Scattering by a cylinder covered with an arbitrary distribution of impedance and application to the optimization of a tramway noise abatement system

Abstract A semi-analytical solution for the two-dimensional scattering of a line source by a cylinder with an arbitrary distribution of surface impedance and its image with respect to a vertical baffle is derived. This description is used to model the shadowing due to a low-height semi-cylindrical noise barrier close to a tramway. After validation against the boundary element method, this solution is used in a gradient-based optimization approach of the admittance distribution to maximize the broadband insertion loss in a given receiver zone. First, a hypothetical but passive distribution is found, showing an improvement of more than 20 dB(A) with respect to a purely rigid barrier. Second, a feasible optimized surface treatment made of a porous layer and a micro-perforated resonant panel is proposed, with an improvement of 14 dB(A) with respect to an entirely rigid barrier and 8 dB(A) with respect to a uniform absorbent barrier. The optimization provides an automatic way of tuning the resonant panel so that the attenuation is enhanced in the frequency band where the source has the most spectral content. The benefit of using a non-uniform admittance distribution is evaluated in this idealized context to be about 8 dB(A).

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