大跨度刚构桥地震动随机响应的新封闭解

New closed-form solution for seismic response of long-span rigid frame bridges under random excitation

针对大跨度刚构桥顺桥向随机地震激励下响应分析比较复杂的问题,提出了一种基于双过滤白噪声随机地震动激励下,全桥顺桥向及竖向耦合振动响应分析简明封闭解法。首先建立考虑刚构桥顺桥向及竖向耦合振动的地震动方程,并利用实模态振型分解法获得以实模态广义变量表示的地震动方程,其中振动参数易通过有限元分析技术获得。其次,基于复模态法和虚拟激励法获得刚构桥桥墩及桥跨结构地震动位移、速度、实模态广义变量等响应量频域统一解,并基于二次式分解法获得了上述响应量0、1、2谱矩和方差的简明封闭解。然后,基于动力学等效原则给出了刚构桥等效地震力的计算式。最后,通过算例验证了所提封闭解的正确性,并研究了刚构桥双向地震动位移和等效地震力与实模态振型的关系。研究表明,刚构桥响应量受多个振型影响,抗震分析时需要考虑多个振型的参与。

In view of the complex problem of response analysis of long-span rigid frame bridges under random excitation along the span of bridge,a concise closed-form method for the analysis of longitudinal and vertical coupling vibration response of the whole bridge under random ground motions excited by double-filtered white noise is proposed.First,the ground motion equation considering the longitudinal and vertical coupling vibration of rigid frame bridge is established,and the dynamic equation expressed by the real mode generalized variable is obtained by using the real mode vibration mode decomposition method,in which the vibration parameters are easily obtained by the finite element analysis technology.Second,based on the complex mode method and the virtual excitation method,the unified frequency domain solutions of the ground motion displacement,velocity,real mode generalized variables and other responses of the rigid frame bridge pier and span structure are obtained,and the concise closed solutions of the 0,1,2 spectral moments and variances of the above responses are obtained based on the quadratic decomposition method.Then,based on the principle of dynamic equivalence,the calculation formula of equivalent seismic force of rigid frame bridge is given.Finally,the correctness of the proposed closed solution is verified by a numerical example,and the relationship between the two-way ground motion displacement and the equivalent seismic force of the rigid frame bridge and the real mode shape is studied.The research shows that the response of the rigid frame bridge is affected by multiple modes,and the participation of multiple modes needs to be considered in the seismic analysis.