A direct hybrid Finite Element - Wave Based Method for the steady-state analysis of acoustic cavities with poro-elastic damping layers using the coupled Helmholtz-Biot equations

Computer Methods in Applied Mechanics and Engineering

Volumn 263, Issue , 2013, Pages 144-157

  Jonckheere, Stijn ^a   Deckers, Elke ^a   Van Genechten, Bert ^a,b   Vandepitte, Dirk ^a   Desmet, Wim ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b LMS INTERNATIONAL   (Belgium)

Author keywords

Biot theory; Direct hybrid approach; Finite Element Method; Poro elastic materials; Wave Based Method

Indexed keywords

BIOT THEORY; DIRECT HYBRID; FINITE-ELEMENT APPROACH; GOVERNING DIFFERENTIAL EQUATIONS; NUMERICAL VALIDATIONS; POROELASTIC MATERIALS; STEADY-STATE ANALYSIS; WAVE BASED METHOD;

ACOUSTIC FIELDS; DAMPING; DIFFERENTIAL EQUATIONS; ELASTICITY; EQUATIONS OF STATE; HELMHOLTZ EQUATION; NUMERICAL METHODS;

FINITE ELEMENT METHOD;

EID: 84879136444     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2013.04.013     Document Type: Article

References (49)

1. Lalor N., Priebsch H.H. The prediction of low- and mid-frequency internal road vehicle noise: A literature survey. Proc. Inst. Mech. Eng. Part D: J. Automobile Engrg. 2007, 221-245.
2. M.H.C. Hannink, Y.H. Wijnant, A. de Boer, Optimised sound absorbing trim panels for the reduction of aircraft cabin noise, in: 11th International Congress on Sound and Vibration, ICSV 11, July 5-8, 2004, St. Petersburg, Russia.
3. Biot M.A. The theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. II. Higher frequency range. J. Acoust. Soc. Am. 1956, 28:168-191.
4. Johnson D.L., Koplik J., Dashen R. Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mech. 1987, 176:379-402.
5. Champoux Y., Allard J.F. Dynamic tortuosity and bulk modulus in air-saturated porous media. J. Appl. Phys. 1991, 70:1975-1979.
6. Allard J.F., Atalla N. Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials 2009, John Wiley & Sons West Sussex, United Kingdom.
7. Delany M.-E., Bazley E.N. Acoustical properties of fibrous materials. Appl. Acoust. 1970, 3:105-116.
8. Miki Y. Acoustical properties of porous materials - modifications of Delany-Bazley models. J. Acoust. Soc. Jpn. 1991, 11:19-28.
9. Panneton R. Comments on the limp frame equivalent fluid for porous media. J. Acoust. Soc. Am. 2007, 122:217-222.
10. Kang Y.J., Bolton J.S. Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements. J. Acoust. Soc. Am. 1995, 98:635-643.
11. Panneton R., Atalla N. An efficient finite element scheme for solving the three dimensional poro-elasticity problems in acoustics. J. Acoust. Soc. Am. 1997, 101:3287-3297.
12. Hörlin N.-E., Nordström M., Göransson P. A 3-D hierarchical FE formulation of Biot's equations for elasto-acoustic modelling of porous media. J. Sound Vib. 2001, 245:633-652.
13. Atalla N., Panneton R., Debergue P. Enhanced weak integral formulation for the mixed (u,p) poroelastic equations. J. Acoust. Soc. Am. 2001, 109:3065-3068.
14. Debergue P., Panneton R., Atalla N. Boundary conditions for the weak formulation of the mixed (u,p) poroelasticity problem. J. Acoust. Soc. Am. 1999, 106:2383-2390.
15. Rigobert S., Atalla N., Sgard F.C. Investigation of the convergence of the mixed displacement-pressure poroelastic materials using hierarchical elements. J. Acoust. Soc. Am. 2003, 114:2607-2617.
16. Dazel O., Brouard B., Depollier C., Griffiths S. An alternative Biot's displacement formulation for porous materials. J. Acoust. Soc. Am. 2007, 121:3509-3516.
17. Bouillard P., Ihlenburg F. Error estimation and adaptivity for the finite element method in acoustics: 2D and 3D applications. Comput. Methods Appl. Mech. Engrg. 1999, 176:147-163.
18. Ihlenburg F., Babuska I. Finite element solution of the Helmholtz equation with high wave number. Part I: The h-version of the FEM. Comput. Math. Appl. 1995, 30(9):9-37.
19. Ihlenburg F., Babuska I. Finite element solution of the Helmholtz equation with high wave number. Part II: The h-p-version of the FEM. SIAM J. Numer. Anal. 1997, 34(1):315-358.
20. Dauchez N., Sahraoui S., Atalla N. Convergence of poroelastic finite elements based on Biot displacement formulation. J. Acoust. Soc. Am. 2001, 109:33-40.
21. Craig R., Bampton M. Coupling of substructures for dynamic analyses. AIAA J. 1968, 6:1313-1319.
22. Allard J.F., Depollier C., Rebillard P., Lauriks W., Cops A. Inhomogeneous Biot waves in layered media. J. Appl. Phys. 1989, 66:2278-2284.
23. Ghinet S., Atalla N. Vibro-acoustic behaviour of multi-layer orthotropic panels. Can. Acoust. 2002, 30:72-73.
24. A. Omrani, L. Mebarek, M.A. Hamdi, Transmission loss modeling of trimmed vehicle components, in: Proceedings of the International Conference on Noise and Vibration Engineering, ISMA 2006, September 18-20, 2006, Leuven, Belgium, pp. 4373-4386.
25. W. Desmet, A wave based prediction technique for coupled vibro-acoustic analysis, Katholieke Universiteit Leuven, Ph.D. Thesis 98D12, Leuven, 1998.
26. E. Trefftz, Ein Gegenstück zum Ritzschen Verfahren, in: Proceedings of the 2nd International Congress on Applied Mechanics, Zurich, Switzerland, 1926, pp. 131-137.
27. Pluymers B., van Hal B., Vandepitte D., Desmet W. Trefftz-based methods for time-harmonic acoustics. Arch. Comput. Methods Engrg. 2007, 14:343-381.
28. Van Genechten B., Atak O., Bergen B., Deckers E., Jonckheere S., Lee J., Maressa A., Vergote K., Pluymers B., Vandepitte D., Desmet W. An efficient Wave Based Method for solving Helmholtz problems in three-dimensional bounded domains. Engrg. Anal. Bound. Elem. 2012, 36:63-75.
29. Bergen B., Van Genechten B., Vandepitte D., Desmet W. An efficient Trefftz-based method for three-dimensional Helmholtz problems in unbounded domains. CMES Comput. Model. Engrg. 2010, 61:155-175.
30. C. Vanmaele, Development of a wave based prediction technique for the efficient analysis of low- and mid-frequency structural vibrations, KU Leuven, division PMA, Ph.D. Thesis 2007D11, 2007.
31. Vanmaele C., Vandepitte D., Desmet W. An efficient wave based prediction technique for plate bending vibrations. Comput. Methods Appl. Mech. Engrg. 2007, 196:3178-3189.
32. Deckers E., Hörlin N.E., Vandepitte D., Desmet W. A Wave Based Method for the efficient solution of the 2D poroelastic Biot equations. Comput. Methods Appl. Mech. Engrg. 2012, 201-204:245-262.
33. Deckers E., Vandepitte D., Desmet W. A Wave Based Method for the axisymmetric dynamic analysis of acoustic and poroelastic problems. Comput. Methods Appl. Mech. Engrg. 2013, 257:1-16.
34. Pluymers B., Desmet W., Vandepitte D., Sas P. On the use of a wave based prediction technique for steady-state structural-acoustic radiation analysis. J. Comput. Model. Engrg. Sci. 2005, 7:173-184.
35. Pluymers B., Desmet W., Vandepitte D., Sas P. Application of an efficient wave based prediction technique for the analysis of vibro-acoustic radiation problems. J. Comput. Appl. Math. 2004, 168:353-364.
36. Van Genechten B., Vandepitte D., Desmet W. A Trefftz-based numerical modelling framework for Helmholtz problems with complex multiple scatterer configurations. J. Comput. Phys. 2010, 229:6623-6643.
37. Van Genechten B., Vergote K., Vandepitte D., Desmet W. A multi-level wave based numerical modelling framework for the steady-state dynamic analysis of bounded Helmholtz problems with multiple inclusions. Comput. Methods Appl. Mech. Engrg. 2010, 199:1881-1905.
38. O. Atak, B. Bergen, D. Huybrechs, B. Pluymers, W. Desmet, Coupling of boundary element and wave based methods for efficient solution of complex acoustic multiple scattering problems, J. Comput. Phys., submitted for publication.
39. van Hal B., Desmet W., Vandepitte D., Sas P. Hybrid finite element - wave based method for acoustic problems. Comput. Assist. Mech. Engrg. Sci. 2003, 11:375-390.
40. Van Genechten B., Pluymers B., Vandepitte D., Desmet W. A hybrid wave based - modally reduced finite element method for the efficient analysis of low- and mid-frequency car cavity acoustics. SAE Int. J. Passenger Cars Mech. Syst. 2009, 2(1):1494-1504.
41. Van Genechten B., Vandepitte D., Desmet W. A direct hybrid Finite Element - Wave based modelling technique for efficient coupled vibro-acoustic analysis. Comput. Methods Appl. Mech. Engrg. 2011, 200:742-764.
42. Brezzi F., Fortin M. Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics 1991, vol. 15. Springer.
43. Morse P.M., Ingard K.U. Theoretical Acoustics 1968, McGraw-Hill, New York.
44. Biot M.A., Willis D.G. The elastic coefficients of consolidation. J. Appl. Mech. 1957, 34:594-601.
45. Zienkiewicz O.C., Taylor R., Zhu J. The Finite Element Method: Its Basics and Fundamentals 2005, Butterworth-Heinemann. sixth ed.
46. B. Pluymers, Wave Based modelling methods for steady-state vibro-acoustics, KU Leuven, division PMA, Ph.D. Thesis 2006D04, Leuven, 2006.
47. Vigran T.E., Kelders L., Lauriks W., Leclaire P., Johansen A.F. Prediction and measurement of the influence of boundary conditions in a standing wave tube. Acta Acust. United Ac. 1997, 83:419-423.
48. M.S.C. Nastran, Quick Reference Guide.
49. N.-E. Hörlin, Hierarchical finite element modelling of Biot's equations for vibro-acoustic modelling of layered poroelastic media, Kungliga Tekniska Högskolan, Ph.D. Thesis, Stockholm, 2004.