Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces may have a strong effect on the dynamics of jointed structures. The multi-scale nature of manufactured surfaces makes finite element (FE) simulations computationally challenging or even infeasible, especially for long-duration transient dynamic simulations. We recently proposed a multi-scale method to enable topography resolving simulations. In that method, the contact region is modeled using half-space theory implemented on a fine grid of boundary elements (BE), whereas the underlying bodies are described using a relatively coarse FE model. So far, this FE-BE multi-scale method has been limited to quasi-static analysis. In the present work, we extend the method dynamic analysis, in the form of time integration and Harmonic Balance. As numerical benchmark system, the well-known S4 Beam is used, for which actual topography measurements are available. The proposed method demonstrates high robustness and efficiency, permits relatively large and mesh-independent time steps, and shows no evidence of numerical damping. The simulation results are in overall very good agreement with explicit and implicit full-FE analyses. In the partial slip regime, some discrepancy is found to be of physical origin: Depending on the load history, the system settles to a slightly different equilibrium, which is associated with a distinct residual contact stress field.

翻译：结构及系统的阻尼常受连接处摩擦耗散主导，其预测仍是一个长期存在的科学挑战。以往研究表明，接触界面的实际地形对装配结构的动力学特性可能具有显著影响。加工表面多尺度特性使得有限元仿真面临计算挑战甚至难以实现，尤其是长时域瞬态动力学仿真。我们近期提出了多尺度方法以实现地形分辨仿真：该方法采用半空间理论在精细边界单元网格上建立接触区域模型，而底层结构则通过较粗的有限元模型描述。此前该有限元-边界单元多尺度方法局限于准静态分析。本研究将该方法扩展至动力学分析，具体采用时间积分与谐波平衡形式。数值基准测试选用具有实测地形数据的S4梁，该方法展现出高鲁棒性与高效性，允许较大且网格无关的时间步长，未发现数值阻尼现象。仿真结果与显式及隐式全有限元分析整体吻合良好。在部分滑移工况中，发现的偏差具有物理本质：取决于载荷历史，系统将趋于略有差异的平衡状态，这与特有的残余接触应力场相关。