×

Modelling techniques for vibro-acoustic dynamics of poroelastic materials. (English) Zbl 1348.74096

Summary: Given the quest for mass reduction while preserving proper vibration and acoustic comfort levels in industrial machinery and vehicles, lightweight poroelastic materials have gained a lot of importance. Often, these materials are applied in a multilayered configuration, which can consist of a number of acoustic, elastic, viscoelastic and poroelastic layers. Among these, poroelastic materials are the main focus of this paper. A poroelastic material comprises two constituents, being the elastic solid constituent, also called the frame, and the fluid filling the voids. Depending on the frequency range of interest, the motion of both constituents can be strongly coupled. Poroelastic materials can dissipate energy very effectively by structural, thermal and viscous means. Considerable research effort has been put in the development of robust models and prediction techniques which are capable of accurately describing the damping phenomena of these materials. After a broad introduction, this paper reviews the most commonly used models, ranging from simple empirical relations to detailed models accounting for the coupled behaviour of both phases and the CAE modelling techniques currently being applied for the analysis of the time-harmonic vibro-acoustic behaviour of these materials. Commonly used methods, such as the Finite Element Method and the Transfer Matrix Method which are mainly fitted for low-freqency and high-frequency applications, respectively, are discussed as well as extensions to improve their efficiency and applicability. The two final sections pay special attention to the promising Wave Based Method, a Trefftz-based technique, the application range of which was recently extended towards poroelastic problems.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

Software:

OASES
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Passchier-Vermeer W, Passchier WF (2000) Noise exposure and public health. Environ Health Perspect 108(1):123-131 · doi:10.1289/ehp.00108s1123
[2] Bathe KJ (1996) Finite element procedures. Prentice Hall, New Jersey
[3] Zienkiewicz OC, Taylor RL, Zhu JZ, Nithiarasu P (2005) The Finite Element Method: the three volume set, 6th edn. Butterworth-Heinemann, London · Zbl 1259.76053
[4] Banerjee PK, Butterfield R (1981) Boundary Element Methods in engineering science. McGraw-Hill Book Co., UK · Zbl 0499.73070
[5] Von Estorff O (2000) Boundary elements in acoustics: advances and applications. WIT Press, Southampton · Zbl 0987.76515
[6] Bouillard P, Ihlenburg R (1999) Error estimation and adaptivity for the Finite Element Method in acoustics: 2D and 3D applications. Comput Methods Appl Mech Eng 176:147-163 · Zbl 0954.76040
[7] Freymann R (2000) Advanced numerical and experimental methods in the field of vehicle structural-acoustics. Hieronymus Buchreproduktions GmbH
[8] Marburg S (2002) Six boundary elements per wavelength: is that enough? J Comput Acoust 10:25-51 · Zbl 1360.76168 · doi:10.1142/S0218396X02001401
[9] Lyon RH, De Jong RG (1995) Theory and application of Statistical Energy Analysis, 2nd edn. Butterworth-Heinemann, London · Zbl 1217.74137
[10] Erlangga YA (2008) Advances in iterative methods and preconditioners for the Helmholtz equation. Arch Comput Methods Eng 15:37-66 · Zbl 1158.65078 · doi:10.1007/s11831-007-9013-7
[11] Craig RR Jr, Kurdila AJ (2005) Fundamentals of structural dynamics, 2nd edn. Wiley, New York
[12] Farhat C, Harari I, Franca LP (2001) The Discontinuous Enrichment Method. Comput Methods Appl Mech Eng 190:6455-6479 · Zbl 1002.76065
[13] Melenk J, Babuška I (1996) The Partition of Unity Finite Element Method: basic theory and applications. Comput Methods Appl Mech Eng 139:289-314 · Zbl 0881.65099
[14] Trefftz E (1926) Ein Gegenstück zum Ritzschen Verfahren. In: Proceedings of the 2nd international congress on applied mechanics. Zurich, Switzerland, pp 131-137
[15] Mace B, Shorter P (2000) Energy flow models from Finite Element Analysis. J Sound Vib 233:369-389
[16] Maxit L, Guyader J-L (2001) Estimation of SEA coupling loss factors using a dual formulation and FEM modal information, part I: theory. J Sound Vib 239:907-930
[17] Langley RS, Cordioli JA (2009) Hybrid deterministic-statistical analysis of vibro-acoustic systems with domain couplings on statistical components. J Sound Vib 321:893-912 · doi:10.1016/j.jsv.2008.10.007
[18] Shorter P, Langley R (2005) On the reciprocity relationship between direct field radiation and diffuse reverberant loading. J Acoust Soc Am 117:85-95 · doi:10.1121/1.1810271
[19] Coussy O (2004) Poromechanics. Wiley, New York
[20] Wang HF (2000) Theory of linear poroelasticity, with applications to geomechanics and hydrogeology. Princeton University Press, Princeton
[21] Jensen FB, Kuperman WA, Porter MB, Schmidt H (2011) Computational ocean acoustics, 2nd edn. Springer, Berlin · Zbl 1234.76003 · doi:10.1007/978-1-4419-8678-8
[22] Smit TH, Hyghe JM, Cowin SC (2002) Estimation of the poroelastic parameters of cortical bone. J Biomech 35:829-835 · doi:10.1016/S0021-9290(02)00021-0
[23] Allard JF, Atalla N (2009) Propagation of sound in porous media: modeling sound absorbing materials, 2nd edn. Wiley, West Sussex · doi:10.1002/9780470747339
[24] Zwikker C, Kosten CW (1949) Sound absorbing materials. Elsevier, New York
[25] Biot MA (1956) The theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. J Acoust Soc Am 28:168-178 · doi:10.1121/1.1908239
[26] Delany M-E, Bazley EN (1970) Acoustical properties of fibrous materials. Appl Acoust 3:105-116 · doi:10.1016/0003-682X(70)90031-9
[27] Miki Y (1990) Acoustical properties of porous materials: modifications of Delany-Bazley models. J Acoust Soc Jpn 11:19-24 · doi:10.1250/ast.11.19
[28] Mechel FP (1976) Ausweitung der Absorberformel von Delany und Bazley zu tiefen Frequenzen. Acustica 35:210-213
[29] Komatsu T (2008) Improvement of the Delany-Bazley and Miki models for fibrous sound-absorbing materials. Acoust Sci Technol 29:121-129
[30] Kirchhoff G (1868) Über der Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung. Annalen der Physik and Chemie 134:177-193 · Zbl 1124.74045
[31] Stinson MR (1991) The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross-sectional shape. J Acoust Soc Am 89:550-558 · doi:10.1121/1.400379
[32] Biot MA (1956) The theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J Acoust Soc Am 28:179-191 · doi:10.1121/1.1908241
[33] Craggs A, Hildebrandt JG (1986) The normal incidence absorption coefficient of a matrix of narrow tubes with constant cross-section. J Sound Vib 105:101-107 · doi:10.1016/0022-460X(86)90223-3
[34] Attenborough K (1983) Acoustical characteristics of rigid fibrous absorbents and granular media. J Acoust Soc Am 73:785- 799 · Zbl 0516.73117
[35] Johnson DL, Koplik J, Dashen R (1987) Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J Fluid Mech 176:379-402 · Zbl 0612.76101 · doi:10.1017/S0022112087000727
[36] Champoux Y, Allard JF (1991) Dynamic tortuosity and bulk modulus in air-saturated porous media. J Appl Phys 70:1975- 1979
[37] Perrot C, Chevilotte F, Hoang MT, Bonnet G, Bécot F-X, Gautron L, Duval A (2012) Microstructures, transport, and acoustic properties of open-cell foam samples: experiments and three-dimensional numerical simulations. J Appl Phys 111:014911 · doi:10.1063/1.3673523
[38] Hoang MT, Perrot C (2013) Identifying local characteristic lenghts governing sound wave properties in solid foams. J Appl Phys 113:084905 · doi:10.1063/1.4793492
[39] Lauriks W, Leclaire P (2008) Chapter 61: Materials testing. In: Havelock D, Kuwano S, Vorländer M (eds) Handbook of signal processing in acoustics. Springer, New York
[40] Lafarge D, Lemarinier P, Allard JF, Tarnow V (1997) Dynamic compressibility of air in porous structures at audible frequencies. J Acoust Soc Am 102:1995-2006 · doi:10.1121/1.419690
[41] Perrot C, Panneton R, Olny X (2007) Periodic unit cell reconstruction of porous media: application to open-cell aluminum foams. J Appl Phys 101:113538 · doi:10.1063/1.2745095
[42] Auriault JL (1991) Heterogeneous medium. Is an equivalent macroscopic description possible? Int J Eng Sci 29:785-795 · Zbl 0749.73003 · doi:10.1016/0020-7225(91)90001-J
[43] Wilson DK (1993) Relaxation-matched modeling of propagation through porous media, including fractal pore structure. J Acoust Soc Am 94:1136-1145 · doi:10.1121/1.406961
[44] Pride SR, Morgan FD, Gangi FA (1993) Drag forces of porous media acoustics. Phys Rev B 47:4964-4975 · doi:10.1103/PhysRevB.47.4964
[45] Lafarge D (1993) Propagation du son dans les matériaux poreux à structure rigide saturés par un fluide viscothermique: Définition de paramètres géométrique, analogie electromagnétique, temps de relaxation. PhD thesis, Université du Maine, France · Zbl 0622.65105
[46] Panneton R, Olny X (2006) Acoustical determination of the parameters governing viscous dissipation in porous media. J Acoust Soc Am 119:2027-2040 · doi:10.1121/1.2169923
[47] Olny X, Panneton R (2008) Acoustical determination of the parameters governing thermal dissipation in porous media. J Acoust Soc Am 123:814-824 · doi:10.1121/1.2828066
[48] Panneton R (2007) Comments on the limp frame equivalent fluid model for porous media. J Acoust Soc Am 122:217-222
[49] Doutres O, Dauchez N, Génevaux J-M, Dazel O (2007) Validity of the limp model for porous materials: a criterion based on the Biot theory. J Acoust Soc Am 122:2038-2048 · Zbl 1111.68629 · doi:10.1121/1.2769824
[50] Boutin C, Royer P, Auriault JL (1998) Acoustic absorption of porous surfacing with dual porosity. Int J Solids Struct 35:4709-4737 · Zbl 0930.76079 · doi:10.1016/S0020-7683(98)00091-2
[51] Olny X, Boutin C (2003) Acoustic wave propagation in double porosity media. J Acoust Soc Am 114:73-89 · doi:10.1121/1.1534607
[52] Atalla N, Sgard F, Olny X, Panneton R (2001) Acoustic absorption of macro-perforated porous materials. J Sound Vib 243:659-678 · doi:10.1006/jsvi.2000.3435
[53] Sgard FC, Olny X, Atalla N, Castel F (2005) On the use of perforations to improve the sound absorption of porous materials. Appl Acoust 66:625-651 · doi:10.1016/j.apacoust.2004.09.008
[54] Lanoye R (2007) Assessment of the absorption performance of sound absorbing materilas. Use of the Trefftz’s method and of a new dual particle velocity-pressure sensor. KULeuven, Department of Civil Engineering and Department of Acoustics and Thermal Physics, PhD thesis · Zbl 1202.74049
[55] Biot MA (1962) Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33:1482-1498 · Zbl 0104.21401 · doi:10.1063/1.1728759
[56] Burridge R, Keller JB (1981) Poroelasticity equations derived from microstructure. J Acoust Soc Am 70:1140-1146 · Zbl 0519.73038 · doi:10.1121/1.386945
[57] Pride SR, Gangi AF, Morgan FD (1992) Deriving the equations of motion for porous isotropic media. J Acoust Soc Am 92:3278-3290 · doi:10.1121/1.404178
[58] Biot MA, Willis DG (1957) The elastic coefficients of consolidation. J Appl Mech 34:594-601
[59] Dovstam K (1995) Augmented Hooke’s law in frequency domain. Int J Solids Struct 32:2835-2852 · Zbl 0880.73001 · doi:10.1016/0020-7683(94)00269-3
[60] Hörlin N-E, Nordström M, Göransson P (2001) A 3-D hierarchical FE formulation of Biot’s equations for elasto-acoustic modelling of porous media. J Sound Vib 245:633-652 · Zbl 1259.76053
[61] Göransson P (2006) Acoustic and vibrational damping in porous solids. Philos Trans R Soc A 364:89-108 · doi:10.1098/rsta.2005.1688
[62] Kurzeja PS, Steeb H (2012) About the transition frequency in Biot’s theory. JASA Exp Lett 131:454-460
[63] Debergue P, Panneton R, Atalla N (1999) Boundary conditions for the weak formulation of the mixed (u, p) poroelasticity problem. J Acoust Soc Am 106:2383-2390 · doi:10.1121/1.428075
[64] Hörlin N-E (2004) Hierarchical Finite Element Modelling of Biot’s equations for vibro-acoustic modelling of layered poroelastic media. Doctoral thesis, KTH Aeronautical and Vehicle Engineering, Stockholm, Sweden · Zbl 1144.74009
[65] Rigobert S, Atalla N, Sgard FC (2003) Investigation of the convergence of the mixed displacement-pressure poroelastic materials using hierarchical elements. J Acoust Soc Am 114:2607-2617 · doi:10.1121/1.1616579
[66] Sagartzazu X, Hervella-Nieto L, Pagalday JM (2008) Review in sound absorbing materials. Arch Comput Methods Eng 15:311-342 · Zbl 1144.74009 · doi:10.1007/s11831-008-9022-1
[67] Jaouen L, Renault A, Deverge M (2008) Elastic and damping characterizations of acoustical porous materials: Available experimental methods and applications to a melamine foam. Appl Acoust 69:1129-1140
[68] Pan J, Jackson P (2009) Review of test methods for materials properties of elastic porous materials. SAE Int J Mater Manuf 2:570-579
[69] Jaouen L (2011) Characterization of acoustic and elastic parameters of porous media. In: Proceedings of the symposium on the acoustics of poro-elastic materials, SAPEM2011, Ferrara (Italy)
[70] Vashishth A, Khurana P (2004) Waves in stratified anisotropic poroelastic media: a transfer matrix approach. J Sound Vib 277:239-275 · doi:10.1016/j.jsv.2003.08.024
[71] Khuruna P, Boeckx L, Lauriks W, Leclaire P, Dazel O, Allard JF (2009) A description of transversely isotropic sound absorbing porous materials by transfer matrices. J Acoust Soc Am 125:915-921 · doi:10.1121/1.3035840
[72] Carcione JM (2007) Wave fields in real media: Wave propagation in anisotropic, anelastic, porous and electromagnetic media, 2nd edn. Elsevier, Amsterdam · Zbl 0519.73038
[73] Hörlin N-E, Göransson P (2010) Weak, anisotropic symmetric formulations of Biot’s equations for vibro-acoustic modelling of porous elastic materials. Int J Numer Methods Eng 84:1519-1540 · Zbl 1202.74049 · doi:10.1002/nme.2955
[74] Göransson P, Hörlin N-E (2010) Vibro-acoustic modelling of anisotropic porous elastic materials: a preliminary study of the influence of anisotropy on the predicted performance in a multi-layer arrangement. Acta Acust United Acust 96:258-265 · doi:10.3813/AAA.918275
[75] Lind Nordgren E, Göransson P, Deü J-F, Dazel O (2013) Vibroacoustic response sensitivity due to relative alignment of two anisotropic poro-elastic layers. JASA Express Lett 133:426-430
[76] Bécot F-X, Dazel O, Jaouen L (2010) Structural effects in double porosity materials: analytical modeling and numerical validation. In: Proceedings of the conference on noise and vibration engineering 2010, ISMA2010, Leuven, Belgium · Zbl 0749.73003
[77] Dazel O, Bécot F-X, Jaouen L (2012) Biot effects for sound absorbing double porosity materials. Acta Acust United Acust 98:567-576 · doi:10.3813/AAA.918538
[78] Dauchez N, Sahraoui S, Atalla N (2001) Convergence of poroelastic finite elements based on Biot displacement formulation. J Acoust Soc Am 109:33-40 · doi:10.1121/1.1289924
[79] Dauchez N, Sahraoui S, Atalla N (2002) Investigation and modelling of damping in a plate with a bonded porous layer. J Sound Vib 265:437-449 · Zbl 1236.74281
[80] Tanneau O, Lamary P, Chevalier Y (2006) A boundary element method for porous media. J Acoust Soc Am 120:1239-1251 · doi:10.1121/1.2221407
[81] Craggs A (1978) A finite element model for rigid porous absorbing materials. J Sound Vib 61:101-111 · Zbl 0388.76085 · doi:10.1016/0022-460X(78)90044-5
[82] Göransson P (1995) Acoustic Finite Element formulation of a flexible porous material: a correction for inertial effects. J Sound Vib 185:559-580 · Zbl 1049.74778
[83] Kang YJ, Bolton JS (1995) Finite Element modeling of isotropic elastic porous materials coupled with acoustical finite elements. J Acoust Soc Am 98:635-643
[84] Panneton R, Atalla N (1997) An efficient Finite Element scheme for solving the three dimensional poro-elasticity problems in acoustics. J Acoust Soc Am 101:3287-3297
[85] Coyette JP (1999) The use of Finite-Element and Boundary-Element models for predicting the vibro-acoustic behaviour of layered structures. Adv Eng Softw 30:133-139 · Zbl 0612.76101
[86] Easwaran V, Lauriks W, Coyette JP (1996) Displacement-based Finite Element method for guided wave propagation problems: application to poroelastic media. J Acoust Soc Am 100:2989-3002
[87] Göransson P (1998) A 3-D symmetric Finite Element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium. Int J Numer Methods Eng 41:167-192 · Zbl 0909.76048
[88] Atalla N, Hamdi MA, Panneton R (2001) Enhanced weak integral formulation for the mixed (u, p) poroelastic equations. J Acoust Soc Am 109:3065-3068 · doi:10.1121/1.1365423
[89] Atalla N, Panneton R, Debergue P (1998) A mixed displacement-pressure formulation for poroelastic materials. J Acoust Soc Am 104:1444-1452 · doi:10.1121/1.424355
[90] Dazel O, Brouard B, Depollier C, Griffiths S (2007) An alternative Biot’s displacement formulation for porous materials. J Acoust Soc Am 121:3509-3516 · doi:10.1121/1.2734482
[91] Hörlin N-E (2010) A symmetric weak form of Biot’s equations based on redundant variables representing the fluid, using a Helmholtz decomposition of the fluid displacement vector field. Int J Numer Methods Eng 84:1613-1637 · Zbl 1202.74048 · doi:10.1002/nme.2956
[92] Kang YJ, Gardner BC, Bolton JS (1999) An axisymmetric poroelastic Finite Element formulation. J Acoust Soc Am 106:565-574
[93] Östberg M, Hörlin NE, Göransson P (2010) Weak formulation of Biot’s equations in cylindrical coordinates with harmonic expansions in the circumferential direction. Int J Numer Methods Eng 81:1439-1454 · Zbl 1183.74083
[94] Rigobert S, Sgard FC, Atalla N (2004) A two-field hybrid formulation for multilayers involving poroelastic, acoustic, and elastic materials. J Acoust Soc Am 115:2786-2797 · doi:10.1121/1.1698758
[95] Dazel O, Sgard F, Lamarque CH, Atalla N (2002) An extension of complex modes for the resolution of Finite-Element poroelastic problems. J Sound Vib 253:421-445
[96] Dazel O, Sgard F, Lamarque CH (2003) Application of generalized complex modes to the calculation of the forced response of three-dimensional poroelastic materials. J Sound Vib 268:555-580 · doi:10.1016/S0022-460X(03)00373-0
[97] Sgard F, Atalla N, Panneton R (1997) A modal reduction technique for the Finite Element formulation of Biot’s poroelasticity equations in acoustics. In: 134th ASA meeting, San Diego, USA
[98] Davidsson P, Sandberg G (2006) A reduction method for structure-acoustic and poroelastic-acoustic problems using interface-dependent Lanczos vectors. Comput Methods Appl Mech Eng 195:1933-1945 · Zbl 1124.74045 · doi:10.1016/j.cma.2005.02.024
[99] Dazel O, Brouard B, Dauchez N, Geslain A (2009) Enhanced Biot’s Finite Element displacement formulation for porous materials and original resolution methods based on normal modes. Acta Acust United Acust 95:527-538
[100] Dazel O, Brouard B, Dauchez N, Geslain A, Lamarque CH (2010) A free interface CMS technique to the resolution of coupled problem involving porous materials, application to a monodimensional problem. Acta Acust United Acust 96:247-257 · doi:10.3813/AAA.918274
[101] Rumpler R, Deü J-F, Göransson P (2012) A modal-based reduction method for sound absorbing porous materials in poro-acoustic Finite Element models. J Acoust Soc Am 132:3162-3179
[102] Rumpler R, Göransson P, Deü J-F (2013) A residue-based mode selection and sorting procedure for efficient poroelastic modeling in acoustic Finite Element applications. J Acoust Soc Am 134:4730 · Zbl 1352.74112
[103] Rumpler R (2012) Efficient Finite Element approach for structural-acoustic applications including 3D modelling of sound absorbing porous materials. Doctoral Thesis in Technical Acoustics, Stockholm, Sweden · Zbl 1360.76168
[104] Dazel O, Brouard B, Groby J-P, Göransson P (2013) A normal modes technique to reduce the order of poroelastic models: application to 2D and coupled 3D models. Int J Numer Methods Eng 96:110-128 · Zbl 1352.74105
[105] Allard JF, Champoux Y, Depollier C (1987) Modelization of layered sound absorbing materials with transfer matrices. J Acoust Soc Am 82:1792-1796 · doi:10.1121/1.395796
[106] Allard JF, Depollier C, Rebillard P, Lauriks W, Cops A (1989) Inhomogeneous Biot waves in layered media. J Appl Phys 66:2278-2284 · doi:10.1063/1.344284
[107] Villot M, Guigou C, Gagliardini L (2001) Predicting the acoustical radiation of finite size multi-layered structures by applying spatial windowing on infinite structures. J Sound Vib 245:433-455 · doi:10.1006/jsvi.2001.3592
[108] Ghinet S, Atalla N (2002) Vibro-acoustic behaviour of multi-layer orthotropic panels. Can Acoust 30:72-73
[109] Atalla N, Sgard F, Amedin CK (2006) On the modeling of sound radiation from poroelastic materials. J Acoust Soc Am 120:1990-1995 · doi:10.1121/1.2261244
[110] Rhazi D, Atalla N (2010) Transfer matrix modeling of the vibroacoustic response of multi-materials structures under mechanical excitation. J Sound Vib 329:2532-2546 · doi:10.1016/j.jsv.2010.01.013
[111] Vigran TE (2010) Sound transmission in multilayered structures: introducing finite structural connections in the Transfer Matrix Method. Appl Acoust 71:39-44
[112] Legault J, Atalla N (2009) Numerical and experimental investigation of the effect of structural links on the sound transmission of a lightweight double panel structure. J Sound Vib 324:712-732 · doi:10.1016/j.jsv.2009.02.019
[113] Legault J, Atalla N (2010) Sound transmission through a double panel structure periodically coupled with vibration insulators. J Sound Vib 329:3082-3100 · doi:10.1016/j.jsv.2010.02.013
[114] Verdière K, Panneton R, Elkoun S, Dupont T, Leclaire P (2013) Prediction of acoustic properties of parallel assemblies by means of Transfer Matrix Method. In: Proceedings of meetings on acoustics, vol 19
[115] Alimonti L, Atalla N, Berry A, Sgard F (2013) A hybrid modelling approach for vibroacoustic systems with attached sound packages. In: Proceedings of meetings on acoustics, vol 19 · Zbl 0104.21401
[116] Tournour M, Kosaka M, Shiozaki H (2007) Modeling fast acoustic trim, using transfer matrix admittance and Finite Element Method. In: SAE 2007 noise and vibration conference and exhibition. St. Charles, IL, USA
[117] Pope LD, Wilby EG, Willis CM, Mayes WH (1983) Aircraft interior noise models: sidewall trim, stiffened structures and cabin acoustics with floor partition. J Sound Vib 89:371-417 · doi:10.1016/0022-460X(83)90544-8
[118] Duval A, Dejaeger L, Bischoff L, Morgenstern C (2012) Trim FEM simulation of a headliner cut out module with structureborne and airborne excitations. In: Proceedings of the 7th international styrian noise, vibration and harshness congress: the European automotive noise conference, ISNVH2012, Graz, Austria · Zbl 0749.73003
[119] Duval A, Dejaeger L, Bischoff L, Lhuillier F, Monet-Descombey J (2013) Generalized light-weight concepts: a new insulator 3D optimization procedure. In: Proceedings of the SAE 2013 noise and vibration conference and exhibition, Gran Rapids, USA
[120] Pluymers B, Van Hal B, Vandepitte D, Desmet W (2007) Trefftz-based methods for time-harmonic acoustics. Arch Comput Methods Eng 14:343-381 · Zbl 1170.76332 · doi:10.1007/s11831-007-9010-x
[121] Chazot JD, Nennig B, Perrey-Debain E (2013) Performances of the Partition of Unity Finite Element Method for the analysis of two-dimensional interior sound field with absorbing materials. J Sound Vib 332:1918-1929
[122] Lanoye R, Vermeir G, Lauriks W, Sgard F, Desmet W (2008) Prediction of the sound field above a patchwork of absorbing materials. J Acoust Soc Am 123:793-802 · doi:10.1121/1.2823781
[123] Teixeira de Freitas JA, Toma M (2009) Hybrid-Trefftz stress elements for incompressible biphasic media. Int J Numer Methods Eng 79:205-238 · Zbl 1171.74457 · doi:10.1002/nme.2560
[124] Moldovan ID (2008) Hybrid-Trefftz Finite Elements for elastodynamic analysis of saturated porous media. PhD thesis, Universidade Técnica de Lisboa
[125] Teixeira de Freitas JA, Moldovan ID (2011) Hybrid-Trefftz stress elements for bounded and unbounded poroelastic media. Int J Numer Methods Eng 85:1280-1305 · Zbl 1217.74137
[126] Teixeira de Freitas JA, Moldovan ID, Cismaşiu C (2011) Hybrid-Trefftz displacements elements for poroelastic media. Comput Mech 48:659-673 · Zbl 1334.74034 · doi:10.1007/s00466-011-0612-7
[127] Nennig B, Perry-Debain E, Chazot JD (2011) The method of fundamental solutions for acoustic wave scattering by a single and a periodic array of poroelastic scatterers. Eng Anal Boundary Elem 35:1019-1028 · Zbl 1259.76053 · doi:10.1016/j.enganabound.2011.03.007
[128] Gabard G (2007) Discontinuous Galerkin methods with plane waves for time-harmonic problems. J Comput Phys 225:1961-1984 · Zbl 1123.65102 · doi:10.1016/j.jcp.2007.02.030
[129] Dazel O, Gabard G (2013) Discontinuous Galerkin methods for poroelastic materials. In: Proceedings of meeting on acoustics, ICA 2013 Montreal, Canada · Zbl 1352.74145
[130] Desmet W (1998) A Wave Based prediction technique for coupled vibro-acoustic analysis. KULeuven, division PMA, PhD. thesis 98D12
[131] Desmet W, Pluymers B, Atak O, Bergen B, D’Amico R, Deckers E, Jonckheere S, Koo K, Lee JS, Maressa A, Navarrete N, Van Genechten B, Vandepitte D, Vergote K (2012) Chapter 1: The Wave Based Method. In: Desmet W, Pluymers B, Atak O (eds) CAE methodologies for mid-frequency analysis in vibration and acoustics. KULeuven , pp 1-60
[132] Deckers E, Atak O, Coox L, D’Amico R, Devriendt H, Jonckheere S, Koo K, Pluymers B, Vandepitte D, Desmet W (2013) The Wave Based Method: an overview of 15 years of research. Wave Motion 51:550-565 · Zbl 1456.35006
[133] Helmholtz HLF (1958) Über integrale der hydrodynamischen Gleichungen, welch den Wirbelbewegungen entsprechen. Crelles J 55:25-55 · ERAM 055.1448cj
[134] Cessenat O, Deprès B (2003) Using plane waves as base functions for solving time harmonic equations with the Ultra Weak Variational Formulation. J Comput Acoust 11:227-238 · Zbl 1360.76127
[135] Herrera I (1984) Boundary methods: an algebraic theory. Applicable mathematic series. Pitman Advanced Publishing Programm, London
[136] Van Hal B (2004) Automation and performance optimization of the Wave Based Method for interior structural-acoustic problems. PhD Thesis, Faculty of Engineering, Katholieke Universiteit Leuven
[137] Van Genechten B, Bergen B, Vandepitte D, Desmet W (2010) A Trefftz-based numerical modelling framework for Helmholtz problems with complex multiple scatterer configurations. J Comput Phys 229(18):6623-6643 · Zbl 1425.35020 · doi:10.1016/j.jcp.2010.05.016
[138] Van Genechten B, Vergote K, Vandepitte D, Desmet W (2010) 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 Eng 199:1881-1905 · Zbl 1231.76222
[139] Van Genechten B, Vandepitte D, Desmet W (2011) A direct hybrid Finite Element-Wave Based modelling technique for efficient coupled vibro-acoustic analysis. Comput Methods Appl Mech Eng 200:742-764 · Zbl 1225.74110
[140] Huttunen T, Gamallo P, Astley RJ (2009) Comparison of two wave element methods for the Helmholtz problem. Commun Numer Methods Eng 25:35-52 · Zbl 1158.65347 · doi:10.1002/cnm.1102
[141] Zieliński AP, Herrera I (1987) Trefftz method: fitting boundary conditions. Int J Numer Methods Eng 24:871-891 · Zbl 0622.65105 · doi:10.1002/nme.1620240504
[142] Varah JM (1979) A practical examination of some numerical methods for linear discrete ill-posed problems. SIAM Rev 21:100-111 · Zbl 0406.65015 · doi:10.1137/1021007
[143] Varah JM (1983) Pitfalls in the numerical solution of linear ill-posed problems. SIAM J Sci Stat Comput 4:164-176 · Zbl 0533.65082 · doi:10.1137/0904012
[144] Pluymers B (2006) Wave based modelling methods for steady-state vibro-acoustics. KU Leuven, division PMA, PhD thesis 2006D04, Leuven · Zbl 1425.35020
[145] Deckers E, Bergen B, Van Genechten B, Vandepitte D, Desmet W (2012) An efficient Wave Based Method for 2D acoustic problems containing corner singularities. Comput Methods Appl Mech Eng 241-244:286-301 · Zbl 1353.76057
[146] Van Genechten B, Atak O, Bergen B, Deckers E, Jonckheere S, Lee JS, Maressa A, Vergote K, Pluymers B, Vandepitte D, Desmet W (2012) An efficient Wave Based Method for solving Helmholtz problems in three-dimensional bounded domains. Eng Anal Bound Elem 36:63-75 · Zbl 1259.76057
[147] Pluymers B, Desmet W, Vandepitte D, Sas P (2005) On the use of a Wave Based prediction technique for steady-state structural-acoustic radiation analysis. Comput Model Eng Sci 7(2):173-184 · Zbl 1189.76344
[148] Colton D, Kress R (1998) Inverse acoustic and electromagnetic scattering theory, 2nd edn. Springer, Berlin · Zbl 0893.35138 · doi:10.1007/978-3-662-03537-5
[149] Bergen B, Van Genechten B, Vandepitte D, Desmet W (2010) An efficient Trefftz-based method for three-dimensional Helmholtz problems in unbounded domains. Comput Model Eng Sci 61(2):155-175 · Zbl 1231.76259
[150] Bergen B, Pluymers B, Van Genechten B, Vandepitte D, Desmet W (2012) A Trefftz based method for solving Helmholtz problems in semi-infinite domains. Eng Anal Bound Elem 36:30-38 · Zbl 1259.76039 · doi:10.1016/j.enganabound.2011.04.007
[151] Bergen B (2011) Wave based modelling techniques for unbounded acoustic problems. KULeuven, division PMA, PhD thesis 2011D07
[152] Vanmaele C, Vandepitte D, Desmet W (2007) An efficient Wave Based prediction technique for plate bending vibrations. Comput Methods Appl Mech Eng 196:3178-3189 · Zbl 1173.74483
[153] Vanmaele C, Vandepitte D, Desmet W (2009) An efficient Wave Based prediction technique for dynamic plate bending problems with corner stress singularities. Comput Methods Appl Mech Eng 198:2227-2245 · Zbl 1229.74157
[154] Vanmaele C, Vergote K, Vandepitte D, Desmet W (2012) Simulation of in-plane vibrations of 2D structural solids with singularities using an efficient Wave Based prediction technique. Comput Assist Mech Eng Sci 19:135-171
[155] Vanmaele C (2007) Development of a Wave Based prediction technique for the efficient analysis of low- and mid-frequency structural vibrations. KU Leuven, division PMA, PhD thesis 2007D11
[156] Deckers E, Hörlin N-E, Vandepitte D, Desmet W (2012) A Wave Based Method for the efficient solution of the 2D poroelastic Biot equations. Comput Methods Appl Mech Eng 201-204:245-262 · Zbl 1239.74023
[157] Deckers E, Van Genechten B, Vandepitte D, Desmet W (2012) Efficient treatment of stress singularities in poroelastic Wave Based models using special purpose enrichment functions. Comput Struct 89:1117-1130
[158] Deckers E, Vandepitte D, Desmet W (2013) A Wave Based Method for the axisymmetric dynamic analysis of acoustic and poroelastic problems. Comput Methods Appl Mech Eng 257:1-16 · Zbl 1286.76132
[159] Jonckheere S, Deckers E, Van Genechten B, Vandepitte D, Desmet W (2013) 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. Comput Methods Appl Mech Eng 263:144-157 · Zbl 1286.76133
[160] Vergote K (2012) Dynamic analysis of structural components in the mid frequency range using the Wave Based Method, Non-determinism and inhomogeneities. KU Leuven, division PMA, PhD thesis 2012D03 · Zbl 0671.65094
[161] Van Genechten B (2010) Trefftz-based mid-frequency analysis of geometrically complex vibro-acoustic problems: hybrid methodologies and multi-level modelling. KU Leuven, division PMA, PhD thesis 2010D08
[162] Keller JB, Givoli D (1989) Exact non-reflecting boundary conditions. J Comput Phys 82:172-192 · Zbl 0671.65094 · doi:10.1016/0021-9991(89)90041-7
[163] Lee JS, Deckers E, Jonckheere S, Desmet W (2011) A direct hybrid Wave Based Finite Element modeling of poroelastic materials. In: Proceedings of the symposium on the acoustics of poro-elastic materials, SAPEM2011, Ferrara, Italy · Zbl 1425.74158
[164] Atak O, Bergen B, Huybrechs D, Pluymers B, Desmet W (2013) Coupling of Boundary Element and Wave Based Methods for efficient solving of complex acoustic multiple scattering problems. J Comput Phys 258:165-184 · Zbl 1349.76414
[165] Vergote K, Van Genechten B, Vandepitte D, Desmet W (2011) On the analysis of vibro-acoustic systems in the mid-frequency range using a hybrid deterministic-statistical approach. Comput Struct 89:868-877 · doi:10.1016/j.compstruc.2011.03.002
[166] Bolton JS, Shiau N-M, Kang YJ (1996) Sound transmission through multi-panel structures lined with elastic porous materials. J Sound Vib 191:317-347 · doi:10.1006/jsvi.1996.0125
[167] Vigran TE, Kelders L, Lauriks W, Leclaire P, Johansen TF (1997) Prediction and measurements of the influence of boundary conditions in a standing wave tube. Acta Acust United Acust 83:419-423
[168] Allard JF (1998) Propagation of sound in porous media: modeling sound absorbing materials, 1st edn. Elsevier, New York
[169] Sinclair GB (2004) Stress singularities in classical elasticity-I: removal, interpretation and analysis. Appl Mech Rev 57:254-297
[170] Deckers E (2012) A Wave Based approach for steady-state Biot models of poroelastic materials. KULeuven, Department of Mechanical Engineering, PhD thesis 2012D12 · Zbl 1158.65347
[171] Brezzi F, Fortin M (1991) Mixed and hybrid Finite Element Methods, vol 15. Springer series in computational mathematics. Springer, Berlin · Zbl 0788.73002
[172] van Hal B, Desmet W, Vandepitte D, Sas P (2003) Hybrid Finite Element-Wave Based Method for acoustic problems. Comput Assist Mech Eng Sci 11:375-390 · Zbl 1136.76393
[173] Descheemaeker J (2011) Elastic characterization of porous materials by surface and guided acoustic wave propagation analysis. KU Leuven, Department of Physics, PhD thesis, Leuven
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.