考虑桥梁橡胶支座的作用，建立了双跨连续梁桥的梁-弹簧-杆模型，采用瞬态波函数展开法和组合体瞬态内力法，提出了在先期到达的竖向地震激励作用下，桥梁结构竖向碰撞力的理论求解方法，计算结果表明本文方法可以合理地求解桥面与橡胶支座的多次竖向碰撞力。通过对不同竖向地震反应谱、不同桥梁跨度和不同竖向地震激励幅值下的碰撞次数和碰撞力的计算和分析表明，在浅源近场竖向地震作用下，桥梁可能出现竖向碰撞现象，桥面与橡胶支座的竖向碰撞力的幅值大，对桥梁具有相当大的危害。研究表明，竖向碰撞现象的出现很有可能存在两个条件，即竖向地震激励周期逼近于桥梁整体结构的固有振动周期，以及竖向地震激励幅值过到某个确定的阀值。另外，计算结果还表明，竖向碰撞力随竖向地震激励周期、幅值和桥跨长度的变化，呈现出复杂的非线性效应。%A theoretical solving approach for multiple pounding forces acting on a bridge under near-field vertical earthquake was presented with the consideration of rubber bearings installed.The bridge was simplified as a continuous model of beam-spring-rod,and the problem was solved by making use of the expansion of transient wave functions in a series of eigenfunctions and the transient internal force method to determine the contact interfacial forces in a combined body.The numerical results showed that the presented approach can be used to solve reasonably the multiple pounding forces between the deck of the bridge and rubber bearings.The pounding forces and the pounding number under different vertical earthquake spectra,periods,and amplitudes as well as with different span lengths of the bridge were calculated. It was illustrated that the vertical pounding phenomenon can take place under near-field vertical earthquake,and damage the bridge before the horizontal earthquake reaches;there may exist two conditions leading to vertical poundings,the one is the vertical earthquake period close to the natural period of the bridge and the other is the amplitude of vertical earthquake exceeding some threshold;the vertical pounding force varies with the changes of vertical earthquake period, vertical earthquake amplitude and bridge span length.
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