Acoustic band gaps in arrays of neutral inclusions

We analyse numerically the acoustic stop band properties of an array of orthotropic coated cylinders whose elastic parameters are deduced from a geometric transform [H. Chen, C.T. Chan, Acoustic cloaking in three dimensions using acoustic metamaterials, Appl. Phys. Lett. 91 (2007) 183518]. We find that whereas a single coated inclusion is acoustically neutral at any frequency, an array of them might display some stop bands. More precisely, an array of freely vibrating coated voids is always neutral, whereas an array of clamped coated inclusions might display a zero frequency stop band. Interestingly, an array of radially symmetric coated inclusions behaves as local Helmholtz resonators, for which the eigenfield within each cloak is obtained in closed form, leading to a frequency estimate associated with the lower edge of the low frequency stop band. A finite phononic crystal of such coated cylinders behaves either as an invisible material or a reflector depending on the frequency of an acoustic source.