Tire Noise

  • Yukio NakajimaEmail author


Tire/road noise consists of noise due to tire surface vibration and noise related to aerodynamics. The former noise is usually explained by three elements, namely the external force applied to a tire, vibration properties of the tire and the acoustic field relating to the tire surface and road surface. The external force includes the tread impact associated with the lateral grooves and road roughness. The surface vibration of a tire is calculated by multiplying external forces by the tire’s vibration properties expressed by a transfer function. Tire/road radiation noise is then calculated by surface vibration via the Helmholtz equation [i.e., employing the boundary element method (BEM)]. The most important element for tire noise is the external force because other elements may not be controlled by tire design without deteriorating other tire performances. The external force due to lateral grooves is estimated by using a phenomenological model that uses the contact shape, pattern geometry and contact pressure or by conducting FEA. Meanwhile, the external force due to road roughness is estimated by measuring the spindle force of a tire rolling over a simple roughness and conducting contact analysis employing a Winker model with nonlinear contact stiffness or FEA. The vibration properties of a tire can be predicted by conducting FEA or using an elastic ring model. In pattern design, the phenomenological model is used as a design tool to determine the pattern geometry, and the pitch sequence is optimized by a GA. The Helmholtz resonator may be added to the circumferential grooves to reduce the pipe resonance noise. Furthermore, the special wheel or sound-absorbing material may be used to reduce the acoustic cavity noise.

Supplementary material


  1. 1.
    K. Hardy, Noise. Tire Technol. Int. 32–35 (2002)Google Scholar
  2. 2.
    U. Sandberg, Tyre/road noise - myths and realities. Internoise 2002, 35–55 (2002)Google Scholar
  3. 3.
    JATMA (ed.) On Noise Due to Tire and Road (7th version) (JATMA, 2004) (in Japanese)Google Scholar
  4. 4.
    WHO, Burden of Disease from Environmental Noise. Quantification of Healthy Life Years Lost in Europe (World Health Organization, 2011)Google Scholar
  5. 5.
    Bridgestone (ed.) Fundamentals and Application of Vehicle Tires (Tokyo Denki University Press, Tokyo, 2008) (in Japanese)Google Scholar
  6. 6.
    M. Heckl, Tyre noise generation. Wear 113, 157–170 (1986)CrossRefGoogle Scholar
  7. 7.
    U. Sandberg, J.A. Ejsmont, Tyre/road noise reference book, in Informex (2002)Google Scholar
  8. 8.
    Michelin, The tyre: mechanical and acoustic comfort (Societe de Technologie Michelin, 2002).
  9. 9.
    V.Q. Doan et al., Investigation into the influence of tire construction on coast-by noise. Tire Sci. Technol. 23(2), 96–115 (1995)CrossRefGoogle Scholar
  10. 10.
    Y. Nakajima, Theory on pitch noise and its application. J. Vib. Acoust. 125(3), 252–256 (2003)CrossRefGoogle Scholar
  11. 11.
    F. Liu et al., Modeling of tread block contact mechanics using linear viscoelastic theory. Tire Sci. Technol. 36(3), 211–226 (2008)CrossRefGoogle Scholar
  12. 12.
    F. Liu et al., Prediction of tread block forces for a free-rolling tyre in contact with a smooth road. Wear 269, 672–683 (2010)CrossRefGoogle Scholar
  13. 13.
    F. Liu et al., Prediction of tread block forces for a free-rolling tyre in contact with a rough road. Wear 282–283, 1–11 (2012)CrossRefGoogle Scholar
  14. 14.
    ISO 13473–1, in Characterization of Pavement Texture by Use of Surface Profiles—Part 1: Determination of Mean Profile Depth (1997)Google Scholar
  15. 15.
    PIARC, Optimization of surface characteristics, in Report to the XVIIIth World Road Congress 1987, Brussels, Belgium (Technical Committee on Surface Characteristics, World Road Association (PIARC), Paris, 1987)Google Scholar
  16. 16.
    Y. Nakajima et al., Application of the boundary element method and modal analysis to tire acoustics problem. Tire Sci. Technol. 21, 66–90 (1992)CrossRefGoogle Scholar
  17. 17.
    Y. Nakajima, Application of BEM and FEM modal analysis to tire noise. Nippon Gomu Kyokaishi 66(6), 433–441 (1993). (in Japanese)CrossRefGoogle Scholar
  18. 18.
    J. Perisse, A study of radial vibrations of a rolling tyre for tyre road noise characterisation. Mech. Syst. Signal Pr. 16(6), 1043–1058 (2002)CrossRefGoogle Scholar
  19. 19.
    H. Koike et al., Noise source identification of tire/road noise. Noise Control 22, 11–13 (1998). (in Japanese)Google Scholar
  20. 20.
    M. Satomi, et al., Study on sound source separation of tire pattern noise, in Proceedings of JSAE Conference, No. 882147 (1988)Google Scholar
  21. 21.
    N. Tomita, Low noise pavement and tire-road noise. Sound Control 23, 142–147 (1999). (in Japanese)Google Scholar
  22. 22.
    M. Brinkmeier et al., A finite element approach to the transient dynamics of rolling tires with emphasis on rolling noise simulation. Tire Sci. Technol. 35(3), 165–182 (2007)CrossRefGoogle Scholar
  23. 23.
    M. Brinkmeier, U. Nackenhorst, An approach for large-scale gyroscopic eigenvalue problems with application to high-frequency response of rolling tires. Compu. Mech. 41, 503–515 (2008)zbMATHCrossRefGoogle Scholar
  24. 24.
    E. Skudrzyk, Simple and Complex Vibratory Systems, (The Pennsylvania State University Press, University Park, 1968)zbMATHGoogle Scholar
  25. 25.
    F. Fahy, Foundation of Engineering Acoustics (Elsevier, Amsterdam, 2001)Google Scholar
  26. 26.
    W.F. Reiter Jr., Resonant sound and vibration characteristics of a truck tire. Tire Sci. Technol. 2(2), 130–141 (1974)CrossRefGoogle Scholar
  27. 27.
    R.J. Pinnington, A.R. Briscoe, A wave model for a pneumatic tyre belt. J. Sound Vib. 253(5), 941–959 (2002)CrossRefGoogle Scholar
  28. 28.
    J.S. Bolton, et al., The wave number decomposition approach to the analysis of tire vibration, in Noise Conference, vol. 98, Michigan (1998), pp. 97–102Google Scholar
  29. 29.
    J.S. Bolton, Y.J. Kim, in Visualization of the tire vibration and sound radiation and modeling of tire vibration with an emphasis on wave propagation. Technical Report, The Institute for Safe, Quiet and Durable Highways (2003). Available at:
  30. 30.
    W. Kropp et al., On the sound radiation from tyres. ACUSTICA-Acta Acustica 87, 769–779 (2000)Google Scholar
  31. 31.
    R.A.G. Graf et al., On the horn effect of a tyre/road interface, part I: experiment and computation. J. Sound Vib. 256(3), 417–431 (2002)CrossRefGoogle Scholar
  32. 32.
    R.E. Hayden, Roadside noise from the interaction of a rolling tire with road surface, in Proceedings of Purdue Noise Conference, West Lafayette, IN (1971), pp. 62–67Google Scholar
  33. 33.
    M.J. Gagen, Novel acoustic sources from squeezed cavities in car tires. J. Acoust. Soc. Am. 106(2), 794–801 (1999)CrossRefGoogle Scholar
  34. 34.
    S. Kim et al., Prediction method for tire air-pumping noise using a hybrid technique. J. Acoust. Soc. Am. 119(6), 3799–3812 (2006)CrossRefGoogle Scholar
  35. 35.
    D.G. Crighton, et al., Modern Methods in Analytical Acoustics (Springer, Berlin, 1992)Google Scholar
  36. 36.
    Y. Nakajima, Analytical model of longitudinal tire traction in snow. J. Terramechanics 40(1), 63–82 (2004)CrossRefGoogle Scholar
  37. 37.
    A.H.W.M. Kuijpers, Tyre/road noise modelling: the road from a tyre’s point-of-view. Report No. M + P.MVW.01.8.1 (2001)Google Scholar
  38. 38.
    M. Yabu, The characterisitcs of tire on NVH, in Symposium of JSAE, 9435225 (1994)Google Scholar
  39. 39.
    T. Beckenbauer, et al., Tyre/road noise prediction: a comparison between the SPERoN and HyRoNE models—part I, in Euronoise Acoustics’08 (2008)Google Scholar
  40. 40.
    W. Kropp, A mathematical model of tyre noise generation. Int. J. Vehicle Des. 6, 310–329 (1999)CrossRefGoogle Scholar
  41. 41.
    K. Larsson, W. Kropp, A high-frequency three-dimensional tyre model based on two coupled elastic layers. J. Sound Vib. 253(4), 889–908 (2002)CrossRefGoogle Scholar
  42. 42.
    D.J. O’Boy, A.P. Dowling, Tyre/road interaction noise—Numerical noise prediction of a patterned tyre on a rough road surface. J. Sound Vib. 323, 270–291 (2009)CrossRefGoogle Scholar
  43. 43.
    F. Böhm, Mechanik des Gürtelreifens. Archive Appl. Mech. 3, 582–101 (1966)Google Scholar
  44. 44.
    P. Kindt et al., Development and validation of a three-dimensional ring-based structural tyre model. J. Sound Vib. 326, 852–869 (2009)CrossRefGoogle Scholar
  45. 45.
    M. Koishi, et al., Radiation noise simulation of a rolling tire excited by tread pattern, in SIMULIA Customer Conference (2011)Google Scholar
  46. 46.
    E.J. Ni et al., Radiated noise from tire/wheel vibration. Tire Sci. Technol. 25(1), 29–42 (1997)MathSciNetCrossRefGoogle Scholar
  47. 47.
    J. Biermann et al., Computational model to investigate the sound radiation from rolling tires. Tire Sci. Technol. 35(3), 209–225 (2007)CrossRefGoogle Scholar
  48. 48.
    T. Saguchi,, Tire radiation-noise prediction using FEM, in Inter-noise 2006, Honolulu, USA (2006)Google Scholar
  49. 49.
    M. Brinkmeier, U. Nackenhorst, Computational investigations on the dynamics of tires rolling on rough roads. Tire Sci. Technol. 37(1), 47–59 (2009)CrossRefGoogle Scholar
  50. 50.
    M. Brinkmeier et al., A finite element approach for the simulation of tire rolling noise. J. Sound Vib. 309, 20–39 (2008)CrossRefGoogle Scholar
  51. 51.
    P.B.U. Andersson, W. Kropp, Time domain contact model for tyre/road interaction including nonlinear contact stiffness due to small-scale roughness. J. Sound Vib. 318, 296–312 (2008)CrossRefGoogle Scholar
  52. 52.
    P.B.U. Andersson, et al., Numerical modelling of tyre/road interaction. Univ. Pitesti Sci. Bull. Automotive Ser. 22(1) (2008)Google Scholar
  53. 53.
    B.R. Mace et al., Finite element prediction of wave motion in structural waveguides. J. Acoust. Soc. Am. 117(5), 28350–2843 (2005)CrossRefGoogle Scholar
  54. 54.
    W. Kropp, et al., Reduction potential of road traffic noise. Appl. Acous. (2007)Google Scholar
  55. 55.
    Y. Waki et al., Free and forced vibrations of a tyre using a wave/finite element approach. J. Sound Vib. 323, 737–756 (2009)CrossRefGoogle Scholar
  56. 56.
    P. Sabiniarz, W. Kropp, A waveguide finite element aided analysis of the wave field on a stationary tyre, not in contact with the ground. J. Sound Vib. 329, 3041–3064 (2010)CrossRefGoogle Scholar
  57. 57.
    Y. Waki, et al., Estimation of noise radiating parts of a tire using the wave finite element method, in Proceedings of Inter-noise 2011 (2011)Google Scholar
  58. 58.
    C. Hoever, in The influence of modelling parameters on the simulation of car tyre rolling losses and rolling noise. Ph.D. Thesis, Chalmers University of Technology (2012)Google Scholar
  59. 59.
    W. Kropp et al., On the sound radiation of a rolling tyre. J. Sound Vib. 331, 1789–1805 (2012)CrossRefGoogle Scholar
  60. 60.
    J.J. Lee, A.E. Ni, Structure-Borne tire noise statistical energy analysis model. Tire Sci. Technol. 25(3), 177–186 (1997)CrossRefGoogle Scholar
  61. 61.
    P. Bremner, et al., A model study of how tire construction and material affect vibration-radiated noise, in SAE Paper, No. 972049 (1997)Google Scholar
  62. 62.
    J.J. Lee et al., Structure-borne vibration transmission in a tire and wheel assembly. Tire Si. Technol. 26(3), 173–185 (1998)CrossRefGoogle Scholar
  63. 63.
    T. Beckenbauer, et al. Simulation of tyre/road noise as a tool for the evaluation of the acoustic behavior of road surfaces, in 5th Eurasphalt & Eurobitume Congress, Istanbul (2012)Google Scholar
  64. 64.
    F.D. Roo, et al., Predictive performance of the tyre-road noise model TRIAS, in Inter-noise 2001, Hague, Netherlands (2001)Google Scholar
  65. 65.
    M. Li, et al., New approach for modelling tyre/road noise, in Inter-noise 2009, Canada (2009)Google Scholar
  66. 66.
    K. Iwao, I. Ymamazaki, A study on the mechanism of tire/road noise. JSAE Rev. 17, 139–144 (1996)CrossRefGoogle Scholar
  67. 67.
    N.A. Nilsson, Possible method of reducing external tyre noise”, Proc. Int. Tire Noise Conf. 1979, Stockholm, Sweden, 1979Google Scholar
  68. 68.
    K. Klaus, D. Ronneberger, Noise radiation from rolling tires—sound amplification by the “horn-effect”, in Inter-noise 1982, San Francisco, USA (1982)Google Scholar
  69. 69.
    D. Ronneberger, Towards quantitative prediction of tyre/road noise, in Workshop on Rolling Noise Generation (Institute fur Technisc Technische Universitat, Berlin, 1989)Google Scholar
  70. 70.
    C.Y. Kuo et al., Horn amplification at a tyre/road interface-Part II: ray theory and experiment. Inter-noise 1999, 125–130 (1999)Google Scholar
  71. 71.
    T. Sakata et al., Effects of tire cavity resonance on vehicle road noise. Tire Sci. Technol. 18(2), 68–79 (1990)MathSciNetCrossRefGoogle Scholar
  72. 72.
    J.K. Thompson, Plane wave resonance in the air cavity as a vehicle interior noise source. Tire Sci. Technol. 23(1), 2–10 (1995)CrossRefGoogle Scholar
  73. 73.
    T.L. Richards, Finite element analysis if structural-acoustic coupling in tyres. J. Sound Vib. 149, 235–243 (1991)CrossRefGoogle Scholar
  74. 74.
    L.R. Molisani et al., A coupled tire structure/acoustic cavity model. Int. J. Solid Struct. 40, 5125–5138 (2003)zbMATHCrossRefGoogle Scholar
  75. 75.
    H. Yamaguchi, Y. Akiyoshi, Theoretical analysis of tire acoustic cavity noise and proposal of improvement technique. JSAE Rev. 23, 89–94 (2002)CrossRefGoogle Scholar
  76. 76.
    J.J. Lee et al., Structure-borne vibration transmission in a tire and wheel assembly. Tire Sci. Technol. 26(3), 173–185 (1998)CrossRefGoogle Scholar
  77. 77.
    M.J. Subler, et al., Experimental study of the acoustic cavity resonance in automobile tire dynamic response, in Proceedings of ASME, Noise Control and Acoustic Division, vol. 26 (1999), pp. 177–183Google Scholar
  78. 78.
    R. Gunda et al., Analytical model of tire cavity resonance and coupled tire/cavity modal model. Tire Sci. Technol. 28(1), 33–49 (2000)CrossRefGoogle Scholar
  79. 79.
    M. Tanaka, K. Fujisawa, Development of low noise tire. JSAE J. 60(4), 81–84 (2006). (in Japanese)Google Scholar
  80. 80.
    H.M.R. Aboutorabi, L. Kung, Application of coupled structural acoustic analysis and sensitivity calculations to a tire noise problem. Tire Sci. Technol. 40(1), 25–41 (2012)CrossRefGoogle Scholar
  81. 81.
    A. Selamet et al., Theoretical, computational and experimental investigation of Helmholtz resonators with fixed volume: lumped versus distributed analysis. J. Sound Vib. 187(2), 358–367 (1995)CrossRefGoogle Scholar
  82. 82.
    S. Fujiwara et al., Reduction of tire groove noise using slot resonators. Tire Sci. Technol. 37(3), 207–223 (2009)CrossRefGoogle Scholar
  83. 83.
    Y. Tozawa, Y. Suzuki, Road noise and tire vibration characteristics. JSAE J. 40(12), 1624–1929 (1986). (in Japanese)Google Scholar
  84. 84.
    T. Saguchi, et al., Vehicle interior noise prediction using tire characteristics and vehicle transmissibility, in SAE Paper, No. 2007-01-1533 (2007)Google Scholar
  85. 85.
    Y. Nakajima, A. Abe, Application of genetic algorithms of optimization of tire pitch sequences. Jpn. J. Ind. Appl. Math. 17(3), 403–426 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  86. 86.
    P. Campanac et al., Application of vibration analysis of linear systems with time-periodic coefficients to dynamics of a rolling tyre. J. Sound Vib. 231, 37–77 (2000)CrossRefGoogle Scholar
  87. 87.
    P. Andersson et al., High frequency dynamic behaviour of smooth and patterned passenger car tyres. Acta Acustica United Acustica 90(3), 445–456 (2004)Google Scholar
  88. 88.
    J.H. Varterasian, Quieting noise mathematically—its application to snow tires, in SAE Paper, No. 690520 (1969)Google Scholar
  89. 89.
    P.R. Willett, Tire tread pattern sound generation. Tire Sci. Technol. 3(4), 252–266 (1975)CrossRefGoogle Scholar
  90. 90.
    Japanese Patent No. 3-23366Google Scholar
  91. 91.
    Japanese Patent No. 4-232105Google Scholar
  92. 92.
    Japanese Patent No. 4-363234Google Scholar
  93. 93.
    European Patent No. 0 543 493 A1Google Scholar
  94. 94.
    Y. Nakajima, et al., New tire design procedure based on optimization technique, in SAE Paper, 960997 (1996)Google Scholar
  95. 95.
    A. Abe et al., Optimum Young’s modulus distribution in tire design. Tire Sci. Technol. 24, 204–219 (1996)CrossRefGoogle Scholar
  96. 96.
    Y. Nakajima et al., Theory of optimum tire contour and its application. Tire Sci. Technol. 24, 184–203 (1996)CrossRefGoogle Scholar
  97. 97.
    U. S. Patent, in Method of determining a pitch arrangement of a tire. US258567, US5717613Google Scholar
  98. 98.
    K.M. Hoffmeister, J.E. Bernard, Tread pitch arrangement optimization through the use of a genetic algorithm. Tire Sci. Technol. 26(1), 2–22 (1998)CrossRefGoogle Scholar
  99. 99.
    H. Sugimoto, Discrete optimization of truss structures and genetic algorithms, in Proceedings of Korea-Japan Joint Seminar on STRUCTURAL OPTIMIZATION (1992)Google Scholar
  100. 100.
    E. Zwicker, H. Fastl, Psychoacoustics: Facts and Models (Springer, Berlin, 1990)Google Scholar
  101. 101.
    M. Ohashi, et al., in Noise quality evaluation system. Technical Report of Onosokki, No. 11 (1998), p. 23Google Scholar
  102. 102.
    B. Moor, (translated by K. Ogushi), in Introduction of Psychoacoustics (Seishinshobou, 1994)Google Scholar
  103. 103.
    H. Fastl, Calibration signals for meters of loudness, sharpness, fluctuation strength, and roughness. Inter-noise 93, 1257–1260 (1993)Google Scholar
  104. 104.
    F.S. Buss, in Subjective perception of pattern noise, a tonal component of the tyre/road noise, and its objective characterization by spectral analysis and calculating contours. Ph.D. Thesis, Oldenburg (2006)Google Scholar
  105. 105.
    M. Kikuchi, et al., Evaluation of timbre of air-conditioner noise, in Proceedings of Acoustical Society of Japan (1992), p. 699Google Scholar
  106. 106.
    E.C. Frank, et al., In-vehicle tire sound quality prediction from tire noise data, in SAE Paper, 2007-1-2253 (2007)Google Scholar
  107. 107.
    F.K. Brandel, et al., Objective assessment of vehicle noise quality as a basis for sound engineering, in JSAE Conference, Paper No. 9833368 (1998)Google Scholar
  108. 108.
    Japanese Patent No. 2008-58458Google Scholar
  109. 109.
    A.M. Jessop, J.S. Bolton, Tire surface vibration and sound radiation resulting from the tire cavity mode. Tire Sci. Technol. 39(4), 245–255 (2011)CrossRefGoogle Scholar
  110. 110.
    B. Peeters, et al., Reduction of the horn effect for car and truck tyres by sound absorbing road surfaces, in Inter-noise 2010, Lisbon (2010)Google Scholar
  111. 111.
    W.R. Graham et al., Characterisation and simulation of asphalt road surfaces. Wear 271, 734–747 (2011)CrossRefGoogle Scholar
  112. 112.
    R.J. Pinnington, A particle-envelope surface model for road-tyre interaction. Int. J. Solid Struct. 49, 546–555 (2012)CrossRefGoogle Scholar
  113. 113.
    R.J. Pinnington, Tyre-road contact using a particle–envelope surface model. J. Sound Vib. 332, 7055–7075 (2013)CrossRefGoogle Scholar
  114. 114.
    J. Suh, et al., Development of input loads for road noise analysis, in SAE Paper, 2003-01-1608 (2003)Google Scholar
  115. 115.
    H. Yamada, et al., Development of road noise prediction method, in JSAE Conference, Paper No. 20005007 (2000)Google Scholar
  116. 116.
    I. Shima, V.Q. Doan, Method of simulating tire noise. Trans. JSAE 37(6), 27–31 (2006)Google Scholar
  117. 117.
    J. Cesbron et al., Experimental study of tyre/road contact forces in rolling conditions for noise prediction. J. Sound Vib. 320, 125–144 (2009)CrossRefGoogle Scholar
  118. 118.
    T. Koizumi et al., An analysis of radiated noise from rolling tire vibration. JSAE Review 24, 465–469 (2003)CrossRefGoogle Scholar
  119. 119.
    D. Belluzzo et al., New predictive model for the study of vertical forces (up to 250 Hz) induced on the tire hub by road irregularities. Tire Sci. Technol. 30(1), 2–18 (2002)CrossRefGoogle Scholar
  120. 120.
    T. Shibata, et al., Proposal for the modeling method of the input for road noise and verification for accuracy of prediction analysis, in Proceedings of JSAE Conference, Paper No. 20025457 (2002)Google Scholar
  121. 121.
    T. Nakagawa, et al., An analyzing method of the exciting force on tire for road noise, in Proceedings of JSAE Conference, Paper No. 9838570 (1998)Google Scholar
  122. 122.
    K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1985)Google Scholar
  123. 123.
    T. Fujikawa et al., Definition of road roughness parameters for tire vibration noise control. Appl. Acoust. 66, 501–512 (2005)CrossRefGoogle Scholar
  124. 124.
    J. Cesbron et al., Numerical and experimental study of multi-contact on an elastic half-space. Int. J. Mech.l Sci. 51, 33–40 (2009)zbMATHCrossRefGoogle Scholar
  125. 125.
    J. Cesbron, H.P. Yin, Contact analysis of road aggregate with friction using a direct numerical method. Wear 268, 686–692 (2010)CrossRefGoogle Scholar
  126. 126.
    G. Dubois et al., Numerical evaluation of tyre/road contact pressures using a multi-asperity approach. Int. J. Mech. Sci. 54, 84–94 (2012)CrossRefGoogle Scholar
  127. 127.
    T.G. Clapp et al., Development and validation of a method for approximating road surface texture-induced contact pressure in tire-pavement interaction. Tire Sci. Technol. 16(1), 2–17 (1988)CrossRefGoogle Scholar
  128. 128.
    L.A. Galin, Contact problems in the theory of elasticity, Department of Mathematics, North Carolina State University, Raleigh, N.C. (1961)Google Scholar
  129. 129.
    F. Wullens, W. Kropp, A three-dimensional contact model for tyre/road interaction in rolling conditions. Acta Acustica United Acustica 90, 702–711 (2004)Google Scholar
  130. 130.
    F. Yang, Indentation of an incompressible elastic film. Mech. Mater. 30, 275–286 (1998)CrossRefGoogle Scholar
  131. 131.
    J.T. Tielking, Plane vibration characteristics of a pneumatic tire model, in SAE Paper, No. 650491 (1965)Google Scholar
  132. 132.
    H.B. Pacejka, Tire in-plane dynamics, in Mechanics of Pneumatic Tires, ed. by S.K. Clark (National Beaureau of Standards Monograph, 1971)Google Scholar
  133. 133.
    J. Padovan, On viscoelasticity and standing waves in tires. Tire Sci. Technol. 4(4), 233–246 (1976)CrossRefGoogle Scholar
  134. 134.
    L.E. Kung et al., Free vibration of a pneumatic tire-wheel unit using a ring on an elastic foundation and a finite element model. J. Sound Vib. 107(2), 181–194 (1986)CrossRefGoogle Scholar
  135. 135.
    S. Gong, in A study of in-plane dynamics of tires. Ph. D. Thesis, Delft University of Technology (1993)Google Scholar
  136. 136.
    Y.K. Kim, W. Soedel, On ring models for tire vibrations, in Noise-Con 98 (1998), Michigan, pp. 91–96Google Scholar
  137. 137.
    W. Kropp, Structure-borne sound on a smooth tyre. Appl. Acoust. 26, 181–192 (1989)CrossRefGoogle Scholar
  138. 138.
    R.J. Pinnington, Radial force transmission to the hub from an unloaded stationary tyre. J. Sound Vib. 253(5), 961–983 (2002)CrossRefGoogle Scholar
  139. 139.
    J.M. Muggleton et al., Vibrational response prediction of a pneumatic tyre using an orthotropic two-plate wave model. J. Sound Vib. 264, 929–950 (2003)CrossRefGoogle Scholar
  140. 140.
    R.F. Keltie, Analytical model of the truck tire vibration sound mechanism. J. Acoust. Soc. Am. 71(2), 359–367 (1982)CrossRefGoogle Scholar
  141. 141.
    Y.J. Kim, J.S. Bolton, Effects of rotation on the dynamics of a circular cylindrical shell with application to tire vibration. J. Sound Vib. 275, 605–621 (2004)CrossRefGoogle Scholar
  142. 142.
    A. Dowling, Design and implementation of solution at validation sites work package test of new quiet passenger tyre designs, in TIP4-CT-2005-516420 (2005)Google Scholar
  143. 143.
    R.J. Pinnington, A wave model of a circular tyre. Part 1: belt modelling. J. Sound Vib. 290, 101–132 (2006)CrossRefGoogle Scholar
  144. 144.
    R.J. Pinnington, A wave model of a circular tyre. Part 2: side-wall and force transmission modelling. J. Sound Vib. 290, 133–168 (2006)CrossRefGoogle Scholar
  145. 145.
    B.S. Kim et al., The identification of sound generating mechanisms of tyres. Appl. Acoust. 68, 114–133 (2007)CrossRefGoogle Scholar
  146. 146.
    I. Lopez et al., Modelling vibrations on deformed rolling tyres-a modal approach. J. Sound Vib. 307, 481–494 (2007)CrossRefGoogle Scholar
  147. 147.
    C. Lecomte, W.R. Graham, in A tyre belt model based on a 2D beam theory. Technical Report, CUED/A-AERO/TR.28 (2008)Google Scholar
  148. 148.
    C. Lecomte et al., Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire. Tire Sci. Technol. 37(2), 62–102 (2009)CrossRefGoogle Scholar
  149. 149.
    C. Lecomte et al., A shell model for tyre belt vibrations. J. Sound Vib. 329, 1717–1742 (2010)CrossRefGoogle Scholar
  150. 150.
    G.H. Koopmann, Application of sound intensity computations based on the Helmholtz equation, in 11 e ICA, Paris (1983), p. 83Google Scholar
  151. 151.
    I. Kido, Tire and road input modeling for low-frequency road noise prediction, in SAE Paper, No. 2011-01-1690 (2011)Google Scholar
  152. 152.
    P. Kindt et al., Effects of rotation on the tire dynamic behavior: experimental and numerical analyses. Tire Sci. Technol. 41(4), 248–261 (2013)Google Scholar
  153. 153.
    S. Suzuki, et al., Coupling of the boundary element method and modal analysis for structural acoustic problems. Trans. JSME, 52, 310–317 (1985) (in Japanese)Google Scholar
  154. 154.
    H.A. Schenck, Improved integral formulation for acoustic radiation problems. J. Acoust. Soc. Am. 44, 41–58 (1968)CrossRefGoogle Scholar
  155. 155.
    L. Pahlevani, et al., Tire/road dynamic contact; study of different approaches to modelling of a tire, in Proceedings of 9th International Conference on Structural Dynamics (2014), pp. 1783–1788Google Scholar
  156. 156.
    T. Beckenbauer, et al, Influence of the road surface texture on the tyre road noise, Research program 03.293R95M, German Ministry of Transport and German Highway Research Institute (2001)Google Scholar
  157. 157.
    Y. Miyama et al., Development of tire eigenvalue control technology for optimization of road noise spectrum. Trans. JSAE 40(5), 1133–11138 (2009)Google Scholar
  158. 158.
    T. Saguchi, Influence of the rolling condition given to the natural frequency of a tire, in JSAE Symposium, No. 9840829 (1998)Google Scholar
  159. 159.
    B. Mills, J.W. Dunn, The mechanical mobility of rolling tyres, in Proceedings of Vibration and Noise in Motor Vehicles (IMechE C104/7), London, UK (1971), pp. 90–101Google Scholar
  160. 160.
    T. Ushijima, M. Takayama, Modal analysis of tire and system simulation, in SAE Paper, No. 880585 (1988)Google Scholar
  161. 161.
    E. Vinesse, Tyre vibration testing from modal analysis to dispersion relations, in Proceedings of ISATA 88, vol. 1, Paper No. 88048 (1988)Google Scholar
  162. 162.
    F. Fahy, P. Cardonio, Sound and Structural Vibration, 2nd edn. (Academic Press, New York, 2007)Google Scholar
  163. 163.

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mechanical Science and Engineering, School of Advanced EngineeringKogakuin UniversityHachiojiJapan

Personalised recommendations