Wave scattering of non-planar trifurcated waveguide by varying the incident through multiple regions

Afsar, Haleem; Nawaz, Rab; Jan, Aasim Ullah

doi:10.1177/1687814020975283

Cited by 16 publications

(6 citation statements)

References 19 publications

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“…The algebraic system of equations required to compute the unknown wave amplitudes is generated next. 23,25…”

Section: Overview Of the Acoustic Problemmentioning

confidence: 99%

“…The algebraic system of equations required to compute the unknown wave amplitudes is generated next. 23,25 Starting with the expansion, equation ( 4) expressing continuity of pressure is multiplied by the transversal modal function J 0 a s r=R 1 ð Þ , with s = 0, 1, 2, ., N a , and integrated over S A . This leads to ð…”

Section: Overview Of the Acoustic Problemmentioning

confidence: 99%

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Computational approach for the acoustic modelling of large aftertreatment devices with multimodal incident sound fields

Sánchez-Orgaz,

Denia,

Martínez-Casas

et al. 2023

Advances in Mechanical Engineering

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The influence of multimodal incident sound fields on the acoustic behaviour of large aftertreatment devices incorporating a monolith is modelled and analysed in detail. The analytical mode matching method is applied to the compatibility conditions of the three-dimensional acoustic fields at the device geometric discontinuities, leading to the computation of the complex wave amplitudes in all the subdomains involved and the corresponding device transmission loss. To have a realistic model, three-dimensional propagation must be considered in the inlet/outlet ducts and chambers, while one-dimensional wave propagation has to be assumed along the small capillaries of the aftertreatment device monolith (such catalytic converters and particulate filters); therefore, the monolith can be replaced by a plane wave four-pole transfer matrix from an acoustical point of view. On the other hand, for large aftertreatment device inlet ducts such as those found in heavy-duty and off-road engines, the usual models with plane incident wave excitation are not accurate since the onset of higher order incident modes in the inlet duct is expected for the frequency range of interest. Therefore, a variation of the acoustic attenuation performance is likely to occur depending on these modes, similar to the results previously found in the case of large dissipative silencers. Results are presented for three different multimodal incident sound field hypotheses: equal modal amplitude, equal modal power and equal modal energy density. A relevant influence on the sound attenuation is found for the test problems considered in the current investigation.

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“…The algebraic system of equations required to compute the unknown wave amplitudes is generated next. 23,25…”

Section: Overview Of the Acoustic Problemmentioning

confidence: 99%

Section: Overview Of the Acoustic Problemmentioning

confidence: 99%

Computational approach for the acoustic modelling of large aftertreatment devices with multimodal incident sound fields

Sánchez-Orgaz,

Denia,

Martínez-Casas

et al. 2023

Advances in Mechanical Engineering

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show abstract

“…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%

“…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%

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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“…In the absence of phase discontinuities, the MM technique was used to address the acoustic dispersion in planar trifurcated and pentafurcated waveguides structures carrying compressible fluid. Current research in this field is noticeable using specified references [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Energy distribution of bifurcated waveguide structure with planar and non-planar surfaces

Afsar

Akbar

2022

Mathematics and Mechanics of Solids

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The present communication addresses the reflection and transmission analysis of a two-dimensional waveguide structure with planar and non-planar surfaces. In the fields of physics, engineering and applied mathematics, research is being carried out to control or reduce unwanted and harmful noise to an acceptable level. Our aim is to solve the boundary value problem developed to simulate the transmission and reflection of a bifurcated waveguide structure in the channels or ducts that have abrupt changes in the height together with planar and non-planar surfaces. Furthermore, the eigenfunctions are linearly independent and non-orthogonal. To solve non-orthogonal eigenfunctions, a generalized orthogonality relation has been developed. Solution is obtained using mode matching technique (MMT) along with generalized orthogonal relations. In the last section, solution is viewed graphically in the inner and outer ducts or channels for different frequencies and height. The expressions for energy distribution in different duct regions are obtained and sketched subject to the various properties of the waveguide material. The results are well supported for a number of mathematical and physical reasons.

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Wave scattering of non-planar trifurcated waveguide by varying the incident through multiple regions

Cited by 16 publications

References 19 publications

Computational approach for the acoustic modelling of large aftertreatment devices with multimodal incident sound fields

Computational approach for the acoustic modelling of large aftertreatment devices with multimodal incident sound fields

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

Energy distribution of bifurcated waveguide structure with planar and non-planar surfaces

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