要参数对索拱幅频响应的影响。研究结果表明:结构体系产生内共振时,索拱的时程曲线呈现此消彼长的现象,能量在索拱之间相互转换,拱对索的振动影响更为明显;索、拱参数对索的非线性振动特性影响显著,对拱的振动影响很小。The one-to-one internal resonance is investigated and parameter analysis is carried on for the cable-stayed arch in civil engineering,which provides a basis for vibration control in arch bridge construction process.Using the connection condition and boundary condition of cable-stayed arch,the nonlinearity coupled differential equations of cable-stayed arch are derived by means of Hamilton variational principle,the geometric nonlinearity of cable-stayed arch is considered,and the longitudinal vibration of them is neglected.Then,the one-to-one internal resonance of cable-stayed arch in the case of primary resonance of arch is analyzed by the use of the Galerkin method in conjunction with the multiple scales method.Subsequently,taking a cable-stayed arch of the construction process as example,the energy transfer from the arch/cable to cable/arch is revealed by means of a one-to-one resonance.The nonlinear interaction maximizes its amplitude;the influence of these structural and geometric parameters on amplitude frequency response of the cable-stayed arch is simulated numerically.According to the results of numerical simulation,the amplitude of cable increases with the decrease of the amplitude of arch in the course of internal resonance,the energy exchanges between cable and arch when the system experiences internal resonance;these parameters have significant impacts on the vibration of cable,and they have little effect on that of arch.

关 键 词：索拱结构 1:1内共振 索参数 拱参数 幅频响应 

分 类 号：O322[理学—一般力学与力学基础]