M. Abramowitz and I. A. , Stegun: Handbook of mathematical functions, p.23, 1972.

H. T. Anastassiu, D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary condition (SIBC), IEEE Transactions on Antennas and Propagation, vol.50, issue.1, pp.59-66, 2002.
DOI : 10.1109/8.992562

P. B. Andersson, High frequency tyre vibrations, 2002.

. Anfosso-lédée, Application de la méthode deséquationsdeséquations intégralesintégralesà la modéisation du bruit aux abords des routes -Interaction chaussée / ´ ecran antibruit, Ecole Nationale des Ponts et Chaussées, issue.3, 1996.

K. Attenborough, Acoustical impedance models for outdoor ground surfaces, Journal of Sound and Vibration, vol.99, issue.4, pp.521-544, 1985.
DOI : 10.1016/0022-460X(85)90538-3

K. Attenborough and T. Waters-fuller, Effective impedance of rough porous ground surfaces, The Journal of the Acoustical Society of America, vol.108, issue.3, pp.949-956, 2000.
DOI : 10.1121/1.1288940

K. Attenborough, Developments in modelling ground effects on outdoor sound, Proceedings of I.C.A. 2001, 2001.

J. Ballie and . Gal, Noise reduction induced by use of very thin wearing courses and crumb rubber particles, Proceedings of inter.noise, 2000.

A. Beckenbauer, . N. Kuijpers, D. C. Chandler-wilde, and . Hothersall, Prediction of pass-by levels depending on road surface parameters S Sound propagation above an inhomogeneous impedance plane, Journal of Sound and Vibration, vol.98, issue.4 6, pp.475-491, 1985.

S. N. Chandler-wilde and D. C. Hothersall, Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane, Journal of Sound and Vibration, vol.180, issue.5, pp.705-724, 1995.
DOI : 10.1006/jsvi.1995.0110

C. F. Chien and W. W. Soroka, Sound propagation along an impedance plane, Journal of Sound and Vibration, vol.43, issue.1, pp.9-20, 1975.
DOI : 10.1016/0022-460X(75)90200-X

C. F. Chien and W. W. Soroka, A note on the calculation of sound propagation along an impedance surface, Journal of Sound and Vibration, vol.69, issue.2, pp.340-343, 1980.
DOI : 10.1016/0022-460X(80)90618-5

T. G. Clapp, Approximation and analysis of tire / pavement contact information resulting from road surface roughness, p.4, 1985.

J. P. Coyette and B. Van-de-nieuwenhof, A conjugated infinite element method for half-space acoustic problems, The Journal of the Acoustical Society of America, vol.108, issue.4, pp.1464-1473, 2000.
DOI : 10.1121/1.1289921

L. Cremer and M. Heckl, Structure-borne sound ? Structural vibrations and sound radiation at audio frequencies, pp.528-535, 1973.

M. Cremer and . Wang, Die synthese eines von einem beliebigen körper in luft erzeugten feldes aus kugelschallfeldern und deren realisierung in durchrechnung und experiment, Acustica, vol.65, issue.21, pp.53-74, 1988.

Y. Defrance and . Gabillet, A new analytical method for the calculation of outdoor noise propagation, Applied Acoustics, vol.57, issue.2, pp.109-127, 1999.
DOI : 10.1016/S0003-682X(98)00047-4

E. N. Delany and . Bazley, Acoustical properties of fibrous absorbent materials, Applied Acoustics, vol.3, issue.2, pp.105-116, 1970.
DOI : 10.1016/0003-682X(70)90031-9

. Duhamel, EFFICIENT CALCULATION OF THE THREE-DIMENSIONAL SOUND PRESSURE FIELD AROUND A NOISE BARRIER, Journal of Sound and Vibration, vol.197, issue.5, pp.547-571, 1996.
DOI : 10.1006/jsvi.1996.0548

J. A. Ejsmont and U. Sandberg, Texturing of cement concrete pavements to reduce traffic noise, Noise Control Engineering Journal, vol.46, issue.6, pp.231-243, 1998.

A. Fadavi, H. P. Duhamel, and . Yin, Tyre road noise : finite element modelling The Hague, The Netherlands, Proceedings of inter.noise, 2001.

A. Fadavi, Modélisation numérique des vibrations d'un pneumatique et de la propagation du bruit de contact, Ecole Nationale des Ponts et Chaussées, vol.3, p.6, 2002.

. Fong, Tyre noise prediction from computed road surface texture induced contact pressure, Proceedings of inter.noise 98, 1998.

J. Forssén, Calculation of noise barrier performance in a turbulent atmosphere by using substitute sources above the barrier, Acustica -Acta Acustica, vol.86, pp.269-275, 1921.

J. Forssén, Calculation of noise barrier performance using the substitute-sources method for a three-dimensional turbulent atmosphere, Acustica -Acta Acustica, vol.88, issue.21, pp.181-189, 2002.

H. Fujikawa, Y. Hoike, H. Oshino, and . Tachibana, Generation mechanism of tire / road noise -Part 1: Tire vibration caused by road roughness, Proceedings of Internoise 1999, 1999.

F. Gerretsen, F. De-roo, and . Van-gorkum, A prediction model for tyre-road noise emission, International Symposium on Pavement Surface Characteristics, 1996.

E. Gerretsen and E. H. Mulder, TRIAS : a comprehensive tyre-road noise model and its validation, 2001.

R. A. Graf, C. Y. Kuo, A. P. Dowling, and W. R. Graham, Horn amplification at a tyre/road interface ? Part I: experiment and amplification, Proceedings of Internoise 1999, 1999.

R. A. Graf, C. Kuo, A. P. Dowling, and W. R. Graham, ON THE HORN EFFECT OF A TYRE/ROAD INTERFACE, PART I: EXPERIMENT AND COMPUTATION, Journal of Sound and Vibration, vol.256, issue.3, pp.417-431, 2002.
DOI : 10.1006/jsvi.2001.4238

D. Habault, Etude de l'influence des sols sur la propagation sonore, 1984.

D. Habault, Sound propagation above an inhomogeneous plane: Boundary integral equation methods, Journal of Sound and Vibration, vol.100, issue.1, pp.55-67, 1985.
DOI : 10.1016/0022-460X(85)90342-6

J. Hamet, J. M. Clairet, and J. C. Bruyère, Bruit extérieur pneumatique / chaussée - Aménagement et instrumentation du laboratoire de Grenoble, 1991.

J. Hamet, Modélisation acoustique d'un enrobé drainant -Prise en compte des phénomènes de thermoconductivité dans une nouvelle formulation phénoménologique, INRETS, vol.1, issue.3, 1992.

J. Hamet and P. Klein, Use of a rolling model for the study of the correlation between road texture and tire noise The Hague, The Netherlands, Proceedings of inter.noise, 2001.

&. Bruit-'et and S. R. Us, Recherches physiques sur le bruit de roulement dans les projets 'Texture, Proceedings of Journées d'´ etude Bruit du Trafic Routier, 2001.

R. E. Hayden, Road side noise from the interaction of a rolling tire with the road surface, 81st meeting of the Acoust. Soc. of America, 1971.

. Holste, AN EQUIVALENT SOURCE METHOD FOR CALCULATION OF THE SOUND RADIATED FROM AIRCRAFT ENGINES, Journal of Sound and Vibration, vol.203, issue.4, pp.667-695, 1921.
DOI : 10.1006/jsvi.1996.0891

S. C. Huang and W. , Soedel Response of rotating rings to harmonic and periodic loading and comparison with the inverted problem, Journal of Sound and Vibration, vol.118, issue.2 2, pp.255-270, 1987.

S. C. Huang and C. K. Su, In-plane Dynamics of Tires on the Road Based on an Experimentally Verified Rolling Ring Model, Vehicle System Dynamics, vol.122, issue.1, pp.247-267, 1992.
DOI : 10.1115/1.3423597

. Huschek, Characterization of pavement surface texture and its influence on tyre / road noise, 3rd International symposium on pavement surface characteristics, 1996.

E. L. Ince, Ordinary Differential Equations, The Mathematical Gazette, vol.18, issue.231, p.19, 1956.
DOI : 10.2307/3605524

U. Ingard, On the Reflection of a Spherical Sound Wave from an Infinite Plane, The Journal of the Acoustical Society of America, vol.23, issue.3, pp.329-335, 1951.
DOI : 10.1121/1.1906767

M. E. Mcintyre and J. Woodhouse, On the fundamentals of bowed?string dynamics, Acustica, vol.43, issue.2 3, pp.93-108, 1979.

K. L. Johnson, Contact mechanics, 1985.

M. E. Johnson, S. J. Elliot, K. Baek, and J. Garcia-bonito, An equivalent source technique for calculating the sound field inside an enclosure containing scattering objects, The Journal of the Acoustical Society of America, vol.104, issue.3, pp.1221-1231, 1998.
DOI : 10.1121/1.424330

D. I. Kaklamani and H. T. Anastassiu, Aspects of the method of auxiliary sources (MAS) in computational electromagnetics. IEEE Antenna's and Propagation Magazine Appendix I, pp.255-270, 2002.

M. Karamehmedovic and O. Breinbjerg, A convergent method of auxiliary sources for twodimensional impedance scatterers with edges, Conference on Applied Electromagnetic and Communication, Croatia, 1921.

P. Klein, Effetdì adre ? Etude du modàle de Kropp, 1998.

P. Klein, Texture/ Bruit " ? Etude de la relation bruit/texture sur la base de mesures effectuées dans le cadre de la phase 1, Projet PREDIT, 2000.

P. Klein, Tyre noise horn effect on an absorbing surface -2D analytical modelling using the multipole synthesis, Proceedings of Forum Acusticum, 2002.

G. H. Koopmann, L. Song, and J. B. , A method for computing acoustic fields based on the principle of wave superposition, The Journal of the Acoustical Society of America, vol.86, issue.6, pp.2433-2438, 1989.
DOI : 10.1121/1.398450

J. Kragh, Nordic prediction for road traffic noise. New basic input values due to the tightening of vehicle noise limits, 1991.

J. Kragh, News and needs in outdoor noise prediction The Hague, The Netherlands, Proceedings of inter, 2001.

R. Kress and A. Mohsen, On the simulation source technique for exterior problems in acoustics, Mathematical Methods in the Applied Sciences, vol.10, issue.1, pp.585-597, 1921.
DOI : 10.1002/mma.1670080138

W. Kropp, Structure-borne sound on a smooth tyre, Applied Acoustics, vol.26, issue.3, pp.181-188, 1989.
DOI : 10.1016/0003-682X(89)90051-0

W. Kropp, Ein Model zur Beschreibung des Rollgeräusches eines unprofilierten Guertlreifens auf rauher Strassenoberfläche, 1992.

P. Kropp and . Svensson, Application of the time domain formulation of the method of Equivalent Sources to radiation and scattering problems, Acustica, vol.81, pp.528-543, 1921.

W. Kropp and J. Bérillon, A theoretical model to investigate the acoustic performance of building facades in the low and middle frequency range, Acustica -Acta Acustica, vol.84, pp.681-688, 1998.

W. Kropp and J. Bérillon, A theoretical model to consider the influence of absorbing surfaces inside the cavity of balconies, Acustica -Acta Acustica, vol.86, issue.21, pp.485-494, 2000.

W. Kroppb-), F. Bécot, and S. Barrelet, On the sound radiation from tyres. Acustica -Acta Acustica, pp.769-779, 2000.

W. Kropp, K. Larsson, F. Wullens, P. F. Andersson, T. Bécot et al., The modelling of tyre / road noise ? a quasi three-dimensional model The Hague, The Netherlands, Proceedings of inter.noise, 2001.

P. A. Krutitskii, Method of interior boundaries for the impedance problem in scattering theory, Applied Mathematics and Computation, vol.135, issue.1, pp.147-160, 2003.
DOI : 10.1016/S0096-3003(01)00320-4

A. Kuijpers and G. J. Van-bokland, Tyre / road noise models in the last two decades : a critical evaluation The Hague, The Netherlands, Proceedings of inter.noise, 2001.

C. Kuo, R. A. Graf, A. P. Dowling, and W. R. Graham, ON THE HORN EFFECT OF A TYRE/ROAD INTERFACE, PART II: ASYMPTOTIC THEORIES, Journal of Sound and Vibration, vol.256, issue.3, pp.433-445, 2002.
DOI : 10.1006/jsvi.2001.4217

K. Larsson, Modelling of dynamic contact ? Exemplified on the tyre / road interaction, 2002.

K. Larsson, S. Barrelet, and W. Kropp, The modelling of the dynamic behaviour of tyre tread blocks, Applied Acoustics, vol.63, issue.6, pp.659-677, 2002.
DOI : 10.1016/S0003-682X(01)00059-7

Y. L. Li and M. J. White, Near???field computation for sound propagation above ground???Using complex image theory, The Journal of the Acoustical Society of America, vol.99, issue.2, pp.755-759, 1996.
DOI : 10.1121/1.414652

K. U. Machens, Approximate solutions for acoustic radiation problems: a critical appraisal of the method of comparative sources, Acustica -Acta Acustica, vol.85, pp.764-779, 1999.

M. B. Magalhaes, R. A. Tenenbaum, and M. , Zindeluk Application of equivalent sources methods in acoustical holography The Hague, The Netherlands, Proceedings of inter.noise, 2001.

H. M. Miedema, Noise & health: how does noise affect us The Hague, The Netherlands, Proceedings of inter.noise, 2001.

D. Miller, E. T. Moyer, H. Huang, and H. , A comparison between the boundary element method and the wave superposition approach for the analysis of the scattered fields from rigid bodies and elastic shells, The Journal of the Acoustical Society of America, vol.89, issue.5, pp.2185-2196, 1991.
DOI : 10.1121/1.400969

M. Morse and K. , Ingard Theoretical acoustics, p.949, 1968.
DOI : 10.1063/1.3035602

P. A. Nelson, Some inverse problems in acoustics, Sixth International Congress on Sound and Vibration, 1921.

N. Nilsson, Air resonant and vibrational radiation ? Possible mechanisms for noise from cross-bar tires, International Tire Noise Conference, pp.93-110, 1979.

M. Ochmann, Calculation of sound radiation from complex machine structures using the multipole radiator synthesis and the boundary element multigrid method, 1980.

M. Ochmann, The source simulation technique for acoustic radiation problems, Acustica, vol.81, pp.512-526, 1995.

M. Ochmann, The full-field equations for acoustic radiation and scattering, The Journal of the Acoustical Society of America, vol.105, issue.5, pp.2574-2584, 1921.
DOI : 10.1121/1.426873

M. Ochmann, Source simulation techniques for the calculation of sound radiation and scattering -An overview Appendix I, Sixth International Congress on Sound and Vibration, Garmisch- Partenkirchen, 2000.

P. J. Papakanellos, D. I. Kaklamani, and C. N. Capsalis, Analysis of an infinite current source above a semi-infinite lossy ground using fictitious current auxiliary sources in conjuction with complex image theory techniques, IEEE Transactions on Antennas and Propagation, issue.10 21, pp.49-491, 2001.

. Périsse, A STUDY OF RADIAL VIBRATIONS OF A ROLLING TYRE FOR TYRE???ROAD NOISE CHARACTERISATION, Mechanical Systems and Signal Processing, pp.1043-1058, 2002.
DOI : 10.1006/mssp.2001.1432

J. Picaut, ContributionàContributionà l'´ etude de la réflexion du son par une façade. Partie I Bibliographies et considérations qualitatives, Laboratoire Central des Ponts et Chaussées, issue.5, 2000.

R. J. Pinnington, A one dimensional wave model for an automotive tyre, Proceedings of inter.noise, 2000.

J. Pinnington and A. R. Briscoe, A WAVE MODEL FOR A PNEUMATIC TYRE BELT, Journal of Sound and Vibration, vol.253, issue.5, pp.941-959, 2002.
DOI : 10.1006/jsvi.2001.3944

H. Press, Numerical recipies, the art of scientific computing, 1986.

K. B. Rasmussen, Sound propagation over grass covered ground, Journal of Sound and Vibration, vol.78, issue.2, pp.247-255, 1981.
DOI : 10.1016/S0022-460X(81)80036-3

T. L. Richards, Finite element analysis of structural-acoustic coupling in tyres, Journal of Sound and Vibration, vol.149, issue.2, pp.235-243, 1991.
DOI : 10.1016/0022-460X(91)90633-U

D. Ronneberger, Towards quantitative prediction of tire / road noise, A workshop on rolling noise generation, 1989.

C. Ronneberger and . Preuss, Optimum positions of microphones in trailers, International tire, 1990.

F. De-roo, E. H. Gerrestsen, and . Mulder, Predictive performance of the tyre-road noise model TRIAS The Hague, The Netherlands, Proceedings of inter.noise, 2001.

J. Ruhala, A study of tire / pavement interaction noise using nearfield acoustical holography, 1999.

S. Saigal and T. Y. Yang, Free vibrations of a tire as a toroidal membrane, Journal of Sound and Vibration, vol.107, issue.1, pp.71-82, 1986.
DOI : 10.1016/0022-460X(86)90283-X

G. Sandberg and . Descornet, Road surface influence in tire/road noise, Proceedings of inter, 1980.

. Sandberg, Will tire / road noise limit future vehicle noise reductions? In Proceedings of inter, 1982.

. Sandberg, Noise emission of road vehicles -effects of regulation. Status report of an I-INCE party, Proceedings of inter.noise 93, 1993.

. Sandberg, Tyre / road noise ? Myths and realities In Proceedings of Inter The Hague, The Netherlands, 2001.

J. A. Sandberg and . Ejsmont, Tyre / road noise reference book Informex, p.640, 2002.

D. Schaaf and . Ronneberger, Noise radiation from rolling tires -Sound amplification by the " horn effect, Proceedings of inter.noise 1982, 1982.

M. R. Schroeder, Integrated???impulse method measuring sound decay without using impulses, The Journal of the Acoustical Society of America, vol.66, issue.2, pp.497-500, 1979.
DOI : 10.1121/1.383103

W. Soedel, On the dynamic response of rolling tires according to thin shell approximations, Journal of Sound and Vibration, vol.41, issue.2, pp.233-246, 1975.
DOI : 10.1016/S0022-460X(75)80099-X

L. Song, G. H. Koopmann, and J. B. Fahnline, Numerical errors associated with the method of superposition for computing acoustic fields, The Journal of the Acoustical Society of America, vol.89, issue.6, pp.2625-2633, 1991.
DOI : 10.1121/1.400701

S. A. Stansfeld, The non?auditory health effects of noise exposure, Acoustique et Techniques, vol.28, 2002.

P. Stanners and . Bourdeau, Europe's environment, 1995.

S. Thomasson, Reflection of waves from a point source by an impedance boundary, The Journal of the Acoustical Society of America, vol.59, issue.4, pp.303-322, 1976.
DOI : 10.1121/1.380943

S. Thomasson, Sound propagation above a layer with a large refraction index, The Journal of the Acoustical Society of America, vol.61, issue.3, pp.659-674, 1977.
DOI : 10.1121/1.381352

T. M. Tomilina, The equivalent sources approach to acoustical design of forced vibrating systems, Proceedings of inter.noise, 1921.

G. J. Too and S. M. Wang, The application of source methods in estimation of an interior sound field, Applied Acoustics, vol.63, issue.3, pp.295-310, 2001.
DOI : 10.1016/S0003-682X(01)00033-0

Z. Wang and S. F. Wu, Helmholtz equation???least-squares method for reconstructing the acoustic pressure field, The Journal of the Acoustical Society of America, vol.102, issue.4, pp.2020-2032, 1997.
DOI : 10.1121/1.419691

G. R. Watts, S. N. Chandler-wilde, and P. A. Morgan, The combined effects of porous asphalt surfacing and barriers on traffic noise, Applied Acoustics, vol.58, issue.3, pp.351-377, 1999.
DOI : 10.1016/S0003-682X(98)00045-0

T. Weaver, Image Theory for an Arbitrary Quasi-Static Field in the Presence of a Conducting Half Space, Radio Science, vol.22, issue.11, pp.647-653, 1971.
DOI : 10.1029/RS006i006p00647

E. G. Williams, Inverse Problems in Sound Radiation, Proceedings of ICA 2001, 1921.

T. Ten-wolde, On the validity and application of reciprocity in acoustical mechano?acoustical and other dynaminal systems, Acustica -Acta Acustica, vol.28, issue.1, pp.23-32, 1973.

F. Wullens, Towards an optimisation of tyre / road parameters for noise reduction, 2002.

C. Zwikker and C. W. Kosten, Sound absorbing materials, 1949.