多尺度动态边界逼近分析方法研究及试验验证
Study on multi-scale dynamic boundary approximation analysis method and experimental verification

摘要 基于动力平衡方程和有限元思想，提出求解局部振动问题的多尺度动态边界逼近分析方法：首先建立较大尺度整体有限元模型并计算，进而针对所关注区域进行细化处理，利用目标区域在较大尺度模型中的动力响应作为边界条件，通过精度递进和反复迭代，最终完成精细模型的动力响应求解.在阐明分析流程和理论推导的基础上，以简支钢梁为例，对所提方法的有效性进行了模型试验验证，并探讨了细化过程中合理单元尺寸比的选取范围.研究表明，该方法精细化计算结果与试验测试结果相吻合，多次逼近分析迭代后结果稳定性较好.在计算成本较小的递进分析中，所提方法可应用于大跨度铁路钢桥整体节点和正交异性钢箱梁等复杂结构体系的局部振动问题.
Abstract：Based on dynamic equilibrium equation and finite element method, a multi-scale dynamic boundary approximation method is proposed to solve local vibration problems. First, a large-scale full finite element model is established and calculated. Then the area where the refine is needed will be in thinning process. Using the dynamic responses of the target area in large-scale model as the boundary condition, dynamic responses of refined model is solved through progressive precisions and repeated iterations. Taking simple-supported steel beams as the study example, the effectiveness of the proposed method is validated by model tests. And during refinement processes, what is the optimal ratio of element size is discussed. The study demonstrates that the analytical dynamic responses approximately agree with the experimental ones. When the scale of progressive analysis is smaller, this method could be used for local vibration problems in complex structural systems such as orthotropic bridge decks and integral joint in long-span steel railway bridges.