Dynamics of structures with wideband autoparametric vibration absorbers: Theory

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 460, Issue 2046, 2004, Pages 1547-1581

  Vyas, Ashwin ^a   Bajaj, Anil K ^a   Raman, Arvind ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Autoparametric system; Internal resonances; Vibration absorber

Indexed keywords

ABSORPTION; ARTICLE; ATTENUATION; DYNAMICS; ELASTICITY; EXCITATION; LINEAR SYSTEM; MATHEMATICAL COMPUTING; OSCILLATOR; SIMULATION; STEADY STATE; THEORY; VIBRATION;

EID: 2542602915     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2003.1204     Document Type: Article

References (30)

1. Agrawal, B. N. & Evan-Iwanowski, R. M. 1973 Resonances in nonstationary nonlinear, multi-degree-of-freedom systems. AIAA J. 11, 907-912.
2. Bajaj, A. K., Chang, S. I. & Johnson, J. 1994 Amplitude modulated dynamics of a resonantly excited autoparametric two degree-of-freedom system. Nonlin. Dynam. 5, 433-457.
3. Bajaj, A. K., Banerjee, B. & Davies, P. 1999 Nonstationary response in two degree-of-freedom nonlinear systems with 1-to-2 internal resonance. In Proc. IUTAM Symp. New Applications Nonlinear Chaotic Dynamics Mechanics, pp. 13-22. Dordrecht: Kluwer Academic.
4. Banerjee, B. & Bajaj, A. K. 1997 Amplitude modulated chaos in two degree-of-freedom systems with quadratic nonlinearities. Acta Mech. 124, 131-154.
5. Banerjee, B., Bajaj, A. K. & Davies, P. 1996 Resonant dynamics of an autoparametric system: a study using higher-order averaging. Int. J. Nonlin. Mech. 31, 21-39.
6. Cartmell, M. & Lawson, J. 1994 Performance enhancement of an autoparametric vibration absorber by means of computer control. J. Sound Vib. 177, 173-195.
7. Cuvalci, O. 2000 The effect of detuning parameters on the absorption region for a coupled system: a numerical and experimental study. J. Sound Vib. 229, 837-857.
8. Cuvalci, O. & Ertas, A. 1996 Pendulum as vibration absorber for flexible structures: experiments and theory. ASME J. Vib. Acoust. 118, 558-566.
9. Den Hartog, J. P. 1956 Mechanical vibrations. McGraw-Hill.
10. Doedel, E. 1986 AUTO: software for continuation and bifurcation problems in ordinary differential equations. Report, Department of Applied Mathematics, California Institute of Technology, Pasadena, CA, USA.
11. Evan-Iwanowski, R. M. 1976 Resonance oscillations in mechanical systems. Elsevier.
12. Haberman, R. 1979 Slowly varying jump and transition phenomena assosciated with algebraic bifurcation problems. SIAM J. Appl. Math. 37, 69-106.
13. Hatwal, H., Mallik, A. K. & Ghosh, A. 1982 Nonlinear vibrations of a harmonically excited autoparametric system. J. Sound Vib. 81, 153-164.
14. Hatwal, H., Mallik, A. K. & Ghosh, A. 1983a Forced nonlinear oscillations of an autoparametric system. Part 1. Periodic responses. ASME J. Appl. Mech. 50, 657-662.
15. Hatwal, H., Mallik, A. K. & Ghosh, A. 1983b Forced nonlinear oscillations of an autoparametric system. Part 2. Chaotic responses. ASME J. Appl. Mech. 50, 663-668.
16. Haxton, R. S. & Barr, A. D. S. 1972 The autoparametric vibration absorber. ASME J. Engng Indust. 94, 119-225.
17. Kevorkian, J. & Cole, J. D. 1996 Multiple scale and singular perturbation methods. Springer.
18. Khajepour, A. & Golnaraghi, M. F. 1997 Experimental control of flexible structures using nonlinear modal coupling. J. Intell. Mater. Syst. Struct. 8, 697-710.
19. Mitropolskii, V. A. 1965 Problems of the asymptotic theory of nonstationary vibrations. Jerusalem: Israel Program Scientific Translations Ltd.
20. Murdock, J. A. 1991 Perturbations: theory and methods. Wiley.
21. Nayfeh, A. H. & Mook, D. T. 1979 Nonlinear oscillations. Wiley.
22. Oueini, S. S., Nayfeh, A. H. & Pratt, J. R. 1999 A review of development and implementation of an active nonlinear vibration absorber. Ingen. Arch. 69, 585-620.
23. Pai, P. F. & Schulz, M. J. 2000 A refined nonlinear vibration absorber. Int. J. Mech. Sci. 42, 537-560.
24. Pai, P. F., Rommel, B. & Schulz, M. J. 2000 Non-linear vibration absorber using higher order internal resonances. J. Sound Vib. 234, 799-817.
25. Raman, A., Bajaj, A. K. & Davies, P. 1996 On the slow transition across instabilities in nonlinear dissipative systems. J. Sound Vib. 192, 835-865.
26. Shyu, I.-M., Mook, D. T. & Plaut, R. H. 1993 Whirling of a forced cantilever beam with static deflection. III. Passage through resonance. Nonlin. Dynam. 4, 461-481.
27. Vakakis, A., Nayfeh, T. & King, M. 1993 A multiple-scales analysis of nonlinear, localized modes in a cyclic periodic system. ASME J. Appl. Mech. 60, 388-397.
28. Vyas, A. & Bajaj, A. K. 2001 Dynamics of autoparametric vibration absorbers using multiple pendulums. J. Sound Vib. 246, 115-135.
29. Wiggins, S. 1990 Introduction to applied nonlinear dynamical systems and chaos. Springer.
30. Yabuno, H., Endo, Y. & Aoshima, N. 1999 Stabilization of 1/3 order subharmonic resonance using an autoparametric vibration absorber. ASME J. Vib. Acoust. 121, 309-315.