The 2.5D MST for sound propagation through arrays of cylinders parallel to the ground

In this work sound propagation through arrays of cylinders oriented parallel to the ground is of interest. The structures are placed in a three-dimensional domain and are insonified by a monopole or incoherent line source. Assuming a cross-sectionally invariant structure one can efficiently obtain the 3D pressure field for such arrangements by post-processing a series of 2D solutions - a technique usually referred to as a 2.5D transform. Since the initiation of the 2.5D transform for outdoor sound propagation it has been successfully applied together with frequency domain methods such as the Boundary Element Method and the Equivalent Sources Method. However, to predict for sound propagation through sonic crystal noise barriers the 2D Multiple Scattering Theory (2D MST) is often used, and has proven to be very efficient. We therefore introduce the 2.5D MST to solve for 3D scattering by clusters of acoustically rigid cylinders. It will be shown that only a few simple substitutions applied to the 2D MST kernel allows us to solve for imaginary wave numbers, which are needed in the 2.5D transform. The proposed method is numerically validated for two basic cases: (i) a point source above rigid ground, and (ii) off-axis scattering by a cylinder in free-field. Both are shown to be in excellent agreement with the respective reference calculations. We further demonstrate some calculation results for sound propagation through graded index sonic crystals, and find that off-axis insonification of these structures shifts the characteristic frequency response upwards, as could be expected. Finally, we also present calculation results for infinite and finite incoherent line sources and display the existence of a spectral smearing effect for both source types