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Diffraction of acoustic waves by multiple semi-infinite arraysa).
M A Nethercote1, A V Kisil1, R C Assier1
1Department of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdom.
The Journal of the Acoustical Society of America
|September 11, 2023
Summary
This study extends the Wiener-Hopf method to analyze acoustic wave diffraction by multiple periodic arrays of scatterers. The novel discrete Wiener-Hopf technique enables solutions for complex geometries previously intractable with traditional methods.
Area of Science:
- Acoustics
- Wave diffraction
- Mathematical physics
Background:
- Analytical methods are crucial for acoustics.
- The Wiener-Hopf method is limited to specific boundary conditions.
- Previous work addressed single arrays of point scatterers.
Purpose of the Study:
- Generalize acoustic wave diffraction analysis.
- Develop a method for discrete, non-parallel boundaries.
- Solve problems involving multiple periodic semi-infinite arrays.
Main Methods:
- Construct coupled systems of equations for each array.
- Employ the discrete Wiener-Hopf technique.
- Invert matrix equations using elementary matrix arithmetic.
Main Results:
- Successfully generalized the Wiener-Hopf method.
- Developed a technique for arbitrary orientations and multiple arrays.
- Achieved accurate numerical results including thousands of scatterers.
Conclusions:
- The discrete Wiener-Hopf technique is effective for complex acoustic diffraction.
- This method overcomes limitations of traditional Wiener-Hopf applications.
- Provides a robust tool for analyzing scattering from periodic structures.
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