Delay effects in shimmy dynamics of wheels with stretched string-like tyres

European Journal of Mechanics, A/Solids

Volumn 28, Issue 3, 2009, Pages 516-525

  Takács, Dénes ^a   Orosz, Gábor ^b   Stépán, Gábor ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b University of California   (United States)

Author keywords

Delay; Hopf bifurcation; Relaxation length; Shimmy; Travelling wave solution

Indexed keywords

AIRCRAFT ENGINES; BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; CREEP; DEFORMATION; DIFFERENTIAL EQUATIONS; DYNAMICS; EQUATIONS OF MOTION; INTEGRODIFFERENTIAL EQUATIONS; NONLINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; VIBRATIONS (MECHANICAL); WAVE TRANSMISSION; WHEELS;

CONTACT LINES; CONTACT POINTS; CONTACT REGIONS; CREEP FORCES; DELAY; DELAY DIFFERENTIAL EQUATIONS; DELAY EFFECTS; GROUND CONTACTS; INTEGRO-DIFFERENTIAL EQUATION]; LABORATORY EXPERIMENTS; LATERAL DEFORMATIONS; LATERAL MOTIONS; LINEAR STABILITIES; MATHEMATICAL FORMS; MEMORY EFFECTS; NON-HOLONOMIC CONSTRAINTS; NUMERICAL SIMULATIONS; PARTIAL DIFFERENTIALS; QUASI-PERIODIC; RELAXATION LENGTH; SELF-EXCITED OSCILLATIONS; SELF-EXCITED VIBRATIONS; SHIMMY; SINGLE DEGREE OF FREEDOMS; STRETCHED STRINGS; TRAVELLING WAVE SOLUTION; ZERO VELOCITIES;

HOPF BIFURCATION;

EID: 60449098800     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2008.11.007     Document Type: Article

References (32)

1. Böhm F. Model for the radial tire for high frequent rolling-contact. Vehicle System Dynamics 18 Suppl. (1989) 72-83
2. Campbell S.A., and Bélair J. Analytical and symbolically-assisted investigations of Hopf bifurcations in delay-differential equations. Canadian Applied Mathematics Quarterly 3 2 (1995) 137-154
3. Chang Y.P., El-Gindy M., and Streit D.A. Literature survey of transient dynamic response tyre models. International Journal of Vehicle Design 34 4 (2004) 354-386
4. Collins R.L. Theories on mechanics of tyres and their application to shimmy analysis. Journal of Aircraft 8 4 (1971) 271-277
5. Engelborghs K., Luzyanina T., and Samaey G. dde-biftool v. 2.00: A Matlab package for bifurcation analysis of delay differential equations. Tech. Rep. TW-330, Department of Computer Science, Katholieke Universiteit Leuven, Belgium. http://www.cs.kuleuven.ac.be/~koen/delay/ddebiftool.shtml
6. Fratila D., and Darling J. Simulation of coupled car and caravan handling behaviour. Vehicle System Dynamics 26 6 (1996) 397-429
7. Goodwine B., and Stépán G. Controlling unstable rolling phenomena. Journal of Vibration and Control 6 1 (2000) 137-158
8. Goodwine B., and Zefran M. Feedback stabilization of a class of unstable nonholonomic systems. Journal of Dynamic Systems Measurement and Control, Transactions of the ASME 124 1 (2002) 221-230
9. Kalker J.J. Wheel rail rolling-contact theory. Wear 144 1-2 (1991) 243-261
10. Kármán T., and von Biot M.A. Mathematical Methods in Engineering (1940), McGraw-Hill Book Company, Inc., New York
11. Lax P.D., and Wendroff B. Systems of conservation laws. Communications on Pure and Applied Mathematics 13 2 (1960) 217-237
12. Le Saux C., Leine R.I., and Glocker C. Dynamics of a rolling disk in the presence of dry friction. Journal of Nonlinear Science 15 1 (2005) 27-61
13. Moreland W.J. The story of shimmy. Journal of the Aeronautical Sciences 21 12 (1954) 793-808
14. Orosz G. Hopf bifurcation calculations in delayed systems. Periodica Polytechnica 48 2 (2004) 189-200
15. Pacejka, H.B., 1966. The wheel shimmy phenomenon. Ph.D. thesis, Technical University of Delft, The Netherlands
16. Pacejka H.B. Tyre and Vehicle Dynamics (2002), Elsevier Butterworth-Heinemann, Oxford
17. Schiehlen W. Computational dynamics: theory and applications of multibody systems. European Journal of Mechanics A/Solids 25 4 (2006) 566-594
18. Schlippe, B., Dietrich, R., 1941. Das Flattern eines bepneuten Rades (Shimmying of a pneumatic wheel). In: Bericht 140 der Lilienthal-Gesellschaft für Luftfahrtforschung. pp. 35-45, 63-66. English translation is available in NACA Technical Memorandum 1365, pp. 125-166, 217-228, 1954
19. Schwab A.L., and Meijaard J.P. Dynamics of flexible multibody systems having rolling contact: application of the wheel element to the dynamics of road vehicles. Vehicle System Dynamics 33 Suppl. (1999) 338-349
20. Segel L. Force and moment response of pneumatic tires to lateral motion inputs. Journal of Engineering for Industry, Transactions of the ASME 88B 1 (1966) 37-44
21. Sharp R.S., Evangelou S., and Limebeer D.J.N. Advances in the modelling of motorcycle dynamics. Multibody System Dynamics 12 3 (2004) 251-283
22. Stépán G. Retarded Dynamical Systems: Stability and Characteristic Functions. Pitman Research Notes in Mathematics vol. 210 (1989), Longman, Essex, England
23. Stépán G. Chaotic motion of wheels. Vehicle System Dynamics 20 6 (1991) 341-351
24. Stépán G. Delay, nonlinear oscillations and shimmying wheels. In: Moon F.C. (Ed). Applications of Nonlinear and Chaotic Dynamics in Mechanics (1998), Kluwer Academic Publisher, Dordrecht 373-386
25. Stépán G. Appell-Gibbs equation for classical wheel shimmy - an energy view. Journal of Computational and Applied Mechanics 3 1 (2002) 85-92
26. Stépán G., and Haller G. Quasiperiodic oscillations in robot dynamics. Nonlinear Dynamics 8 4 (1995) 513-528
27. Szalai R., Stépán G., and Hogan S.J. Continuation of bifurcations in periodic delay-differential equations using characteristic matrices. SIAM Journal on Scientific Computing 28 4 (2006) 1301-1317
28. Takács, D., 2005. Dynamics of Rolling of Elastic Wheels. Master's thesis, Department of Applied Mechanics, Budapest University of Technology and Economics, Hungary
29. Takács, D., Stépán, G., 2007. Experiments on quasi-periodic wheel shimmy. In: Proceedings of IDETC/CIE 2007, ASME Las Vegas, CD-ROM paper no. DETC2007-35336, pp. 1-8
30. Takács D., Stépán G., and Hogan S.J. Isolated large amplitude periodic motions of towed rigid wheels. Nonlinear Dynamics 52 1-2 (2008) 27-34
31. Troger H., and Zeman K. A nonlinear-analysis of the generic types of loss of stability of the steady-state motion of a tractor-semitrailer. Vehicle System Dynamics 13 4 (1984) 161-172
32. Wickert J.A., and Mote Jr. C.D. Classical vibration analysis of axially moving continua. Journal of Applied Mechanics 57 3 (1990) 738-744