Controlling elastic wave propagation in plates using magic squares

Abstract

A magic square is defined as a square array of distinct positive numbers arranged such that the sum along the horizontal, vertical, and main diagonal directions are the same, which is called a magic number. Previously, we leveraged the magic square concept to create a new class of phononic structures whose dispersion behavior can be tuned without altering their global mass and stiffness. In this study, we study the dispersion behavior of a thin plate with non-structural mass arranged in a magic square pattern. The plate unit cell is partitioned into nine portions and individual point masses are embedded at the center of each portion. Our results show that the magic square mass-embedded plate provides a low-frequency out-of-plane bandgap whose widths can be controlled while maintaining the global mass of the plate structure. Additionally, we investigate a magic plate concept by applying different densities at each portion associated with the magic square patterns. Our preliminary results show that the magic density distribution results in the emergence of polarized bandgaps and provides a possibility of altering the plate modal frequency without altering the mode shape or the global mass.