Spacetime design of aeroacoustic metacontinua through optimal response matching

The paper deals with an integrated approach to the design of a metacontinuum capable to attain a specific target response when operating in a flow. The context of the research is related to the development of a general framework for identification of the mechanical properties required by a metamaterial-based, noise-abatement device for aeronautical application. The bulk metamaterial is here represented as an unconventional continuum with peculiar constitutive equations. The propagation of an acoustic perturbation in such a continuum is governed by a generalized wave equation written here in the aeroacoustic spacetime. The spacetime metrics of the generalized D'Alembertian reveals that the acoustic perturbations propagate through a curved spacetime, whose curvature depends jointly by the metacontinuum properties and the background aerodynamic flow. The identification of the mechanical properties of the metacontinuum is achieved by matching its acoustic response with a pre-defined target using numerical optimization. A suitable measure of the distance between the acoustic responses is used as the objective function to be minimized. The problem is completed by the relevant constraints and solved numerically using a meta-heuristic algorithm. Preliminary numerical results show how the developed method can effectively identify the elasticity tensor that induces an acoustic response compatible with the target.