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针对工程中广泛应用的多跨变截面箱梁桥,考虑移动车辆的惯性力,模拟多个移动质量变速运动耦合振动情况。根据梁桥振动理论,建立多移动质量-简支梁系统的振动方程,分离变量法推导出解耦的强迫振动变系数二阶微分方程。采用附加矩阵方法,对移动质量产生的惯性力用形函数进行离散处理。编制桥梁动力响应计算程序,在时域内数值积分对某高速公路上一座三跨变截面箱梁桥在多辆汽车变速运动作用下的振动响应进行求解分析。计算结果表明:多个移动质量变速运动对梁桥产生的整体振动效应是一种非线性叠加关系;变速移动质量作用下梁桥动位移大于移动力作用下的动位移;连续箱梁桥的动力响应与移动质量的初速度和加速度有关。
Aiming at the multi-span box girder bridge with multi-span widely used in engineering, considering the inertia force of moving vehicles, the coupled vibration of multiple moving mass gears is simulated. According to the bridge vibration theory, the vibration equation of multi-moving mass-simply supported beam system is established, and the decoupled forced vibration coefficient second-order differential equation is deduced by separating variable method. Adopting the additive matrix method, the inertial force caused by moving mass is discretized by the shape function. The calculation program of the dynamic response of the bridge is established, and the numerical integral of the vibration response of a three-span box-girder bridge with variable cross section under the variable speed motion of multiple cars on a freeway is analyzed and solved. The calculation results show that the moving vibration of mass transfer is a non-linear superposition of multiple moving masses and the dynamic displacement of the beam is greater than that of the moving beam under the action of variable moving mass. The response is related to the initial velocity and acceleration of the moving mass.