A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with...

Area of Science:

• Fluid mechanics and acoustics
• Computational physics
• Materials science

Background:

• Helmholtz scattering off poro-elastic plates is crucial for modeling fluid-mechanics and acoustics problems.
• Existing methods struggle with variable physical parameters and coupled thin-plate equations in these models.
• Poro-elastic materials offer unique acoustic properties that require advanced simulation techniques.

Purpose of the Study:

• To develop a novel, fast, and accurate boundary spectral method for Helmholtz scattering off multiple variable poro-elastic plates in 2D.
• To overcome the limitations of current methods in handling complex boundary conditions and varying material properties.
• To investigate the aeroacoustic effects of stiffness variations, including those mimicking acoustic black holes.

Main Methods:

• A boundary spectral method based on the collocation of local Mathieu function expansions.
• Implementation for two-dimensional Helmholtz scattering problems involving multiple poro-elastic plates.
• Direct computation of far-field directivity via sine series approximation and stable near-field evaluation.

Main Results:

• The new method demonstrates superior speed and accuracy compared to elastic boundary element methods.
• It enables stable and efficient computation of both near-field and far-field scattering.
• Analysis reveals that a power-law decrease in stiffness parameters creates unique scattering and aeroacoustic effects, akin to an acoustic black hole.

Conclusions:

• The developed boundary spectral method is a powerful and flexible tool for analyzing Helmholtz scattering off complex poro-elastic structures.
• It provides new insights into the acoustic behavior of variable stiffness plates, including phenomena previously difficult to study.
• The findings highlight the potential for designing metamaterials with tailored acoustic properties, such as acoustic black holes.