周期性晶格因其特殊的振动行为已被广泛研究数十年。另一方面,某些类型的非周期晶格可实现周期晶格中无法获得的新现象。本文提出一类受元胞自动机启发的新型非周期晶格。元胞自动机最初作为一种机器自复制算法被提出,此后在计算机科学中得到深入研究。此类算法生成的结构未必具有周期性,却遵循明确定义的规则,并由此产生有趣的图案。本文利用该概念构建遵循此类规则的弹性晶格,并以Ulam-Warburton元胞自动机(UWCA)为例加以演示。从单原子正方晶格出发,构造UWCA晶格并分析其振动行为,结果展现出独特的动力学特性,包括对称的本征频率谱、高重数重复出现的固有频率,以及强局域化的角模态。本文预期,受计算机算法启发的晶格有望揭示新的波动现象,从而超越现有晶格设计的性能。
Periodic lattices have been widely explored for decades, owing to their peculiar vibrational behavior. On the other hand, certain types of aperiodic lattices have enabled new phenomena that may not be otherwise attainable in periodic ones. In this paper, a new class of aperiodic lattices inspired by cellular automaton is introduced. Cellular automata were originally developed as a machine replication algorithm and it has been intensively explored in computer science. These algorithms yield structures that are not necessarily periodic, yet follow well-defined rules that lead to interesting patterns. The concept is utilized here to build elastic lattices following such rules, and Ulam-Warburton Cellular Automaton (UWCA) is demonstrated as an example. Starting from a square monatomic lattice, an UWCA lattice is constructed and its vibrational behavior is analyzed, showing unique dynamical properties, including symmetric eigenfrequency spectra, repeated natural frequencies of large multiplicity, and the emergence of strongly localized corner modes. It is envisioned that computer-algorithm-inspired lattices may unlock new wave phenomena that could outperform existing lattice designs.