Grid metastructures for ultrabroadband acoustic cloaking

Structural grids (grid metastructures) supporting discrete pressure waves similar to the pressure waves in continuous media are considered. The grids consist of links capable of transmitting longitudinal pressure waves and nodes providing equal pressures on the ends of outgoing links. The pressures in the nodes are governed by finite-difference equations approximating, under certain conditions, the wave equation in free space. It is shown that the pressures in the nodes are determined by the acoustic velocities and impedances of links rather than by the coordinates of the nodes and the link lengths. Therefore, a grid approximating pressure waves in a region of uniform homogeneous space can be replaced by an equivalent “deformed” grid with other spatial coordinates of nodes but the same pressure waves in the nodes. In particular, a locally “stretched” equivalent grid can be found that, theoretically, provides a sufficiently large region free from nodes and links. This property makes it possible to use these grids to construct ultrabroadband acoustic cloaks