Emerging three-dimensional printing approaches enable cellular structures with composite walls or struts, creating new opportunities for architected materials with high specific stiffness and damping. This paper describes the damped dynamic response of composite walls comprising elastic and viscoelastic phases, and quantifies the scaling between material and structural loss factors. These descriptions are embedded in a highly efficient finite element framework to predict the steady-state frequency-dependent dynamic response of cellular structures, with an emphasis on structural loss factors arising from viscoelasticity. The framework is then used to compare the response of prismatic structures comprising hexagonal, triangular, rhombic and Kagome cells, and to quantify the scaling relationships between cell properties, structural loss factors and material loss factors. Case studies of structures with heterogeneous cell shapes and composite walls illustrate that significant damping gains are possible through architecture. Increases of a factor of two are possible using simple lattice distortions in a monolithic material, while increases of a factor of ten can be achieved with composite walls when the damping material has a loss factor of $\sim 0.2-1$ and a modulus of at least 1% of the elastic phase. The results strongly suggest that future topology and materials optimization will enable dramatic gains in damping.

新兴的三维打印方法使具有复合壁或支柱的多孔结构成为可能，从而为具有高比刚度和阻尼的建筑材料创造了新的机会。本文描述了包括弹性相和粘弹性相的复合墙体的阻尼动力响应，并量化了材料损耗因子和结构损耗因子之间的比例。这些描述被嵌入到高效的有限元框架中，以预测细胞结构的稳态频率依赖性动态响应，并着重于由粘弹性引起的结构损失因子。然后，该框架用于比较包含六边形，三角形，菱形和Kagome单元的棱柱形结构的响应，并量化单元格属性之间的比例关系，结构损耗因子和材料损耗因子。具有不同单元格形状和复合墙的结构的案例研究表明，通过建筑可以显着降低阻尼。使用整体材料中的简单晶格畸变可以将系数增加两倍，而当阻尼材料的损耗系数为时，复合墙可以将系数增加十倍。$〜0.2-\mathrm{1个}$模量至少为弹性相的1％。结果有力地表明，未来的拓扑和材料优化将使阻尼显着提高。