Acoustic diffraction in a trifurcated waveguide with mean flow

Ayub, M.; Tiwana, M.H.; Mann, A.B.

doi:10.1016/j.cnsns.2010.01.027

Cited by 21 publications

(11 citation statements)

References 13 publications

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“…and 𝑒 1 = 𝜓 2𝑦 (0, 0) is an unknown constant which depicts the membrane behavior at point (𝑥, 𝑦) = (0, 0). In case of zero displacement edge condition (6), this constant always vanishes, 𝑖.𝑒., 𝑒 1 = 0. It is to note that Equation ( 17) contains the unknown sum termed as e1.…”

Section: Region  𝟐 ∶ {𝒙 > 𝟎 𝟎 ≤ 𝒚 ≤ 𝒂}mentioning

confidence: 99%

“…Most of these rectangular archetypes have been modeled by Laplace (or Helmholtz) equations with hard/soft/mixed-type conditions. For simplest geometries, the Wiener-Hopf (WH) approach can successfully be applied to seek solution to the relevant problems, as can be viewed in [6][7][8][9]. This method is adequate for boundary value problems which involve two-part boundary conditions invoked along the single coordinate.…”

Section: Introductionmentioning

confidence: 99%

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Modeling and analysis of scattering in trifurcated guided waves with hard and flexible outer surfaces: A mathematical study

Alahmadi

2023

Z Angew Math Mech

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This article discusses the scattering in a trifurcated guided wave featuring the combination of hard and flexible exterior surfaces. Through the formulation of the relevant boundary value problem and modes matching of orthogonal and non‐orthogonal functions, a comprehensive solution is obtained through infinite linear algebraic equations. The structural complexity of these structures introduces challenges related to non‐linearities in dispersive relations, and uncommon orthogonal characteristics of eigenfunctions. Therefore, by reorganizing the differential system into an algebraic one, a solution is obtained by truncating the system numerically. Further, analytical and numerical tests validate the solution, including graphical representations of relative powers versus frequency. The results reveal that transmission dominates reflection for frequencies above 900Hz in the symmetrical setting, with nearly equal power propagating through regions 2, 3, and 4. In the non‐symmetrical setting, power primarily transmits through region 4 for frequencies above 600Hz whereas most of the power being reflected at cut‐on frequencies when region 3 as rigid‐soft instead of rigid‐rigid. The obtained solution also confirms the properties of eigenfunctions, and the power distribution among different regions validates the accuracy of the solution. This work holds significance as it provides a standard procedure for modeling and solving a broad range of multifurcated problems with multiple dynamic boundary properties. The findings aid the understanding and development of waveguide systems, offering vision to practical applications in various fields involving complex wave propagation.

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Section: Region  𝟐 ∶ {𝒙 > 𝟎 𝟎 ≤ 𝒚 ≤ 𝒂}mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of scattering in trifurcated guided waves with hard and flexible outer surfaces: A mathematical study

Alahmadi

2023

Z Angew Math Mech

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“…The attenuation of sound in infinite bifurcated and trifurcated waveguides has been discussed in earlier studies. [9][10][11][12][13][14][15][16][17][18] One way of noise reduction is the introduction of expansion chamber in the duct wherein it travels. Further addition of sound absorbent material into the expansion chamber is another method that has proved suitable to muffle unwanted noise; see, for instance, earlier studies.…”

Section: Introductionmentioning

confidence: 99%

“…Demir and Cinar 8 considered a coaxial circular waveguide that comprises discontinuous wall impedances along the outer shell and uniform gas flow in inner tube to investigate a plane wave propagation and scattering. The attenuation of sound in infinite bifurcated and trifurcated waveguides has been discussed in earlier studies 9–18 . One way of noise reduction is the introduction of expansion chamber in the duct wherein it travels.…”

Section: Introductionmentioning

confidence: 99%

Acoustic radiation through a flexible shell in a bifurcated circular waveguide

Yaseen

Nawaz

2022

Math Methods in App Sciences

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The current study models and explains the fluid–structure coupled response of a flexible shell connected with two rigid coaxial shells via circular step discontinuities. Radiations from annular and inner regions of inlet rigid shells scatter on interfaces after interaction with the geometric variations and change of material properties. The flexible shell that supports vibrations along the shell is expressed though the Donnell–Mushtari formulation in the differential system. The mode‐matching technique is applied to solve the governing boundary value problem. The solution is projected on the orthogonal characteristics which in flexible casing is generalized as compared with the properties of acoustically rigid setting. The implication of generalized orthogonality relations governs additional constants that are found by defining the physical connection of shell with rigid disc. The clamped and pin‐jointed conditions are considered in this article. The scattering powers and transmission loss are analyzed against frequency, chamber length, and radii of shells for clamped and pin‐jointed edge conditions. It is found that the power propagation in annular shell and inner shell behave conversely. Moreover, configuration can be attenuated through the variation of dimensions of chamber and edge conditions.

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“…[1][2][3][4][5] The reduction of unwanted noise through the parallel plate setting of walls together with rigid, soft, or impedance type bounding characteristics has been discussed by many authors. For instance, the studies [6][7][8][9][10][11] include the acoustic scattering in planar trifurcated waveguides containing rigid, soft, or porous lining along with stationary and moving compressible fluid medium. In all such cases, the duct segments contain constant geometrical and physical properties for which the single field representation remains suitable.…”

Section: Introductionmentioning

confidence: 99%

The scattering analysis of trifurcated waveguide involving structural discontinuities

Nawaz

Afzal

Nawaz

2019

Advances in Mechanical Engineering

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The present article highlights the acoustic waves scattering in a trifurcated waveguide containing compressible fluid together with step discontinuities and change of bounding material properties. The study is important because of its applications in active noise control measures, especially used to control the low-frequency noise and related vibrations. The governing boundary value problem is solved by using the mode-matching technique. The solution is developed for the analysis of symmetric, uniform, and non-uniform cross-sections. The solution procedure begins by determining the expanded form of field potentials in various duct regions of the waveguide. Then, the pressures and the normal velocity modes across the waveguide regions are matched at interface. The energy flux against frequency and various duct configurations is plotted. The solution is validated altogether through the apposite analytical and numerical results.

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Acoustic diffraction in a trifurcated waveguide with mean flow

Cited by 21 publications

References 13 publications

Modeling and analysis of scattering in trifurcated guided waves with hard and flexible outer surfaces: A mathematical study

Modeling and analysis of scattering in trifurcated guided waves with hard and flexible outer surfaces: A mathematical study

Acoustic radiation through a flexible shell in a bifurcated circular waveguide

The scattering analysis of trifurcated waveguide involving structural discontinuities

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