Utilizing nonlinear phenomena to locate grazing in the constrained motion of a cantilever beam

Nonlinear Dynamics

Volumn 57, Issue 3, 2009, Pages 335-349

  Dick, Andrew J ^a   Balachandran, Balakumar ^b   Yabuno, Hiroshi ^c   Numatsu, Masatoshi ^c   Hayashi, Keiichi ^c   Kuroda, Masaharu ^d   Ashida, Kiwamu ^d  

^a Rice University   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c UNIVERSITY OF TSUKUBA   (Japan)

^d NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

Author keywords

Cantilever beam; Grazing; Impact dynamics; Nonlinear oscillations

Indexed keywords

BEAM AXIS; CONSTRAINED MOTION; CONTACT FORCES; CONTACT SURFACE; DYNAMIC BEHAVIORS; EXPERIMENTAL METHODS; FLEXIBLE CANTILEVER BEAM; FUNDAMENTAL FREQUENCIES; GENERAL DYNAMICS; GRAZING; IMPACT DYNAMICS; IMPACTORS; MICRO-SCALES; NON-LINEAR PHENOMENA; NONLINEAR OSCILLATIONS; OFF-RESONANCE; OSCILLATING CANTILEVER; PERIOD DOUBLING; PHASE PORTRAIT; POINCARE; SEPARATION DISTANCES; SOFT IMPACT; SPECTRAL ANALYSIS;

CANTILEVER BEAMS; FREQUENCY RESPONSE; NANOCANTILEVERS; NUMERICAL METHODS; OSCILLATORS (MECHANICAL); PILE FOUNDATIONS; SPECTRUM ANALYSIS; SPECTRUM ANALYZERS;

ATOMIC FORCE MICROSCOPY;

EID: 68249156932     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-008-9445-0     Document Type: Article

References (29)

1. S.W. Shaw P.J. Holmes 1983 A periodically forced piecewise linear oscillator J. Sound Vib. 90 1 129 155
2. L.N. Virgin C.J. Begley 1999 Grazing bifurcations and basins of attraction in an impact-friction oscillator Physica D 130 43 57
3. J. Emans M. Wiercigroch A.M. Krivtsov 2005 Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam systems with impacts Chaos Solitons Fractals 23 1661 1670
4. W. Lin N. Qiao H. Yuying 2006 Bifurcations and chaos in a forced cantilever system with impacts J. Sound Vib. 296 4-5 1068 1078
5. S.L.T. de Souza M. Wiercigroch I.L. Caldas J.M. Balthazar 2008 Suppressing grazing chaos in impacting system by structural nonlinearity Chaos Solitons Fractals 38 864 869
6. M. Wiercigroch V.W.T. Sin 1998 Experimental study of a symmetrical piecewise base-excited oscillator J. Appl. Mech. 65 657 663
7. F. Peterka J. Vacik 1992 Transition to chaotic motion in mechanical systems with impacts J. Sound Vib. 154 1 95 115
8. M. Wiercigroch 1994 Bifurcation analysis of harmonically excited linear oscillator with clearance Chaos Solitons Fractals 4 2 297 303
9. A. Stensson A.B. Nordmark 1994 Experimental investigation of some consequences of low velocity impacts in the chaotic dynamics of a mechanical system Philos. Trans. R. Soc. Lond. 347 439 448
10. de Weger, J., Binks, D., van de Water, W., Molenaar, J.: The universal behavior of oscillators that undergo low velocity impacts. In: Proceedings of the International Conference on Control of Oscillations and Chaos, pp. 166-167. St. Petersburg, Russia, August 27-29, 1997
11. Long, X.-H., Balachandran, B.: Elastic structure excited by harmonic impactor motions: experimental and numerical investigations. In: Proceedings of Fifth EuroMech Nonlinear Dynamics Conference, No. 17-156, pp. 1-8, August 7-12, 2005
12. H. Dankowicz X. Zhao 2005 Local analysis of co-dimension-one and co-dimension-two grazing bifurcations in impact microactuators Physica D 202 238 257
13. K.D. Murphy T.M. Morrison 2002 Grazing instabilities and post-bifurcation behavior in an impacting string J. Acoust. Soc. Am. 111 2 884 892
14. J.P. Hunt D. Sarid 1998 Kinetics of lossy grazing impact oscillators Appl. Phys. Lett. 72 23 2969 2971
15. H. Dankowicz 2006 Nonlinear dynamics as an essential tool for non-destructive characterization of soft nanostructures using tapping-mode atomic force microscopy Philos. Trans. R. Soc. 364 3505 3520
16. J. de Weger W. van de Water J. Molenaar 2000 Grazing impact oscillations Phys. Rev. E 62 2 2030 2041
17. J. Molenaar J. de Weger W. van de Water 2001 Mapping of grazing-impact oscillators Nonlinearity 14 301 321
18. X. Zhao H. Dankowicz 2006 Control of impact microactuators for precise positioning J. Comput. Nonlinear Dyn. 1 65 70
19. N. Choi T. Uchihashi H. Nishijima T. Ishida W. Mizutani S. Akita Y. Nakayama M. Ishikawa H. Tokumoto 2000 Atomic force microscopy of single walled carbon nanotubes using carbon nanotube tip Jpn. J. Appl. Phys. 39 6B 3707 3710
20. S.D. Solares Y. Matsuda W.A. Goddard III 2005 Influence of the carbon nanotube probe tilt angle on the effective probe stiffness and image quality in tapping-mode atomic force microscopy J. Phys. Chem. 109 35 16658 16664
21. T.J. Anderson A.H. Nayfeh B. Balachandran 1996 Experimental verification of the importance of the nonlinear curvature in a response of a cantilever beam J. Vib. Acoust. 118 21 27
22. F. Peterka 1996 Bifurcations and transition phenomena in an impact oscillator Chaos Solitons Fractals 7 10 1635 1647
23. Pishkenari, H.N., Jalili, N., Alasty, A., Meghdari, A.: Nonlinear dynamic analysis and chaotic behavior in atomic force microscopy. In: Proceedings of the ASME IDETC/CIE, Long Beach, CA, September 24-28, 2005
24. B. Balachandran A.H. Nayfeh 1990 Nonlinear motions of beam-mass structure Nonlinear Dyn. 1 39 61
25. B. Balachandran 2003 Dynamics of an elastic structure excited by harmonic and aharmonic impactor motions J. Vib. Control 9 3-4 265 279
26. Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. Wiley, New York (1995)
27. Doedel, E., Kern'evez, J.: Auto: Software for continuation problems in ordinary differential equations. Technical report, California Institute of Technology, Pasadena, CA (1986)
28. Numatsu, M., Yabuno, H., Dick, A.J., Kuroda, M., Ashida, K., Balachandran, B.: Control of impact cantilever to keep constant magnitude of a specific frequency component. In: Proceedings of 2007 ASME IDETC/CIE, Las Vegas, NV, September 4-7, 2007
29. Dick, A.J., Solares, S.: Utilizing period-doubling bifurcations to locate grazing in atomic force microscopy. In: Proceedings of 6th EuroMech Nonlinear Dynamics Conference, St. Petersburg, Russia, June 30-July 4, 2008