人行荷载下梁式结构振动分析的DQ-IQ混合法

为了评估人行荷载作用下梁式结构的振动舒适度，利用微分求积-积分求积，即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程，首先利用IQ法离散与时间相关的Dirac函数，再利用DQ法把控制方程转化为二阶常系数微分方程，最后利用Newmark算法求解微分方程。以某钢结构连廊为例，利用DQ法计算结构自振频率并与解析解进行对比，结果验证了节点选取和边界条件施加的合理性，再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应，计算结果表明，DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。

DQ-IQ hybrid method for structure vibration analysis of beam structure under pedestrian loading

This paper evaluates the vibration serviceability of a girder beam structure under a moving load.Its vibration control equation is a partial differential equation containing Dirac function.Dirac function is discretized by IQ method for time-dependent and the control equation is transformed into a differential equation with constant coefficients of the second order by DQ method.The solution to the differential equation is obtained by using Newmark algorithm.Differential quadrature-integral quadrature hybrid method is used for solving the vibration response of a beam under the action of pedestrians.Take a steel corridor as an example.The natural frequencies of the structure are calculated by DQ method and compared with the analytical solution to illustrate the accuracy of node selection and boundary conditions.The corridor responses at different walking frequencies under corridor response are calculated by using the hybrid DQ-IQ method and modal superposition method,which verify the reliability and accuracy of the DQ-IQ hybrid method.The DQ-IQ hybrid method also can be applied to vibration analysis of a structure under other moving loads such as the dynamic responses of pavements or bridges under vehicle loads.