索-拱组合结构中斜拉索的非线性参数振动

索-拱组合结构是大跨度拱桥施工过程中非常重要的临时结构。对大跨度拱桥施工过程中普遍存在的索-拱组合结构建立了非线性力学模型,考虑由于索的初始垂度、大位移而引起的几何非线性因素的影响,推导索-拱组合结构的非线性运动方程,对索-拱组合结构的边界条件与连接条件进行了简化,拱在连接处的边界条件被简化为用索的抗拉刚度表示的径向弹性支撑,拱在连接处的运动作为对索的周期性激励,建立索的非线性参数振动方程,运用多尺度摄动方法,对拉索可能发生的参数共振和亚谐波共振进行了理论研究和数值分析,确定了索-拱组合结构中拉索参数共振和亚谐波共振的影响因素及发生条件。研究结果表明,在拱的低阶局部振动频率处于一定区域时,拱的小幅振动能够激发拉索的大幅度运动,影响大跨度拱桥施工过程中索-拱组合结构的稳定性和安全性,对于一个给定阻尼和频率比的系统,足够小的激励幅值能够有效避免系统发生参数共振。

Non-linear parametric vibration of cables in cable-arch composite structures

Cable-arch composite structures are important temporary structures during the erection of the long-span arch bridges.A nonlinear mechanical model is presented for the parametric vibration of cable-arch composite structures.The nonlinear equations of motion of cable-arch composite structures are derived,the static sag of the cable as well as the geometric nonlinearity is considered,and a simple connection condition and boundary condition of the cable-arch composite structures are applied.Using the multi-scale perturbation method,the parametric and sub-harmonic resonances of cables are analyzed.These results indicate that small scale vibration of the arches may stimulate the cables to undergo large scale movements when the local vibration frequency of the arches is within certain limits,it affects the cable-arch structure and the stability and security in the process of long-span arch bridge constructions.For a system with the damping and the frequency ratio given,sufficiently low excitation amplitudes may avoid system parametric resonance.