A fast method for computing convolutions with structural Green’s functions: application to tyre dynamic contact problems
Keywords:
dynamic contact, tyre, road, Green’s function, convolution, identificationAbstract
Tyre/road contact is the main source of car noise at speeds greater than 50 km/h. In this context, we have developed a new approach for modelling tyre vibrations and contact with rigid road surfaces during rolling. For tyres, a periodic model is used to compute Green’s functions. The response of tyres can, thus, be modelled over a large frequency range. Then, a fast convolution and a new contact model are developed and examples of computations of contact stress are given for real road textures. Spectra of stress for different tyre velocities are also computed.
Downloads
References
Andersson P. B. U. & Kropp, W. (2008). Time domain contact model for tyre/road interaction
including nonlinear contact stiffness due to small-scale roughness. Journal of Sound and
Vibration, 318, 296–312.
Brinkmeier, M., Nackenhorst, U., Petersen, S., & vonEstorff, O. (2008). A finite element
approach for the simulation of tire rolling noise. Journal of Sound and Vibration, 309,
–39.
Duhamel, D. (2009). A recursive approach for the finite element computation of waveguides.
Journal of Sound and Vibration, 323, 163–172.
Duhamel, D., Erlicher, S., & Nguyen, H. H. (2011). A recursive finite element method for
computing tyre vibrations. European Journal of Computational Mechanics, 20, 9–27.
Hamet, J. F. (2001). Tire/road noise: Time domain Green’s function for the orthotropic plate
model. Acta acoustica united with Acustica, 87, 470–474.
Huang, S. C., & Soedel, W. (1987). Response of rotating rings to harmonic and periodic
loading and comparison with the inverted problem. Journal of Sound and Vibration, 118,
–270.
Larsson, K. (2002). Modelling of dynamic contact-exemplified on tire/road interaction (PhD
thesis). Chalmers University of Technology, Goteborg, Sweden.
McIntyre, M., Schumacher, R., & Woodhouse, J. (1983). On the oscillations of musical
instruments. Journal of the Acoustical Society of America, 74, 1325–1345.
Meftah, R. (2011). Une approche par formalisme de Green réduit pour le calcul des structures en
contact dynamique: application au contact pneumatique chaussée (PhD thesis). Université
Paris-Est.
Nordborg, A. (2002). Rail noise generation due to nonlinear effects and parametric excitation.
Journal of the Acoustical Society of America, 111, 1772–1781.
Waki, Y., Mace, B. R., & Brennan, M. J. (2009). Free and forced vibrations of a tyre using a
wave/finite element approach. Journal of Sound and Vibration, 323, 737–756.
Wang, C., & Kim, J. (1996). New analysis method for a thin beam impacting against a stop
based on the full continuous mode. Journal of Sound and Vibation, 191, 809–823.
Wang, C., & Kim, J. (1997). The dynamic analysis of a thin beam impacting against a stop of
general three-dimensional geometry. Journal of Sound and Vibation, 203, 237–249.
Wullens, F. (2004). Excitation of tyre vibration due to tyre/road interaction (PhD thesis).
Chalmers University of Technology, Goteborg, Sweden.
Prediction and propagation of rolling noise. Technical report, Deufrako P2RN project, 2009.