基于Newmark-β显式直接积分法的三塔斜拉桥非线性地震响应分析

Nonlinear Earthquake Response Analysis on Three-tower Cable-stayed Bridge Based on Newmark-β Explicit Scheme Direct Integration Method

三塔单索面斜拉桥在空间动力行为方面有其独特之处。以济南建邦黄河公路大桥为例,运用有限元方法建立桥梁的空间动力数值分析模型,构建结构特征方程,在频率范围1 600～0cps,频移为1cps基础上运用lanczos法解此方程获得结构空间动力特性;进而利用拟相对速度反应谱SV和拟绝对加速度反应谱SA之间的数学关系,在大量地震记录中选择与场地特征周期基本一致的波谱,对其峰值加速度和持续时间进行调整后直接输入动力数值模型;采用质量和刚度因子法计算结构各振型阻尼比,以恒载作用下结构受力状态作为初始状态,运用Newmark-β显式直接积分法迭代求解结构动力微分方程组,并取γ≥0.5且β≥γ/2以满足其无条件稳定;考虑恒载作用在地震发生过程中对结构产生的二阶效应,获得非线性地震响应数值解,并由此总结出该类桥型的地震响应一般规律。结果可为该类桥型的抗震设计提供参考。

Cable-stayed bridge with three towers and single cable plane has uniqueness on dynamic behavior in space. In this paper, the Jianbang Yellow River Highway Bridge in Jinan is taken, as example, using finite element method to build spatial dynamic numerical analysis rood bridge, and to form a structural characteristic equation, the space dynamic structure is obtained with frequency range of 1 600-0 cps and frequency shif zos methods for the solution of the equation. The mathematical relationship characteristi t 1 cps by us el of the cs of the ing lancbetween pseudo rela tive velocity response spectrum Sv and pseudo absolute acceleration response spectrum SA is used to select the spectra with basically same characteristic site period in a large number of seismic records, whose peak acceleration and duration are adjusted to directly be input to the dynamic numerical analysis model. Using mass and stiffness factor method in calculation on damping ratio of every vibration type, taking stressed state of the structure under dead load as the initial state,Newmark-β explicit scheme direct integration method with Y≥0.5 and β≥Y/2 which make the method being no-conditional stable is used to the solution of the structure dynamic differential e- quations. Considering the second order effect from dead load in the structure during an earthquake, the numerical solution of nonlinear seismic response is obtained. Furthermore, general laws on seismic response of such bridge type is concluded to provide a feasible basis for seismic design of such bridge type.