Scattering characteristics through multiple regions of the wave-bearing trifurcated waveguide

Alahmadi, Hani; Afsar, Haleem; Nawaz, Rab; Alkinidri, Mohammed

doi:10.1080/17455030.2022.2141912

Cited by 11 publications

(7 citation statements)

References 23 publications

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“…In the context of structural difficulties, the phrases "clamped," "pivoted," and "pin-jointed" are frequently used to characterise various sorts of boundary conditions. These conditions explain how a specific structure is either supported or constrained at the edge and can be viewed in many related studies [21,22,[24][25][26]. Moreover in order to ensure matching of pressure and velocity at the junction, we impose the following conditions…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Multiplying above relation on both sides by cos[𝜆 𝑚 (𝑦 − 𝑎)], then integrating over (𝑎, 𝑏) and using the relation (22), we arrive at…”

Section: Region  𝟑 ∶= {𝒙 > 𝟎 𝒂 ≤ 𝒚 ≤ 𝒃}mentioning

confidence: 99%

“…In the context of structural difficulties, the phrases “clamped,” “pivoted,” and “pin‐jointed” are frequently used to characterise various sorts of boundary conditions. These conditions explain how a specific structure is either supported or constrained at the edge and can be viewed in many related studies [21, 22, 24–26]. Moreover in order to ensure matching of pressure and velocity at the junction, we impose the following conditions

$$\begin{equation} {\left.

…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Tiwana et al [20] also studied sound radiation effects due to bifurcated waveguide structures with multiple bounding properties of non-dynamics type. Nevertheless, there is a literature gap in addressing multiple multifurcated problems with flexible boundaries except very few studies are established in recent times [21][22][23]. The consideration of such structures becomes imperative as rectangular waveguides have a much larger bandwidth over which only a single mode can propagate.…”

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: Mathematical Formulationmentioning

confidence: 99%

“…Multiplying above relation on both sides by cos[𝜆 𝑚 (𝑦 − 𝑎)], then integrating over (𝑎, 𝑏) and using the relation (22), we arrive at…”

Section: Region  𝟑 ∶= {𝒙 > 𝟎 𝒂 ≤ 𝒚 ≤ 𝒃}mentioning

confidence: 99%

$$\begin{equation} {\left.

…”

Section: Mathematical Formulationmentioning

confidence: 99%

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

Self Cite

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“…8,9 The Mode-Matching method is particularly effective in infinite ducts with different discontinuities. [11][12][13][14][15] The fields in each region are expressed in terms of these modes and the solution is obtained. If a semi-infinite or finite geometry is in question, a hybrid method can be applied by using the Wiener-Hopf technique on the outer surface of the duct and the Mode-Matching method on the inner surface.…”

Section: Introductionmentioning

confidence: 99%

Acoustic wave radiation from a coaxial pipe with partial lining and inner perforated screen

Tiryakioglu

2023

International Journal of Aeroacoustics

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In this study, the analysis of sound waves from a coaxial pipe with a perforated screen and a partial acoustic absorbing lining is investigated. The geometry under consideration consists of an infinite pipe placed in a semi-infinite cylindrical pipe such that the inner surface of the outer pipe is covered with a partial acoustic absorbing lining. Because of the partial lining, the solution is obtained with both the Jones’ method and the Mode-Matching method. The effects of the problem parameters such as perforated screen and partial lining on the radiation phenomenon are presented.

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Reflection and transmission analysis of an acoustic trifurcated waveguide with wave‐bearing structural discontinuity

Afsar

Alam

2023

Math Methods in App Sciences

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The dilution of undesired and vandalize noise to a sustainable level is the subject of continuing research in the fields of applied mathematics, physics, and engineering. Therefore, the present study investigates the mechanism of an acoustic wave scattering, which includes the force propagation due to the incidence through region of elastic boundary condition. Both planar and nonplanar surfaces are allowed in this waveguide configuration. In this structure, the scattered fields in the regions of the inner surfaces are acoustically rigid and satisfy the standard orthogonality relation, while the fields on the upper outer surfaces are flexural nature that can be tackled using modified orthogonality relation. Thus, we intend to simultaneously take into account the behavior of the scattered field in both planar and nonplanar zones. Solving nonorthogonal eigenfunctions required the development of a modified orthogonality relation. Modified orthogonal relation and the mode‐matching (MM) technique have combined to get the solution of proposed model. The last section graphically discusses the solution for various frequencies and heights to observe the scattering behavior in all regions of the duct. In accordance with different characteristics of the waveguide material, expressions for the distribution of powers in different parts of the channel are developed and schematically depicted. A variety of mathematical and physical justifications provide strong support to results.

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Scattering characteristics through multiple regions of the wave-bearing trifurcated waveguide

Cited by 11 publications

References 23 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 wave radiation from a coaxial pipe with partial lining and inner perforated screen

Reflection and transmission analysis of an acoustic trifurcated waveguide with wave‐bearing structural discontinuity

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