高速铁路周期性桥梁频域有限元法及墩底动反力分析

Study on FEM in Frequency Domain and Analysis of Dynamic Reactions at Pier Bottom of Periodic Bridge of High-speed Railway

基于高速铁路工程中常用的等跨径布置简支梁桥的特点,采用无限周期结构理论和有限元法在频域内建立了桥梁结构的分析模型,提出了任意荷载列作用下桥梁结构周期性单元受等效结点荷载时矢量频谱的计算方法,并且通过与既有文献结果的对比验证了本文计算模型的正确性。以某高铁线路上32 m等跨径布置高架桥为例,分析了其能带特性及其在不同频率轨道不平顺引发的移动简谐荷载激励下的动力响应及墩底动反力。计算结果表明:该周期性桥梁结构在低频段和高频段存在共有的通带频率;由于轨道不平顺的影响,桥梁结构截面位移及墩底动反力均出现明显的周期性特征,且动力响应随激振频率的增大而增大;该周期性理论和频域有限元法可以准确有效地计算出任意跨梁体的动力响应和墩底的动反力,为环境振动研究领域中场地振动荷载源的求解提供了研究思路和计算方法。

According to the characteristics of simply supported beam bridges with equal-span arrangement in high-speed railway,the frequency-domain finite element model of the bridge was established based on the infinite periodic structure theory and the finite element method(FEM),in which an effective method to achieve the spectra of equivalent nodal force vectors under arbitrary load series was proposed.The FEM in frequency domain was first verified by comparison with the existing analytical results,and then the energy band characteristics,the dynamic responses and the dynamic reaction of the pier bottom of a series of high-speed railway viaducts with 32 m equal spans under train loading with different excitation frequency were analyzed.The calculation results show that there exists a common passband frequency in low frequency and high frequency band.Due to the influence of track irregularity,the mid-span displacements and the pier bottom reaction show obvious periodic characteristics,furthermore the dynamic responses increase with the increase of excitation frequencies.The periodic theory and the FEM in frequency domain can be used to calculate dynamic responses of bridge beams and dynamic reactions at pier bottom effectively and accurately,which provides new ideas and calculation methods of obtaining the source excitation applied to the field of the environmental vibration research.