Open Access
Issue
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
Page(s) 1541 - 1579
DOI https://doi.org/10.1051/m2an/2024052
Published online 10 September 2024
  1. L.C. Evans, Partial Differential Equations, 2nd edition. American Mathematical Society (1996). [Google Scholar]
  2. S. Larsson and V. Thomee, Partial Differential Equations with Numerical Methods, 1st edition. Springer, Berlin, Heidelberg (2009). [Google Scholar]
  3. K.L. Johnson, Contact Mechanics. Cambridge University Press (1985). [Google Scholar]
  4. I.G. Goryacheva, Contact Mechanics in Tribology. Springer Science & Business Media (1998). [CrossRef] [Google Scholar]
  5. J.J. Kalker, On the rolling contact of two elastic bodies in the presence of dry friction. Dissertation, TH Delft, Delft (1967). [Google Scholar]
  6. J.J. Kalker, Three-Dimensional Elastic Bodies in Rolling Contact. Springer, Dordrecht (1990). [CrossRef] [Google Scholar]
  7. M. Guiggiani, The Science of Vehicle Dynamics, 2nd edition. Springer International, Cham, Switzerland (2018). [CrossRef] [Google Scholar]
  8. H.B. Pacejka, Tire and Vehicle Dynamics, 3rd edition. Elsevier/BH, Amsterdam (2012). [Google Scholar]
  9. F. Frendo and F. Bucchi, “Brush model” for the analysis of flat belt transmissions in steady-state conditions, in Mechanism and Machine Theory. Vol. 143. Elseiver (2020) 103653. [CrossRef] [Google Scholar]
  10. F. Frendo and F. Bucchi, Enhanced brush model for the mechanics of power transmission in flat belt drives under steady-state conditions: effect of belt elasticity, in Mechanism and Machine Theory. Vol. 153x. Elseiver (2020) 103998. [CrossRef] [Google Scholar]
  11. F. Bucchi and F. Frendo, Validation of the brush model for the analysis of flat belt transmissions in steady-state conditions by finite element simulation, in Mechanism and Machine Theory. Vol. 167. Elseiver (2022) 104556. [CrossRef] [Google Scholar]
  12. F. Marques, P. Flores, J.C. Pimenta Claro and H.M. Lankarani, A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dyn. 86 (2016) 1407–1443. [CrossRef] [Google Scholar]
  13. F. Marques, P. Flores, J.C. Pimenta Claro and H.M. Lankarani, Modeling and analysis of friction including rolling effects in multibody dynamics: a review. Multibody Syst. Dyn. 45 (2019) 223–244. [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Romano, F. Timpone, F. Bruzelius and B. Jacobson, Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction. Meccanica 57 (2022) 165–191. [CrossRef] [MathSciNet] [Google Scholar]
  15. L. Romano, F. Timpone, F. Bruzelius and B. Jacobson, Rolling, tilting and spinning spherical wheels: analytical results using the brush theory, in Mechanism and Machine Theory Mechanism and Machine Theory. Vol. 167. Elseiver (2022) 104836. [CrossRef] [Google Scholar]
  16. L. Romano, Advanced Brush Tyre Modelling. SpringerBriefs in Applied Sciences. Springer, Cham (2022). [CrossRef] [Google Scholar]
  17. J. Deur, Modeling and analysis of longitudinal tire dynamics based on the LuGre friction model. IFAC Proc. Vol. 34 (2001) 91–96. [CrossRef] [Google Scholar]
  18. J. Deur, J. Asgari and D. Hrovat, A dynamic tire friction model for combined longitudinal and lateral motion, in Proceedings of the ASME-IMECE World Conference. ASME (2001). [Google Scholar]
  19. J. Deur, J. Asgari and D. Hrovat, A 3D brush-type dynamic tire friction model. Veh. Syst. Dyn. 42 (2004) 133–173. [CrossRef] [Google Scholar]
  20. J. Deur, V. Ivanovic, M. Troulis, C. Miano, D. Hrovat and J. Asgari, Extensions of the LuGre tyre friction model related to variable slip speed along the contact patch length. Veh. Syst. Dyn. 43 (2005) 508–524. [CrossRef] [Google Scholar]
  21. C. Canudas-de-Wit, P. Tsiotras, E. Velenis, M. Basset and G. Gissinger, Dynamic friction models for road/tire longitudinal interaction. Veh. Syst. Dyn. 39 (2003) 189–226. [CrossRef] [Google Scholar]
  22. P. Tsiotras, E. Velenis and M. Sorine, A LuGre tire friction model with exact aggregate dynamics. Veh. Syst. Dyn. 42 (2004) 195–210. [CrossRef] [Google Scholar]
  23. E. Velenis, P. Tsiotras, C. Canudas-de-Wit and M. Sorine, Dynamic tyre friction models for combined longitudinal and lateral vehicle motion. Veh. Syst. Dyn. 43 (2005) 3–29. [CrossRef] [Google Scholar]
  24. L. Romano, F. Bruzelius and B. Jacobson, An extended LuGre-brush tyre model for large camber angles and turning speeds. Veh. Syst. Dyn. 61 (2022) 1674–1706. [Google Scholar]
  25. F. Marques, L. Woliński, M. Wojtyra, P. Flores and H.M. Lankarani, An investigation of a novel LuGre-based friction force model. Mech. Mach. Theory 166 (2021) 104493. [CrossRef] [Google Scholar]
  26. J.J. Kalker, Transient phenomena in two elastic cylinders rolling over each other with dry friction. J. Appl. Mech. 37 (1970) 677–688. [CrossRef] [Google Scholar]
  27. J.J. Kalker, Transient rolling contact phenomena. ASLE Trans. 14 (1971) 177–184. [CrossRef] [Google Scholar]
  28. E.A.H. Vollebregt, User guide for CONTACT, Vollebregt & Kalker’s rolling and sliding contact model. Techical report TR09-03, version 13. [Google Scholar]
  29. E.A.H. Vollebregt and P. Wilders, FASTSIM2: a second-order accurate frictional rolling contact algorithm. Comput. Mech. 47 (2011) 105–116. [CrossRef] [Google Scholar]
  30. E.A.H. Vollebregt, S.D. Iwnicki, G. Xie and P. Shackelton, Assessing the accuracy of different simplified frictional rolling contact algorithms. Veh. Syst. Dyn. 50 (2012) 1–17. [CrossRef] [Google Scholar]
  31. E.A.H. Vollebregt, Numerical modeling of measured railway creep versus creep-force curves with CONTACT. Wear 314 (2014) 87–95. [CrossRef] [Google Scholar]
  32. L. Romano, F. Bruzelius and B. Jacobson, Transient tyre models with a flexible carcass. Veh. Syst. Dyn. 62 (2024) 1268–1307. [CrossRef] [Google Scholar]
  33. L. Romano, M. Maglio and S. Bruni, Transient wheel-rail rolling contact theories. Tribol. Int. 186 (2023) 108600. [CrossRef] [Google Scholar]
  34. B. Cockburn, S. Hou and C.W. Shu, The Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case. Math. Comp. 54 (1990) 545–581. [MathSciNet] [Google Scholar]
  35. B. Cockburn, G.E. Karniadakis and C.W. Shu, Discontinuous Galerkin Methods – Theory, Computation and Applications. Vol. 11 of Lecture Notes in Computer Science and Engineering. Springer (2000). [CrossRef] [Google Scholar]
  36. B. Cockburn, S. Lin and C.W. Shu, TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. III. One-dimensional systems. J. Comput. Phys. 84 (1989) 90–113. [CrossRef] [MathSciNet] [Google Scholar]
  37. B. Cockburn and C.W. Shu, TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comp. 52 (1989) 411–435. [MathSciNet] [Google Scholar]
  38. D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, 1st edition. Springer Berlin, Heidelberg (2011). [Google Scholar]
  39. E. Burman, E. Ern and M.A. Fernández, Explicit Runge–Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems. SIAM J. Numer. Anal. 48 (2010) 2019–2042. [CrossRef] [MathSciNet] [Google Scholar]
  40. F.J. Massey, Abstract evolution equations and the mixed problem for symmetric hyperbolic systems. Trans. Am. Math. Soc. 168 (1972) 165–188. [CrossRef] [Google Scholar]
  41. T. Kato, Linear evolution equations of “hyperbolic” type. J. Fac. Sci. Univ. Tokyo 17 (1970) 241–258. [Google Scholar]
  42. T. Kato, Perturbation Theory for Linear Operators, 2nd edition. Springer Berlin, Heidelberg (1995). [CrossRef] [Google Scholar]
  43. A.E. Taylor, Introduction to Functional Analysis. Wiley, New York (1958). [Google Scholar]
  44. R.F. Curtain and H. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, 1st edition. Springer New York, NY (2012). [Google Scholar]
  45. R.F. Curtain and H. Zwart, Introduction to Infinite-Dimensional Systems Theory: A State-Space Approach, 1st edition. Springer, New York, NY (2020). [Google Scholar]
  46. H. Tanabe, Equations of Evolution, 1st edition. Pitman (1979). [Google Scholar]
  47. H. Tanabe, Functional Analytic Methods for Partial Differential Equations, 1st edition. CRC Press (1997). [Google Scholar]
  48. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, 1st edition. Springer New York, NY (1983). [Google Scholar]
  49. C. Bardos, Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels, théorèmes d’approximation application à l’équation de transport. Ann. Sci. Éc. Norm. Super. 4 (1970) 185–233. [CrossRef] [Google Scholar]
  50. H.O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier–Stokes Equations. Society for Industrial and Applied Mathematics (2004). [CrossRef] [Google Scholar]
  51. B. Gustafsson, H.O. Kreiss and J. Oliger, Time-Dependent Problems and Difference Methods, 2nd edition. Wiley, Pure and Applied Mathematics (2013). [CrossRef] [Google Scholar]
  52. S. Benzoni-Gavage and D. Serre, Multi-Dimensional Hyperbolic Partial Differential Equations: First-Order Systems and Applications, 1st edition. Oxford Academic (2006). [CrossRef] [Google Scholar]
  53. G. Crippa, C. Donadello and L.V. Spinolo, Initial-boundary value problems for continuity equations with BV coefficients. J. Math. App. 102 (2022) 79–98. [Google Scholar]
  54. C.W. Shu and S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes. J. Comput. Phys. 77 (19988) 439–471. [Google Scholar]
  55. M. Ciavarella and J. Barber, Influence of longitudinal creepage and wheel inertia on short-pitch corrugation: a resonance-free mechanism to explain the roaring rail phenomenon. Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol. 222 (2008) 171–181. [CrossRef] [Google Scholar]
  56. L. Afferrante and M. Ciavarella, Short-pitch rail corrugation: a possible resonance-free regime as a step forward to explain the “enigma”? Wear 266 (2009) 934–944. [CrossRef] [Google Scholar]
  57. L. Afferrante and M. Ciavarella, Short pitch corrugation of railway tracks with wooden or concrete sleepers: An enigma solved? Tribol. Int. 43 (2010) 610–622. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you