Magic phononic structures

Abstract

To alter the dynamical response of a structure, engineers must alter its overall mass or stiffness, frequently at the expense of functional performance. Here, borrowing from the field of recreational mathematics, we propose the idea of magic structures—a new class of structures with invariant global mass and stiffness properties, but varying dynamical response. A magic square is a special array of numbers where all individual rows, columns, and diagonals sum up to the same constant value, called the magic number. Here, working within the context of phononic structures, we treat the total mass of the structure as its magic property. We study the dispersion behavior of an infinite, periodic spring-mass system with a 3 × 3 square unit cell with the magic mass property. While maintaining the magic mass, we study the effect of various mass distributions on the dispersion bands and phononic bandgaps. Our analysis shows that the frequency and width of the phononic bandgaps occurring in such structures can be altered while maintaining the total mass of the structure at a constant magic value. Finally, we present a practical application by altering the density distribution of a 2D plate to create low-frequency bandgaps without altering its global mass.