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分别建立了具有7个自由度的3D整车模型的振动方程和连续曲线梁桥的运动方程,将车辆和曲线梁桥分为相互联系的两个振动子系统——车辆和桥梁系统。利用有限元法及模态叠加综合技术,以车轮与桥面相互接触处保持不脱离为位移协调条件,推导出车桥耦合振动方程,并运用Newmark-β数值方法对耦合系统进行迭代求解。以一实际工程桥梁为背景,分析该曲线梁桥在单车荷载作用时,不同行车速度、不同路面等级的振动响应。结果表明:车速对曲线梁桥的竖向挠度的影响很大,但对横向振动的影响比较小;在同一车速情况下,路面的不平度对曲线桥梁的冲击影响显著,路况越差,冲击越大;曲率半径越大,桥梁的横向振动响应越小,而竖向振动响应却越大。
The vibration equations of a 3D vehicle model with seven degrees of freedom and the equations of motion for a continuous curved beam bridge are established respectively, and the vehicle and curved beam bridge are divided into two interconnected vibration subsystems - a vehicle and a bridge system. By using the finite element method and the modal superposition synthesis technique, the coupling vibration equation of the vehicle-bridge was deduced with the condition that the contact between the wheel and the deck is not separated. The Newmark-β numerical method was used to solve the coupled system iteratively. Based on an actual engineering bridge, the vibration response of the curved beam bridge under different load speeds and different road surface gradients is analyzed. The results show that the influence of vehicle speed on the vertical deflection of curved girder bridge is great, but the impact on the transverse vibration is relatively small. Under the same vehicle speed, the unevenness of the pavement has a significant impact on the curved bridge. The worse the road conditions, The larger the radius of curvature, the smaller the transverse vibration response of the bridge and the greater the vertical vibration response.