Wave Scattering through Step Down Cascading Junctions

Hadia Ali, Mahmood-ul-Hassan (), Ali Akgül and Ali Saleh Alshomrani
Additional contact information
Hadia Ali: Department of Mathematics, COMSATS University, Park Rd, Chak Shahzad, Islamabad 44000, Pakistan
Mahmood-ul-Hassan: Department of Mathematics, COMSATS University, Park Rd, Chak Shahzad, Islamabad 44000, Pakistan
Ali Akgül: Department of Computer Science and Mathematics, Lebanese American University, Beriut P.O. Box 13-5053, Lebanon
Ali Saleh Alshomrani: Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2023, vol. 11, issue 9, 1-14

Abstract: In this paper, we present the scattering of plane waves through two junctions with step-down cascading discontinuities. The solutions in the form of trapped modes corresponding to discrete eigen values are also presented. We illustrate the matching of continuity of pressure and velocity at the edges, conservation of energy, convergence/error of reflection, and reflection and transmission of the incident wave that go through the wider region. We discuss the reflection and transmission amplitudes by varying dimensions of wave-guide structure against wave number. We plot the surface and contour plots along with absolute potential solutions at different frequencies where extrema of field amplitudes occur. We also derive the results of extra ordinary acoustic transmission (EAT) for existing models. We apply the Mode Matching Method (MMM) to tackle the problem. Our model would be beneficial to structure the old and new models containing cavities and junctions. However, these structure models cannot retrieve our proposed geometrical model. The results will be helpful to model the practical exhaust system in noise reduction theory.

Keywords: wave-guide; eigen function expansion; cascaded-discontinuity; wave-scattering; extra ordinary acoustic transmission (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/2027/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/2027/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:9:p:2027-:d:1131840

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().