移动荷载作用下桥梁动态响应的波谱单元法

Spectral Element Method for Bridges Subjected to Moving Loads

现有的波谱单元法都是应用于荷载作用位置固定不变的问题,本文将波谱单元法推广到移动荷载作用下桥梁的动态响应问题。基于能量原理,在频域内通过波谱形函数将作用在桥梁上的移动荷载等效为桥梁端部位置固定不变的节点集中荷载,利用等效后的节点荷载求解移动荷载作用下桥梁的动态响应。将波谱单元法的结果与有限元Newmark法、精细积分法及解析解进行对比,数值分析结果表明,推广后的波谱单元法能有效求解桥梁受移动荷载作用的动态响应问题,大大减少计算单元数量,提高计算效率,且具有很高的计算精度。

The traditional spectral element method（SEM） is limited to structures subjected to loads with fixed positions.The present paper proposals an extended spectral element method for dynamic analysis of bridges subjected to moving loads.Those moving loads were equivalent to fixed concentrated node forces by integrating t he shape function in SEM based on the principle of virtual work.The equivalent node forces were then used to calculate the dynamic responses of bridges in freq uency domain by SEM.Finally,numerical results obtained from SEM were compared with those from Newmark method,precise integration method（PIM） and analytical solution.The results show that the extended SEM can effectively calculate the r esponse of bridges subjected to moving loads.The number of elements can greatly decrease to improve the computational efficiency while high accuracy can be obt ained.