研究目的
To investigate the radiation of acoustic waves from two coaxial opposite semi-infinite circular cylinders with impedance boundaries in the overlapping region and to present an alternative method of formulation which enables to skip the most challenging step of matrix factorization.
研究成果
The study successfully applies the Wiener-Hopf technique to investigate the radiation of sound from two semi-infinite circular cylinders with impedance boundaries in the overlapping region. Numerical solutions demonstrate the effects of various parameters on the radiation phenomenon, showing that appropriate impedance values can attenuate radiation and increase transmission.
研究不足
The study is limited to theoretical modeling and numerical solutions. The practical implementation and experimental validation of the findings are not addressed.
1：Experimental Design and Method Selection:
The study uses the eigenfunction expansion in the overlap region and the Fourier transform technique elsewhere to formulate the problem as two uncoupled modified Wiener-Hopf equations of the second kind.
2：Sample Selection and Data Sources:
The configuration involves two semi-infinite circular cylindrical waveguides of different radii with a common longitudinal axis, immersed in an inviscid and compressible stationary fluid.
3：List of Experimental Equipment and Materials:
The study involves theoretical modeling and numerical solutions without specific experimental equipment.
4：Experimental Procedures and Operational Workflow:
The problem is reduced to two Wiener-Hopf equations, solved through factorization and decomposition procedures, involving two systems of linear algebraic equations with infinitely many unknown expansion coefficients.
5：Data Analysis Methods:
Numerical solutions to the systems are obtained for various values of the problem parameters, and the effects of these parameters on the radiation phenomenon are studied graphically.
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