A finite element solution of a acoustic propagation in rigid porous media

International Journal for Numerical Methods in Engineering

Volumn 62, Issue 10, 2005, Pages 1295-1314

  Bermudez A ^a   Ferrin J L ^a   Prieto, A ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Finite element method; Porous medium; Rigid frame

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; HARMONIC ANALYSIS; MATHEMATICAL MODELS; MULTILAYERS; POROUS MATERIALS;

CIRCULATION MODES; COUPLED SYSTEMS; FINITE MULTILAYER SYSTEMS; HARMONIC EXCITATION;

ACOUSTIC WAVE PROPAGATION;

ACOUSTICS; FINITE ELEMENT METHOD; POROUS MEDIUM;

EID: 14844304654     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1218     Document Type: Article

References (27)

1. Delany MA, Bazley EN. Acoustic properties of fibrous absorbent materials. Applied Acoustics 1970; 3: 105-116.
2. Morse PM, Ingard KU. Theoretical Acoustics. McGraw-Hill: New York, 1978.
3. Johnson DL, Koplik J, Dashen R. Theory of dynamic permeability and tortuosity in fluid saturated porous media. Journal of Fluid Mechanics 1987; 176:379-402.
4. Attenborough K. Acoustical characteristics of rigid fibrous absorbents and granular materials. Journal of Acoustic Society of America 1983; 73:785-799.
5. Allard JF, Depollier C, Nicolas J, Lauriks W, Cops A. Propriétés acoustiques des matériaux poreux saturés d'air et théorie de Biot. Journal of Acoustics 1990; 3:29-38.
6. Champoux Y, Stinson MR. On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors. Journal of Acoustic Society of America 1992; 92(2):1120-1131.
7. Allard J-F, Champoux Y. New empirical equations for sound propagation in rigid frame fibrous materials. Journal of Acoustic Society of America 1992; 91(6):3346-3353.
8. Biot MA. Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Lower frequency range, and II. Higher frequency range. Journal of Acoustic Society of America 1956; 28(2):168-178 and 179-191.
9. Allard J-F, Aknine A, Depollier C. Acoustical properties of partially reticulated foams with high and medium flow resistance. Journal of Acoustic Society of America 1986; 79:1734-1740.
10. Shiau N-M. Multi-dimensional wave propagation in elastic porous materials. Ph.D. Thesis, School of Mechanical Engineering, Purdue University, 1991.
11. Allard J-F. Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials. Elsevier: New York, 1993.
12. Ene HI, Sanchez-Palencia E. Equations et phénomenènes de surface pour l'écoulement dans un modèle de milieu poreux. Journal de Mecanique 1975; 14:73-108.
13. Sanchez-Palencia E. Non-homegeneous Media and Vibration Theory. Lecture Notes in Physics, vol. 127. Springer: Berlin, 1980.
14. Mikelić A. Homogenization Theory and Applications to Filtration through Porous Media. Lecture Notes in Mathematics, vol. 1734. Springer: Berlin, 2000; 127-214.
15. Gilbert RP, Mikelié A. Homogenizing the acoustic properties of the seabed. Part I. Nonlinear Analysis 2000; 40(1-8):185-212.
16. Clopeau Th, Ferrín JL, Gilbert RP, Mikelić A. Homogenizing the acoustic properties of the seabed. Part II. Mathematical and Computer Modelling 2001; 33(8-9):821-841.
17. Ferrín JL, Mikelić A. Homogenizing the acoustic properties of a porous matrix containing an incompressible inviscid fluid. Mathematical Methods in Applied Science 2003; 26(10):831-859.
18. Easwaran V, Lauriks W, Coyette JP. Displacement-based finite element method for guided wave propagation problems: application to poroelastic media. Journal of Acoustic Society of America 1996; 100 5):2989-3002.
19. Panneton R, Atalla N. An efficient finite element scheme for solving the three-dimensional poroelasticity problem in acoustics. Journal of Acoustic Society of America 1997; 101(6):3287-3298.
20. Göransson P. A 3-D, symmetric, finite element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium. International Journal for Numerical Methods in Engineering 1998; 41:167-192.
21. Atalla N, Panneton R, Debergue P. A mixed displacement pressure formulation for poroelastic materials. Journal of Acoustic Society of America 1998; 104:1444-1452.
22. Bermúdez A, Hervella L, Rodríguez R. Finite element computation of the vibrations of a plate-fluid system with interface damping. Computer Methods in Applied Mechanics and Engineering 2001; 190 3021-3038.
23. Raviart PA, Thomas JM. A mixed finite element method for second order elliptic problems. In Mathematical Aspects of Finite Element Methods Lecture Notes in Mathematics, vol. 606. Springer: Berlin, 1977; 292-315.
24. Bermúdez A, Durán R, Muschietti MA, Rodríguez R, Solomin J. Finite element vibration analysis of fluid-solid systems without spurious modes. SIAM Journal on Numerical Analysis 1995; 32 1280-1295.
25. Bermúdez A, Hervella L, Rodríguez R. Finite element computation of three-dimensional elastoacoustic vibrations. Journal of Sound and Vibration 1999; 219(2):279-306.
26. Kiefling L, Feng GC. Fluid-structure finite element vibration analysis. AIAA Journal 1977; 14:292-315.
27. Bermúdez A, Ferrín JL, Prieto A. Finite element solution of new displacement/pressure poroelastic models in acoustics. Computer Methods in Applied Mechanics and Engineering, Accepted for publication.