Skip to main content
SpringerLink
Log in

A mode-matching analysis of flexible shells and waveguides with partitioning and muffler conditions

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

This article explores the waveguide phenomenon that possesses trifurcated rigid inlet/outlet and muffler conditions. Additionally, this waveguide is linked to a finite, thin, and flexible shell with the aid of partitioning discs located at the interfaces. The inside of the discs is coated with sound absorbent material, which can be fibrous or perforated, depending on the impedance conditions of the surface. To demonstrate the use of absorbent material at the interfaces, impedance formulation is used. The mode matching procedure is then utilized to find solution, it relies on the orthogonality conditions accompanying the material characteristics of the bounding surface and within the fluid. The study includes modeling the utilization of absorbent material at interfaces, and numerical experiments to analyze the acoustic attenuation. The analysis focuses on a specific configuration with duct region radii and a half length of the chamber at a frequency of 700 Hz. The results demonstrate that the absorption of power and transmission loss versus frequency vary through the fibrous coating and the edge conditions, and changing the clamped ends to pin-jointed ends optimizes the dispersion powers and the loss due to transmission. The study yields useful information to the acoustic dispersion via flexural expansion chamber, highlighting the importance of material properties, edge conditions, and configuration settings in the acoustic attenuation. The mode matching method and numerical experiments presented in this study can be useful for designing acoustic devices with flexible shells, providing a better understanding of the underlying physics and optimizing their performance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Afzal, M., Nawaz, R., Ayub, M., Wahab, A.: Acoustic scattering in flexible waveguide involving step discontinuity. PLoS ONE 9(8), e103807 (2014)

    Article  PubMed  PubMed Central  ADS  Google Scholar 

  • Afzal, M., Nawaz, T., Nawaz, R.: Scattering characteristics of planar trifurcated waveguide structure containing multiple discontinuities. Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2020.1864062

    Article  Google Scholar 

  • Alahmadi, Hani, Afsar, Haleem, Nawaz, Rab, Alkinidri, Mohammed Omar: Scattering characteristics through multiple regions of the wave-bearing trifurcated waveguide. Waves Random Complex Media (2022). https://doi.org/10.1080/17455030.2022.2141912

    Article  Google Scholar 

  • Alahmadi, H.N., Nawaz, R., Alkinidri, M., et al.: Noise control from dual air cavity membranes in a rigid waveguide. Meccanica 57, 3023–3032 (2022). https://doi.org/10.1007/s11012-022-01611-8

    Article  MathSciNet  Google Scholar 

  • Alkinidri, M., Hussain, S., Nawaz, R.: Analysis of noise attenuation through soft vibrating barriers: an analytical investigation. AIMS Math. 8, 18066–18087 (2023)

    Article  MathSciNet  Google Scholar 

  • Ayub, M., Tiwana, M.H., Mann, A.B.: Acoustic diffraction in a trifurcated waveguide with mean flow. Commun. Nonlinear Sci. Numer. Simul. 15, 3939–3949 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  • Beck, B., Schiller, N., Jones, M.: Impedance assessment of an acoustic metamaterial inspired acoustic liner. J. Acoust. Soc. Am. 134, 4222–4222 (2013)

    Article  ADS  Google Scholar 

  • Brambley, E.J., Peake, N.: Stability and acoustic scattering in a cylindrical thin shell containing compressible mean flow. J. Fluid Mech. 602, 403–426 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  • Campos, L.M.B.C., Oliveira, J.M.G.S.: On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution. J. Acoust. Soc. Am. 116, 3336–3347 (2004)

    Article  CAS  PubMed  ADS  Google Scholar 

  • Cargill, A.M.: Low frequency acoustic radiation from a jet pipe-a second order theory. J. Sound Vib. 83(3), 339–354 (1982)

    Article  ADS  Google Scholar 

  • Demir, A., Cinar, O.Y.: Propagation of sound in an infinite two-part duct carrying mean flow inserted axially into a larger infinite duct with wall impedance discontinuity. J. Appl. Math. Mech. 89, 454–465 (2009)

    MathSciNet  Google Scholar 

  • Denia, F.D., Selamet, A., Fuenmayor, F.J., Kirby, R.: Acoustic attenuation performance of perforated dissipative mufflers with empty inlet/outlet extensions. J. Sound Vib. 302, 1000–1017 (2007)

    Article  ADS  Google Scholar 

  • Fuller, C.R.: Propagation and radiation of sound from flanged circular ducts with circumferentially varying wall admittances, I: Semi-infinite ducts. J. Sound Vib. 93, 321–340 (1984)

    Article  ADS  Google Scholar 

  • Groby, J.P., Huang, W., Lardeau, A., Auregan, Y.: The use of slow waves to design simple sound absorbing materials. J. Appl. Phys. 117, 124903 (2015)

    Article  ADS  Google Scholar 

  • Hassan, M., Mahvish, N., Nawaz, R.: Reflected field analysis of soft-hard pentafurcated waveguide. Adv. Mech. Eng. 9, 1–11 (2017)

    Google Scholar 

  • Hassan, M., Meylan, M.H., Bashir, A.: Mode matching analysis for wave scattering in triple and pentafurcated spaced ducts. Math Meth Appl Sci 39, 3043–3057 (2016)

    Article  MathSciNet  Google Scholar 

  • Ih, J., Lee, B.: Analysis of higher-order mode effects in the circular expansion chamber with mean flow. J. Acoust. Soc. Am. 77(4), 1377–1388 (1985)

    Article  ADS  Google Scholar 

  • Javaid, A., Ayub, M., Hussain, S.: Diffraction of EM-wave by a finite symmetric plate with Dirichlet conditions in cold plasma. Phy. Wave Phen. 28(4), 402–409 (2020)

    Google Scholar 

  • Junger, M.C., Feit, D.: Sound, Structures, and Their Interaction. MIT Press, Cambridge (1972)

    Google Scholar 

  • Kirby, R., Lawrie, J.B.: A point collocation approach to modelling large dissipative silencers. J. Sound Vib. 286, 313–339 (2005)

    Article  ADS  Google Scholar 

  • Lawrie, J.B.: On eigenfunction expansions associated with wave propagation along ducts with wave-bearing boundaries. IMA J. Appl. Math. 72, 376–394 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  • Lee, H., Kwak, M.K.: Free vibration analysis of a circular cylindrical shell using the Raleigh–Ritz method and comparison of different shell theories. J. Sound Vib. 353, 344–377 (2015)

    Article  ADS  Google Scholar 

  • Mangiarotty, R.A.: Acoustic lining concepts and materials for engine ducts. J. Acoust. Soc. Am. 48(3C), 783–794 (1970)

    Article  ADS  Google Scholar 

  • Martin, V., Cummings, A., Gronier, C.: Discrimination of coupled structural/acoustical duct modes by active control: principles and experimental results. J. Sound Vib. 274, 583–603 (2004)

    Article  ADS  Google Scholar 

  • McAlpine, A., Wright, M.C.M.: Acoustic scattering by a spliced turbofan inlet duct liner at supersonic fan speeds. J. Sound Vib. 292, 911–934 (2006)

    Article  ADS  Google Scholar 

  • Miles, J.W.: The analysis of plane discontinuities in cylindrical tubes. Part I J. Acoust. Soc. Am. 17(3), 259–271 (1946)

    Article  MathSciNet  ADS  Google Scholar 

  • Nawaz, T., Afzal, M., Nawaz, R.: The scattering analysis of trifurcated waveguide involving structural discontinuities. Adv. Mech. Eng. 11(7), 1–10 (2019)

    Article  Google Scholar 

  • Nawaz, R., Lawrie, J.B.: Scattering of a fluid-structure coupled wave at a flanged junction between two flexible membrane waveguides. J. Acoust. Soc. Am. 134(3), 1939–1949 (2013)

    Article  PubMed  ADS  Google Scholar 

  • Pullen, R. M., Lawrie, J. B.: Reflection and transmission at the junction between two sections of circular cylindrical shell, ICSV21, Beijing, China, 1–7 (2014)

  • Rawlins, A.D.: Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface. Proc. R. Soc. Lond. A361, 65–91 (1978)

    MathSciNet  ADS  Google Scholar 

  • Regan, B., Eaton, J.: Modeling the influence of acoustic liner non-uniformities on duct modes. J. Sound Vib. 219, 859–879 (1999)

    Article  ADS  Google Scholar 

  • Satti, J.U., Afzal, M., Nawaz, R.: Scattering analysis of a partitioned wave-bearing cavity containing different material properties. Phys. Scr. 94(11), 5223 (2019)

    Article  Google Scholar 

  • Shafique, S., Afzal, M., Nawaz, R.: On mode matching analysis of fluid-structure coupled wave scattering between two flexible waveguides. Can. J. Phys. 95(6), 581–589 (2017)

    Article  CAS  ADS  Google Scholar 

  • Shafique, S., Afzal, M., Nawaz, R.: On the attenuation of fluid-structure coupled modes in a non-planar waveguide. Math. Mech. Solids 25(10), 1–20 (2020)

    Article  MathSciNet  Google Scholar 

  • Tiryakioglu, B.: Mode matching analysis of sound waves in an infinite pipe with perforated screen. Acoust. Phys. 66, 580–586 (2020)

    Article  ADS  Google Scholar 

  • Tiryakioglu, B.: Radiation of acoustic waves by a partially lined pipe with an interior perforated screen. J. Eng. Math. 122, 17–29 (2020)

    Article  MathSciNet  Google Scholar 

  • Watson, W.R., Jones, M.G., Parrott, T.L., Sobieski, J.: Assessment of equation solvers and optimization techniques for non-axisymmetric Liners. AIAA J. 42, 2010–2018 (2004)

    Article  ADS  Google Scholar 

  • Yaseen, Aqsa, Nawaz, Rab: Acoustic radiation through a flexible shell in a bifurcated circular waveguide. Math. Meth. Appl. Sci. 46(5), 6262–6278 (2023)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Park Road, Tarlai Kalan, Islamabad, 45550, Pakistan

    Rab Nawaz & Aqsa Yaseen

  2. Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, 32093, Hawally, Kuwait

    Rab Nawaz

  3. Department of Mathematics, College of Science, Jouf University, P.0. Box 2014, Sakaka, Saudi Arabia

    Hani Alahmadi

  4. Department of Mathematics, Faculty of Arts and Sciences, Marmara University, 34722, Göztepe, İstanbul, Turkey

    Burhan Tiryakioglu

Authors
  1. Rab Nawaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aqsa Yaseen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hani Alahmadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Burhan Tiryakioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rab Nawaz.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nawaz, R., Yaseen, A., Alahmadi, H. et al. A mode-matching analysis of flexible shells and waveguides with partitioning and muffler conditions. Int J Mech Mater Des (2024). https://doi.org/10.1007/s10999-024-09710-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10999-024-09710-y

Keywords

Search

Navigation