Sound absorption and reflection from a resonant metasurface: Homogenisation model with experimental validation

Efficient manipulation of sound waves by some resonant acoustic metasurface designs has recently been reported in the literature. This paper presents a general theoretical framework for the description of sound wave interaction with the resonant metasurface that is independent of the nature of resonators and the excitation. The equations governing the behaviour of the metasurface are upscaled from the rigorous description of its unit cell using the two scale asymptotic homogenisation. The procedure relies on the existence of the boundary layer confined in the vicinity of the resonators operating in the deep subwavelength regime. The model is capable of describing sound interaction with the array of resonators positioned above or upon the substrate, so that the out of plane direction becomes an additional degree of freedom in the design. It is shown that at the leading order, the behaviour of the resonant surface is described in terms of the effective admittance, whose unconventional properties makes it possible to achieve the total sound absorption at multiple frequencies, broadband absorption, the phase reversal of the reflected wave at resonance and the control of the enclosure modes. The theory is validated by experiments performed in the impedance tube and in the anechoic environment using a surface array of spherical Helmholtz resonators with the extended inner neck. Experimental results confirm the effectiveness and robustness of the resonant surface for control of sound waves.