Regulating elastic bandgaps in two‐dimensional lattice grid by periodical cut‐off operations

Abstract

From periodically cutting off rods in two‐dimensional lattice grids, we find an easy and feasible way to control elastic bandgaps (BGs) in them. Due to the periodical cut‐off (PCO) operations, the exposed cantilevers lose the static load‐supporting ability; however, their mass distribution and inertia significantly affect the propagation of elastic waves. We first give several PCO types for square and triangular lattice grids. Then a detailed finite‐element method for the calculation of elastic BGs is described. The BGs in the hexagonal‐type PCO triangular lattice grid are studied for example. Localized resonant BGs are found and predicted. Frequency responses of the finite specimen are also analyzed to support our conclusions. Sketches of three kinds of PCO lattice grids: the PCO square lattice grid (left), the hex‐type PCO triangular lattice grid (center), and the Kagomé‐type PCO triangular lattice grid (right).