粘弹性网络超材料的能量耗散设计原理
Design principles for energy dissipation in viscoelastic network metamaterials
AI总结：
该研究开发了基于图拉普拉斯算子的粘弹性桁架网络高效计算框架，揭示了网络横截面积重新分布对能量耗散的调控规律，为超材料耗散结构设计提供了理论与计算支撑。
AI中文摘要：
网络材料中的机械能耗散与从隔振到冲击防护的各类应用相关，但在无序桁架网络中识别最优耗散结构，采用传统有限元方法计算成本过高。我们开发了一种基于图拉普拉斯算子的高效谱框架，用于粘弹性桁架网络，其中精确保留了每根杆件的完整连续动力学，且问题规模随节点数而非单元级离散点数量缩放。利用该框架，我们研究了在不改变材料组成的前提下，网络内横截面积的重新分布如何控制能量耗散。我们发现，随机重新分布通常会相对于均匀基线降低耗散，而基于梯度的优化会产生非平凡结构，其形式由基础材料的固有衰减长度决定。聚焦于接近网络全局共振模式的驱动频率，我们表明最优质量分布会以衰减长度尺度从源点（受驱动节点）衰减，且在小衰减长度下，最优结构与边界条件无关。这些结果为后续在更复杂的无序结构上研究基于耗散长度尺度的设计原理提供了动力，并为大规模探索此类结构提供了高效计算框架。
英文摘要：
Mechanical energy dissipation in networked materials is relevant for applications from vibration isolation to impact protection, yet identifying optimal dissipative architectures in large disordered truss networks is computationally prohibitive with conventional finite element methods. We develop an efficient graph Laplacian-based spectral framework for viscoelastic truss networks, in which the full continuum dynamics of each rod are retained exactly and the problem size scales with the number of joints rather than element-level discretization points. Using this framework, we investigate how redistributing cross-sectional areas within a network (without changing material composition) controls energy dissipation. We find that random redistribution typically reduces dissipation relative to a uniform baseline, while gradient-based optimization yields nontrivial architectures whose form is governed by the intrinsic attenuation length of the base material. Focusing on driving frequencies near a global resonant mode of the network, we show that the optimal mass distribution decays from the source (driven joint) with the attenuation length scale, and at small attenuation lengths the optimal architecture is independent of the boundary conditions. These results motivate future studies of dissipation length scale based design principles on more complex disordered architectures and provide an efficient computational framework for exploring such structures at scale.
