大跨度曲线弯梁桥车–桥耦合振动分析

Vehicle–bridge Coupling Vibration Analysis of Long-span Curved Bending Beam Bridge

在桥梁结构设计中,需要考虑车辆动荷载的冲击作用。为计算大跨度曲线弯梁桥车致振动响应,通过在结点之间引入高阶位移插值函数,构造了形函数矩阵。基于虚功原理和动力有限元理论,推导了各个结点9个自由度的曲线箱梁空间单元刚度矩阵和质量矩阵;在推导刚度矩阵时考虑了箱梁的约束扭转和剪力滞效应,在推导质量矩阵时考虑了质心与扭心不重合。通过引入7自由度的车辆模型,建立了车–桥耦合振动方程。在MATLAB上采用Newmark–β法直接积分,求解了车辆动荷载作用下系统的振动响应,分析了车速、车重和主梁刚度对冲击系数的影响,同时采用ANSYS建立车–桥耦合非线性有限元模型。结果表明:以位移冲击系数代替弯矩冲击系数和剪力冲击系数进行截面内力设计时将会导致弯矩设计值最大增大2.89%,剪力设计值最大减小34.9%;车重对冲击系数影响很小;位移冲击系数和弯矩冲击系数均随着主梁刚度增大而减小,剪力冲击系数随着主梁刚度增大而增大。有限元分析结果与理论计算结果吻合良好。

The impact effects of the vehicle dynamic loads should be considered in designing bridge structures.To calculate the vibration response of long-span curved bending beam bridge caused by vehicle,form function matrix was created by introducing high order displacement interpolation function in the nodes.Based on virtual work principle and dynamic finite element theory,spatial element stiffness matrix and density matrix of curved box girder bridge with 9 freedom degrees in each node were deduced,the restricted torsion and shear lag effect were considered in deducing stiffness matrix,the influence that mass center didn’t coincides with torsion center was also considered in deducing density matrix.The vibration equations of vehicle-bridge coupling were established by introducing vehicle mode with 7 freedom degrees.Newmark–βmethod was used on MATLAB to solve vibration response of system under vehicle dynamic loads,and influences of vehicle speed,vehicle weight and primary beam stiffness on impact coefficient were analyzed.The results show that when displacement impact coefficient was used to replace moment and shear impact coefficient for section internal force design,moment design value would maximally increase by 2.89%,shear force design value would maximally decrease by 34.9%;vehicle weight had a little influence on impact coefficient;displacement and moment impact coefficients decreased with the increasing of primary beam stiffness,while shear force impact coefficient increased with the increasing of primary beam stiffness;the theoretical calculation values agreed well with the finite element results of ANSYS.