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中文摘要：
近年地下结构震害频发，针对目前地下结构抗震研究中实际存在的多尺度动力问题，提出了地下结构多尺度动力分析方法，该方法不需要任何附加的过滤和阻尼就能有效地消除高频波的虚假反射．以桥域耦合理论为基础，引入拉格朗日乘子将不同尺度区域之间的约束关系，通过能量势函数隐含到动力方程中，推导出不同尺度域的动力控制方程；基于中心差分法，提出了用于地下结构多尺度分析的动力显式算法，以求解所建立的多尺度动力耦合体系．以实际工程为应用实例，通过与传统的位移耦合方法的对比分析，说明了该多尺度方法用于地下结构动力分析的可行性以及对消除高频波虚假反射的有效性．
英文摘要：
Underground structures suffered great damages frequently in recent earthquakes. A number of researchers have developed studies on seismic analysis of underground structures, but failed to address the existing multi-scale dynamic problems. In this paper, a multi-scale method is proposed for the dynamic response analysis of underground structures subjected to dynamic loadings. This method does not result in spurious wave reflections and does not need additional filtering or damping. Based on the bridging coupling theory, Lagrangian multipliers are introduced to append the constraints into the dynamic equations, and the dynamic control equations are deduced for the multi-scale subdomains using the energy potential function. Based on the central differential method, a multi-scale dynamic explicit algorithm is proposed to solve the established multi- scale dynamic coupling systems. As an application, the presented method is used in an existing underground structure. The advantage of the multiscale modeling method in minimizing spurious reflections is verified by providing comparisons with the displacement-coupled method. The research is of great benefit to seismic analysis theories and methods of underground structures, and also provides instructions for dynamic calculation and analysis of underground structures.
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