Acoustic Cloaking of Moving Objects

The paper describes a theoretical and numerical approach to the modeling of an acoustic meta- material for the cloaking of an object moving within a compressible medium and impinged by an acoustic perturbation due to sources co-moving with it. The interest in the extension of the acoustic cloaking theory to objects and sources in arbitrary motion stems from the possibility to apply such a concept to the manipulation of the acoustic emissions produced by transporta- tion media. The ultimate goal is the alleviation of the acoustic impact on the community through the deep modification and/or cancellation of the intensity and directivity of the scat- tered field produced by the moving obstacle. The possible application in the aeronautical field imposes strict requirements on the mechanical properties of the acoustic metamaterial adopted, especially in terms of lightness, thus making the inertial cloaking (IC) approach an unfeasible candidate. Despite this fact, the IC is used here as a preliminary exercise to verify the possi- bility to achieve the cloaking. The generalized acoustic wave equation for the pseudo-pressure is written in a frame of reference rigidly connected to the object. The convected generalized wave equation so obtained is Laplace-transformed and then recast in an original boundary integral form. The Boundary Integral Equation formulation is suitably extended to take into account the equivalent field-source distribution needed to model the mechanical properties of the acoustic metamaterial constituting the cloak. The numerical solution of the resulting Boundary-Field Integral Equation can be obtained, at different frequencies, using a dedicated Boundary Element Method implemented into an in-house developed code. Particular atten- tion is payed to the mechanical properties of the resulting metamaterial, in order to avoid the solutions yielding totally unfeasible configurations.