Elastic Lattices Inspired by Ulam-Warburton Cellular Automaton

Abstract: Periodic lattices have been predominantly 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 automaton was 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 aperiodic patterns. The concept is utilized here to build elastic lattices following such rules, and Ulam-Warburton Cellular Automaton (UWCA) is demonstrated as an example. Resulted UWCA lattices are shown to exhibit 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.