In this paper, a novel design strategy to minimize the dynamic compliance of a vibrating infill structure with a solid outer coating and a periodic uniform infill lattice is presented. The vibration of the linearly elastic infill structure is excited by time-harmonic external mechanical loading. The design optimization of the infill lattice is performed simultaneously with the topology optimization of the macroscale structure, which also includes the coating. Multiscale topological designs of infill structures are presented in numerical examples for different excitation frequencies, different limits on static compliance, different damping properties, and different boundary conditions. The results are obtained by the finite element method and gradient-based optimization using analytical sensitivity analysis, which is derived and presented in the fully discrete setting. The influences of excitation frequencies, static constraints, damping properties, coating thicknesses, and boundary conditions on the optimized macrostructures and microstructures are discussed in the numerical examples. In general, the optimized microstructures reflect the shape characteristics of the macrostructure configuration, where Kagome-like microstructures have been obtained in some examples. Moreover, in the optimized results the microstructures include more but finer structural members for the design optimized for low excitation frequencies.

在本文中，提出了一种新颖的设计策略，以最小化具有固体外涂层和周期性均匀填充晶格的振动填充结构的动态柔量。线弹性填充结构的振动由时谐外部机械载荷激发。填充晶格的设计优化与宏观结构的拓扑优化同时进行，其中还包括涂层。填充结构的多尺度拓扑设计在不同激励频率、不同静态柔量限制、不同阻尼特性和不同边界条件的数值示例中给出。结果是通过有限元方法和基于梯度的优化使用解析灵敏度分析获得的，这是在完全离散的设置中导出和呈现的。数值例子讨论了激励频率、静态约束、阻尼特性、涂层厚度和边界条件对优化后的宏观结构和微观结构的影响。一般来说，优化的微观结构反映了宏观结构配置的形状特征，其中在一些例子中已经获得了类似 Kagome 的微观结构。此外，在优化结果中，微观结构包括更多但更精细的结构构件，用于针对低激发频率优化的设计。在数值例子中讨论了优化的宏观结构和微观结构的边界条件。一般来说，优化的微观结构反映了宏观结构配置的形状特征，其中在一些例子中已经获得了类似 Kagome 的微观结构。此外，在优化结果中，微观结构包括更多但更精细的结构构件，用于针对低激发频率优化的设计。在数值例子中讨论了优化的宏观结构和微观结构的边界条件。一般来说，优化的微观结构反映了宏观结构配置的形状特征，其中在一些例子中已经获得了类 Kagome 微观结构。此外，在优化结果中，微观结构包括更多但更精细的结构构件，用于针对低激发频率优化的设计。