Dynamics of a small vibro-impact pile driver

Nonlinear Analysis: Real World Applications

Volumn 9, Issue 4, 2008, Pages 1361-1377

  Luo, G W ^a   Yao, H M ^a  

^a LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

Bifurcation; Chaos; Impact; Periodic motion; Vibration

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; FREQUENCY RESPONSE; MATHEMATICAL MODELS; PARAMETER ESTIMATION; THREE DIMENSIONAL;

PERIODIC MOTION; PILE DRIVER; TRANSITION CONDITIONS;

MOTION CONTROL;

EID: 43649104853     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.03.004     Document Type: Article

References (60)

1. Aidanpää J.O., and Gupta B.R. Periodic and chaotic behaviour of a threshold-limited two-degree- of-freedom system. J. Sound Vib. 165 2 (1993) 305-327
2. Bapat C.N. The general motion of an inclined impact damper with friction. J. Sound Vib. 184 3 (1995) 417-427
3. Budd C., Dux F., and Cliffe A. The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators. J. Sound Vib. 184 3 (1995) 475-502
4. Chatterjee S., and Mallik A.K. Bifurcations and chaos in autonomous self-excited oscillators with impact damping. J. Sound Vib. 191 4 (1996) 539-562
5. Cone K.M., and Zadoks R.I. A numerical study of an impact oscillator with the addition of dry friction. J. Sound Vib. 188 5 (1995) 659-683
6. Di Benardo M., Champneys A.R., and Budd C.J. Grazing, skipping and sliding: analysis of the non-smooth dynamics of the dc/dc buck converter. Nonlinearity 11 4 (1998) 858-890
7. Di Bernardo M., Feigin M.I., Hogan S.J., and Homer M.E. Local analysis of C-bifurcations in N-dimensional piecewise-smooth dynamical systems. Chaos, Solitons Fractals 10 11 (1999) 1881-1908
8. DiBernardo M., Johansson K.H., and Vasca F. Self-oscillations and sliding in relay feedback systems: symmetry and bifurcations. Int. J. Bifurcation Chaos 4 11 (2001) 1121-1140
9. Foale S., and Bishop S.R. Dynamical complexities of forced impacting systems. Philos. Trans. R. Soc. London 338 A (1992) 547-556
10. Halse C., Homer M., and Di Bernardo M. C-bifurcations and period-adding in one-dimensional piecewise- smooth maps. Chaos, Solitons Fractals 18 5 (2003) 953-976
11. Han P.R.S., and Luo A.C.J. Chaotic motion of a horizontal impact pair. J. Sound Vib. 181 2 (1995) 231-250
12. Heiman M.S., Bajaj A.K., and Sherman P.J. Periodic motions and bifurcations in dynamics of an inclined impact pair. J. Sound Vib. 124 1 (1988) 55-78
13. Hu H.Y. Controlling chaos of a periodically forced nonsmooth mechanical system. Acta Mech. Sinica 11 3 (1995) 251-258
14. Hu H.Y. Controlling chaos of a dynamical system with discontinuous vector field. Physica D 106 1 (1997) 1-8
15. Ivanov A.P. Stabilization of an impact oscillator near grazing incidence owing to resonance. J. Sound Vib. 162 3 (1993) 562-565
16. Ivanov A.P. Bifurcation in impact systems. Chaos, Solitons Fractals 7 10 (1996) 1615-1634
17. Kahraman A., and Singh R. Non-linear dynamics of a geared rotor-bearing system with multiple clearances. J. Sound Vib. 144 3 (1991) 469-506
18. Karpenko E.V., Wiercigroch M., Pavlovskaia E.E., and Cartmell M.P. Piecewise approximate analytical solutions for a Jeffcott rotor with a snubber ring. Int. J. Mech. Sci. 44 3 (2002) 475-488
19. Knudsen J., and Massih A.R. Dynamic stability of weakly damped oscillators with elastic impacts and wear. J. Sound Vib. 263 1 (2003) 175-204
20. Kozol J.E., and Brach R.M. Two-dimensional vibratory impact and chaos. J. Sound Vib. 148 2 (1991) 319-327
21. Kunert A., and Pfeiffer F. Stochastic model for rattling in gear-boxes. Nonlinear dynamics in engineering system. In: Schiehlen W. (Ed). Nonlinear Dynamics in Engineering Systems (1990), Springer, Berlin, Heidelberg 173-180
22. Lee J.Y., and Yan J.J. Control of impact oscillator. Chaos, Solitons Fractals 28 1 (2006) 136-142
23. Luo A.C.J. Period-doubling induced chaotic motion in the LR model of a horizontal impact oscillator. Chaos, Solitons Fractals 19 (2004) 823-839
24. Luo A.C.J. Grazing and chaos in a periodically forced, piecewise linear system. J. Vib. Acoust. 128 (2006) 29-34
25. Luo G.W. Period-doubling bifurcations and routes to chaos of the vibratory systems contacting stops. Phys. Lett. A 323 (2004) 210-217
26. Luo G.W. Hopf-flip bifurcations of vibratory systems with impacts. J. Nonlinear Anal. Real World Appl. 7 5 (2006) 1029-1041
27. Luo G.W. Dynamics of an impact-forming machine. Int. J. Mech. Sci. 48 11 (2006) 1295-1313
28. Luo A.C.J., and Chen L. Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts. Chaos, Solitons Fractals 24 2 (2005) 567-578
29. Luo G.W., and Xie J.H. Codimension two bifurcation of periodic vibro-impact and chaos of a dual component system. Phys. Lett. A 313 (2003) 267-273
30. Luo G.W., Yu J.N., Yao H.M., and Xie J.H. Periodic-impact motions and bifurcations of the vibratory system with a clearance. Chin. J. Mech. Eng. 42 (2006) 88-94
31. G.W. Luo, Y.L. Zhang, J.G. Zhang, Codimension two bifurcations of fixed points in a class of vibratory systems with rigid stops, J. Nonlinear Anal. Real World Appl. (2007), doi:101016/j.nonrwa.2006.07.003.
32. Mejaard J.P., and De Pater A.D. Railway vehicle systems dynamics and chaotic vibrations. Int. J. Non-Linear Mech. 24 1 (1989) 1-17
33. Mikhlin Y.V. Direct and inverse problems encountered in vibro-impact oscillations of a discrete system. J. Sound Vib. 216 (1998) 227-250
34. Murphy K.D., and Morrison T.M. Grazing instabilities and post-bifurcation behavior in an impacting string. J. Acoust. Soc. Am. 111 2 (2002) 884-892
35. Natsiavas S. Dynamics of multiple-degree-of-freedom oscillators with colliding components. J. Sound Vib. 165 3 (1993) 439-453
36. Nguyen D.T., Noah S.T., and Kettleborough C.F. Impact behaviour of an oscillator with limiting stops, part I: a parametric study. J. Sound Vib. 109 2 (1986) 293-307
37. Nordmark A.B. Non-periodic motion caused by grazing incidence in an impact oscillator. J. Sound Vib. 145 2 (1991) 279-297
38. Pavlovskaia E.E., Karpenko E.V., and Wiercigroch M. Non-linear dynamic interactions of a Jeffcott rotor with preloaded snubber ring. J. Sound Vib. 276 (2004) 361-379
39. Pavlovskaia E.E., Wiercigroch M., and Grebogi C. Two-dimensional map for impact oscillator with drift. Phys. Rev. E 70 (2004) 036201
40. Pavlovskaia E.E., Wiercigroch M., Woo K.C., and Rodger A.A. Modeling of ground moling dynamics by an impact oscillator with a frictional slider. Meccanica 38 (2003) 85-97
41. Peterka F., Kotera T., and Čipera S. Explanation of appearance and characteristics of intermittency chaos of the impact oscillator. Chaos, Solitons Fractals 19 5 (2004) 1251-1259
42. Peterka F., and Vacik J. Transition to chaotic motion in mechanical systems with impacts. J. Sound Vib. 154 (1992) 95-115
43. Peterka F., and Tondl A. Phenomena of subharmonic motions of oscillator with soft impacts. Chaos, Solitons Fractals 19 5 (2004) 1283-1290
44. Pi B.Q. Concrete and Piling Mechanism (1982), Chinese Architectural Industry Press, Beijing
45. Shaw S.W., and Holmes P.J. A periodically forced piecewise linear oscillator. J. Sound Vib. 90 1 (1983) 129-155
46. Shaw S.W., and Holmes P.J. Periodically forced linear oscillator with impacts: chaos and long-period motions. Phys. Rev. Lett. 51 (1983) 849-857
47. Shaw S.W., and Holmes P.J. A periodically forced impact oscillator with large dissipation. J. Appl. Mech. 50 (1983) 849-857
48. Shu Z.Z., and Shen X.Z. Theoretical analysis of complete stability and automatic vibration isolation of impacting and vibrating systems with double masses. Chin. J. Mech. Eng. 26 3 (1990) 50-57
49. deSouza S.L.T., and Caldas I.L. Calculation of Lyapunov exponents in systems with impacts. Chaos, Solitons Fractals 19 3 (2004) 569-579
50. Sung C.K., and Yu W.S. Dynamics of harmonically excited impact damper: bifurcations and chaotic motion. J. Sound Vib. 158 2 (1992) 317-329
51. Thompson J.M.T. Complex dynamics of compliant offshore structures. Proc. R. Soc. London A 387 (1983) 407-427
52. Wagg D.J. Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator. Chaos, Solitons Fractals 22 (2004) 541-548
53. Wagg D.J. Periodic sticking motion in a two-degree-of-freedom impact oscillator. Int. J. Non-Linear Mech. 40 8 (2005) 1076-1087
54. Wiercigroch M., and Sin V.T.W. Experimental study of base excited symmetrically piecewise linear oscillator. ASME J. Appl. Mech. 65 3 (1998) 657
55. Whiston G.S. Singularities in virbo-impact dynamics. J. Sound Vib. 152 3 (1992) 427-460
56. Wood L.A., and Byrne K.P. Analysis of a random repeated impact process. J. Sound Vib. 78 3 (1981) 329-345
57. Xie J.H. The mathematical model for the impact hammer and global bifurcations. Acta Mech. Sinica 29 4 (1997) 456-463
58. Yang Z.Z. A study on the dynamics of a small vibration-impact pile driver. Trans. Chin. Soc. Agric. Mach. 30 6 (1999) 36-40
59. Yang Z.Z. Optimization of impact position and simulation of small vibratory pile driver. J. Hydraul. Eng. 8 (1999) 72-76
60. Zeng J., and Hu S. Study on frictional impact and derailment for wheel and rail. J. Vib. Eng. 14 1 (2001) 1-6