基于车-桥随机振动模型的简支梁桥墩顶垂向动反力特征研究

Random characteristics for vertical dynamic reaction force of pier-top of a simply supported girder bridge based on train-bridge random vibration model

为研究高速铁路简支梁桥墩顶垂向动反力的随机性特征,基于虚拟激励法和有限元方法,建立了列车-轨道-桥梁耦合系统竖向随机振动模型。采用多体动力学理论建立具有二系悬挂的质量-弹簧-阻尼系统列车模型;采用有限元方法建立轨道-桥梁有限元模型;基于等效Hertz线性轮轨接触关系建立列车-轨道-桥梁耦合系统动力学方程。通过虚拟激励法将轨道高低不平顺转化为一系列简谐不平顺的叠加,将非平稳随机振动问题转化为确定性时间历程问题,推导了列车-轨道-桥梁耦合时变系统随机振动计算模型。基于该计算模型,以五跨32 m预应力混凝土简支箱梁桥为研究对象,研究了轨道不平顺和车速对墩顶垂向动反力随机特征的影响。结果表明:墩顶垂向动反力受列车轴重引起的确定性激励控制,轨道不平顺随机激励对其影响显著;不同轨道不平顺随机激励下墩顶动反力均方根(σ)不同,基于3σ法得到的限值(μ±3σ)相差较大;随着车速的增大,墩顶动反力均方根(σ)逐渐增大。

In order to study random characteristics of vertical dynamic reaction force of pier-top（ VDRFP） of a simply supported girder bridge,a vertical random vibration model for a train-track-bridge coupled system was established based on the pseudo-excitation method（ PEM） and the finite element method. A mass-spring-damper system model with two-layer suspensions for the train was built utilizing the multibody dynamics theory,and the track-bridge model was built with the finite element method. The dynamic equations of the train-track-bridge coupled system were established based on the equivalent Hertz linear wheel/rail contact relation. Adopting the pseudo-excitation method（ PEM）,the vertical track profile irregularity was converted into a superposition of harmonic excitations,then a non-stationary random vibration problem was converted into a deterministic time history problem,and a random vibration calculation model for the traintrack-bridge coupled time-varying system was deduced. Based on the calculation model,taking a 5-span 32 m prestressed concrete simply supported box girder bridge as a study object,the effects of track irregularity and train speed on VDRFP random characteristics were analyzed. The results showed that VDRFP is controlled by the deterministic excitation caused by vehicle axle load,and track irregularity-induced random excitation affects it significantly; RMSs（ σ） of VDRFP are different under different track irregularity-induced random excitations,and the limit values（ μ ± 3σ） obtained based on the 3σ method are quite different; with increase in train speed,RMSs（ σ） of VDRFP increase gradually.