Research PaperNo Access

Experimental Validation of a Coupled Acoustic Fluid-Poroelastic-Plate Model with Frontal and Lateral Source Excitations

Ikerlan Technological Research Center, P^o J. M. Arizmendiarreta, 2, 20500 Arrasate-Mondragón, Gipuzkoa, Spain

Centro de Investigación en Tecnologías de la, Información y las Comunicaciones, Universidade da Coruña, Campus de Elviña, s/n, 15008 A Coruña, Spain

E-mail Address: luis.hervella@udc.es

Search for more papers by this author

, and

A. Prieto

https://orcid.org/0000-0002-4399-6878

Centro de Investigación y Tecnología, Matemática de Galicia, Universidade da Coruña, Campus de Elviña, s/n, 15008 A Coruña, Spain

E-mail Address: andres.prieto@udc.es

Search for more papers by this author

https://doi.org/10.1142/S2591728524500075Cited by:0 (Source: Crossref)

Abstract

This work deals with a coupled acoustic problem involving a compressible fluid and a poroelastic material contained in a cavity whose walls are all rigid except for the top, where a flexible plate is placed. The fluid is described utilizing its acoustic pressure, whereas, for the plate, the Naghdi shell model is used. The mechanical behaviour of the absorbing layer attached to the plate is described by using the Biot-Allard model, where the governing equations are written in the displacement-based formulation. The main novelty of this work lies in addressing the coupling between the plate and the poroelastic medium using the Reissner-Mindlin formulation for the Naghdi’s shell model and the displacement-based formulation for the Biot-Allard model. A comprehensive three-dimensional analysis is performed, comparing numerical and experimental results and showing the advantages of using the Biot-Allard poroelastic model in combination with the Naghdi shell model to predict the in-plane displacements of the plate structure over other fluid-equivalent formulations, such as the Allard-Champoux model.

Keywords:

References

1. A. Prieto A. Bermúdez, L. Hervella-Nieto and R. Rodriguez, Validation of acoustic models for time-harmonic dissipative scattering problems, Journal of Computational Acoustics, 15(01) (2007) 95–121. Link, Google Scholar
2. J. F. Allard and Y. Champoux, New empirical equations for sound propagation in rigid frame fibrous materials, J. Acoust. Soc. Am., 91 (1992) 3346–3353. Crossref, Google Scholar
3. J. F. Allard and N. Atalla, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials (John Wiley & Sons, 2009). Crossref, Google Scholar
4. D. K. Anthony and S. J. Elliot, A comparison of three methods of measuring the volume velocity of an acoustic source, J. Audio Eng. Soc., 39 (1991) 355–365. Google Scholar
5. D. N. Arnold and R. S. Falk, Asymptotic analysis of the boundary layer for the reissner-mindlin plate model, SIAM Journal on Mathematical Analysis, 27(2) (1996) 486–514. Crossref, Google Scholar
6. N. Atalla and R. Panneton, Acoustic absorption of macro-perforated porous materials. J. Sound and Vibration, 243 (2001) 659–678. Crossref, Google Scholar
7. N. Atalla, R. Panneton and P. Debergue, A mixed displacement-pressure formulation for poroelastic materials, J. Acoust. Soc. Am., 104(3) (1998) 1444–1452. Crossref, Google Scholar
8. N. Atalla, F. Sgard and C. K. Amedin, On the modeling of sound radiation from poroelastic materials, Journal of the Acoustical Society of America, 120(4) (2006) 1990–1995. Crossref, Google Scholar
9. D. Barpanda and J. M. Tudor, Solutions-based approach for reducing noise in washing machines, Sound and Vibration, 43(11) (2009) 6–10. Google Scholar
10. K. J. Bathe and E. N. Dvorkin, A four-node plate bending element based on mindlind/reissner plate theory and a mixed interpolation, Int. J. Numer. Meth. Engng, 21 (1985) 367–383. Crossref, Google Scholar
11. I. I. Beranek and I. L. Vér, Noise and Vibration Control Engineering: Principles and Applications (Wiley-Interscience, 1992). Google Scholar
12. A. Bermúdez, J. L. Ferrín and A. Prieto, A finite element solution of acoustic propagation in rigid porous media, International Journal for Numerical Methods in Engineering, 62(10) (2005) 1295–1314. Crossref, Google Scholar
13. A. Bermúdez, J. L. Ferrín and A. Prieto, Finite element solution of new displacement/pressure poroelastic models in acoustics, Computer Methods in Applied Mechanics and Engineering, 195(17–18) (2006) 1914–1932. Crossref, Google Scholar
14. A. Bermúdez, P. Gamallo, L. Hervella-Nieto and R. Rodríguez, Finite element analysis of pressure formulation of the elastoacoustic problem, Numer. Math., 95 (2003) 29–51. Crossref, Google Scholar
15. A. Bermúdez, L. M. Hervella-Nieto and R. Rodríguez, Finite element computation of the vibration of a plate-fluid system with interface damping, Comput. Meth. Appl. Mech. Engrg., 190 (2001) 3021–3038. Crossref, Google Scholar
16. A. Bermúdez, P. Gamallo, L. Hervella-Nieto, R. Rodríguez and D. Santamarina, Fluid-structure acoustic interaction, In S. Marburg and B. Nolte, editors, Computational Acoustics of Noise Propagation in Fluids (Springer-Verlag, 2008), 253–286. Crossref, Google Scholar
17. M. A. Biot, The theory of propagation of elastic waves in a fluid saturated porous solid, J. Acoust. Soc. Am, 28 (1956) 168–178. Crossref, Google Scholar
18. T. Bravo and C. Maury, Sound attenuation and absorption by anisotropic fibrous materials: Theoretical and experimental study, J. Sound Vib., 417 (2018) 165–181. Crossref, Google Scholar
19. R. Caracciolo, A. Gasparetto and M. Giovagnoni, An experimental technique for complete dynamic characterization of a viscoelastic material, J. Sound Vib., 272 (2004) 1013–1032. Crossref, Google Scholar
20. G. Ciaburro and G. Iannace, Modeling acoustic metamaterials based on reused buttons using data fitting with neural network, J. Acoust. Soc. Am., 150(1) (2021) 51–63. Crossref, Google Scholar
21. D. Chapelle and K. J. Bathe, The Finite Element Analysis of Shells - Fundamentals (Springer, 2003). Crossref, Google Scholar
22. R. G. Durán, E. Hernández, L. Hervella-Nieto, E. Liberman and R. Rodríguez, Error estimates for low-order isoparametric quadrilateral finite elements for plates, SIAM J. Numer. Anal., 41 (2003) 1751–1772. Crossref, Google Scholar
23. D. Vandepitte, E. Deckers, S. Jonckheere and W. Desmet, Modelling techniques for vibro-acoustic dynamics of poroelastic materials, Arch. Comput. Meth. Engng., 22 (2015) 183–236. Crossref, Google Scholar
24. U. Berardi, A. Putra, S. M. Mousavi, M. Faridan, S. E. Samaei, E. Taban, P. Soltani and A. Khavanin, Measurement, modeling, and optimization of sound absorption performance of kenaf fibers for building applications, Building and Environment, 180(107087), (2020). Google Scholar
25. ASTM E756-04, Standard Test Method for Measuring Vibration-Damping Properties of Materials (American Society for Testing and Materials, 2004). Google Scholar
26. Y. Fan and Z. Ji, Finite element approach for three-dimensional linearized potential equation with application to muffler acoustic attenuation prediction, Journal of Theoretical and Computational Acoustics, 31(01) (2023). Link, Google Scholar
27. Z. E. A. Fellah and C. Depollier, On the propagation of acoustic pulses in porous rigid media: A time-domain approach, Journal of Computational Acoustics, 09(03) (2001) 1163–1173. Link, Google Scholar
28. P. Göransson, A weighted residual formulation of the acoustic wave propagation through a flexible porous material and comparison with a limp material model, J. Sound Vib., 182 (1995) 479–494. Crossref, Google Scholar
29. M. A. Heckl, Analytical model of nonlinear thermo-acoustic effects in a matrix burner, J. Sound Vib., 332 (2013) 4021–4036. Crossref, Google Scholar
30. E. Hernández and L. Hervella-Nieto, Finite element approximation of free vibration of folded plates, Comput. Methods Appl. Mech. Engng., 198 (2009) 1360–1367. Crossref, Google Scholar
31. K. V. Horoshenkov and K. Sakagami, A method to calculate the acoustic response of a thin, baffled, simply supported poroelastic plate, Journal of the Acoustical Society of America, 110(2) (2001) 904–917. Crossref, Google Scholar
32. K. V. Horoshenkov, K. Sakagami and M. Morimoto, On the dissipation of acoustic energy in a thin, infinite, poroelastic plate, Acta Acustica United with Acustica, 88(4) (2002) 500–506. Google Scholar
33. D. L. Johnson, J. Koplik and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mechanics, 176 (1987) 379–402. Crossref, Google Scholar
34. A. K. Kan, X. X. Zhang, Z. F. Chen and D. Cao, Effective thermal conductivity of vacuum insulation panels prepared with recyclable fibrous cotton core, International Journal of Thermal Sciences, 187(108176) (2023). Google Scholar
35. Y. Liu and A. Sebastian, Effects of external and gap mean flows on sound transmission through a double-wall sandwich panel, J. Sound Vib., 344 (2015) 399–415. Crossref, Google Scholar
36. M. A. Hamdi N. Atalla and R. Panneton, Enhanced weak integral formulation for the mixed (u,p) poroelastic equations, J. Acoust. Soc. Am., 109(6) (2001) 3065–3068. Crossref, Google Scholar
37. N. Javani, I. Dincer, D. F. Naterer and G. L. Rohrauer, Modeling of passive thermal management for electric vehicle battery packs with PCM between cells, Applied Thermal Engineering, 73(1) (2014) 307–316. Crossref, Google Scholar
38. P. M. Naghdi, The theory of shells and plates, In C. Truesdell, editor, Linear Theories of Elasticity and Thermoelasticity: Linear and Nonlinear Theories of Rods, Plates, and Shells, pp. 425–640. (Springer, Berlin, Heidelberg, 1973). Crossref, Google Scholar
39. L. Nagler, P. Rong, M. Schanz and O. Von Estorff, Sound transmission through a poroelastic layered panel, Computational Mechanics, 53(4) (2014) 549–560. Crossref, Google Scholar
40. L. Nagler and M. Schanz, An extendable poroelastic plate formulation in dynamics, Archive of Applied Mechanics, 80(10) (2010) 1177–1195. Crossref, Google Scholar
41. R. Panneton and N. Atalla, Numerical prediction of sound transmission through finite multilayer systems with poroelastic materials, J. Acoust. Soc. Am., 100(1) (1996) 346–354. Crossref, Google Scholar
42. R. Panneton and N. Atalla, An efficient finite element scheme for solving the three dimensional poroelasticity problem in acoustics, J. Acoust. Soc. Am., 101(6) (1997) 3287–3298. Crossref, Google Scholar
43. X. Sagartzazu and L. Hervella-Nieto, Impedance prediction for several porous layers on a moving plate: Application to a plate coupled to an air cavity, Journal of Computational Acoustics, 19(04) (2011) 379–94. Link, Google Scholar
44. X. Sagartzazu, L. Hervella-Nieto and J. M. Pagalday, Review in sound absorbing material, Arch. Comput. Meth. Engng., 15 (2008) 311–342. Crossref, Google Scholar
45. X. Sagartzazu, L. Hervella-Nieto and J. M. Pagalday, Numerical computation of the acoustic pressure in a coupled covered plate/fluid problem: Experimental validation, Acta Acustica United with Acustica, 96 (2010) 317–327. Crossref, Google Scholar
46. J. Sladek, V. Sladek, M. Gfrerer and M. Schanz, Mindlin theory for the bending of porous platesm Acta Mechanica, 226(6) (2015) 1909–1928. Crossref, Google Scholar
47. P. Soltani and M. Norouzi, Prediction of the sound absorption behavior of nonwoven fabrics: Computational study and experimental validation, J. Sound Vib., 485(115607) (2020). Google Scholar
48. A. Takezawa, T. Yamamoto, X. Zhang, K. Yamakawa, S. Nakano and M. Kitamura, An objective function for the topology optimization of sound-absorbing materials, J. Sound Vib., 443 (2019) 804–819. Crossref, Google Scholar
49. G. H. Yoon, Unified analysis with mixed finite element formulation for acoustic-porous-structure multiphisics system, Journal of Computational Acoustics, 23(01) (2015). Link, Google Scholar
50. T. G. Zieliński, R. Venegas, C. Perrot, M. Červenka, F. Chevillotte and K. Attenborough, Benchmarks for microstructure-based modelling of sound absorbing rigid-frame porous media, J. Sound Vib., 483(115441) (2020). Google Scholar