Scattering matrices in non-uniformly lined ducts

International Journal of Advances in Engineering and Pure Sciences

2019

In this study, semi-infinite rigid pipe is considered. An analytical solution is presented for the diffraction problem of acoustic waves spreading from a ring source by semi-infinite pipe. Applying the boundary and continuity conditions in conjunction with the Fourier transform technique, the boundary value problem is solved analytically. The influence of the problem parameters on the diffraction phenomenon is displayed graphically.

Section: Introductionmentioning

confidence: 99%

A Note on Ring Source over Semi-Infinite Rigid Pipe

International Journal of Advances in Engineering and Pure Sciences

2019

“…F − (ρ, α) and F + (ρ, α) are analytical functions in the lower and upper half plane of complex α plane (Demir, 2017), respectively. The solution of Eq.…”

Section: Derivations Of the Modified Wiener-hopf Equationsmentioning

confidence: 99%

“…The first geometry is defiened by {ρ = a, z ∈ (−∞, 0)} ∪ {ρ ∈ (a, b), z = 0} ∪ {ρ = b, z ∈ (0, ∞)}, and the second geometry is defined by {ρ = b, z ∈ (−∞, l)} ∪ {ρ ∈ (b, c), z = l} ∪ {ρ = c, z ∈ (l, ∞)}. The problem is reformulated according to geometries and scattering matrices are found by the help of Wiener-Hopf equation (Demir, 2017). Matrix sizes vary according to the number of incoming, reflected or transmitted modes.…”

Section: Scattering Matrices Techniquementioning

confidence: 99%

Archives of Acoustics

Demír

2020

Scattering of sound waves in two stepped cylindrical duct which walls are coated with different acoustically absorbent materials is investigated by using Wiener-Hopf technique directly and by determining scattering matrices. First, by using Fourier transform technique we obtain a couple of modified Wiener-Hopf equations whose solutions involve four sets of infinitely many unknown expansion coefficients providing systems of linear algebraic equations. Then we determine scattering matrices of the problem and we state the total transmitted field by using generalized scattering matrix method. Numerical results are compared for different parameters.

“…Analysis of sound wave propagation in waveguides with discontinuities has received wide attention due to its importance in acoustics. Up until now, numerous analytical and numerical studies have been derived [1][2][3][4][5][6]. One method of reducing noise is to introduce linings to absorb the noise as it travels along the pipe.…”

Section: Introductionmentioning

confidence: 99%

Sound Radiation from Non-Uniformly Lined Duct with Partial Rigidity

Comput. Math. and Math. Phys.

2021

Radiation of sound waves by a semi-infinite circular cylindrical pipe with non-uniform lining is analyzed by using the Jones' method in conjunction with the mode matching technique. This mixed method of formulation gives rise to a scalar Wiener-Hopf equation. The inner surface of the duct is coated by acoustically absorbing different linings. In the present study, different linings with partial rigidity make the problem more interesting when it is compared with the uniform lining. The solution of the considered problem involves three infinite sets of coefficients satisfying three infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the radiation phenomenon are shown graphically. The solution is compared graphically with a similar study existing in the literature. A perfect agreement is observed between the both results.