Abstract
We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduce a second-order absorber that is coupled with the plant through user-defined cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequency, we show the existence of a saturation phenomenon. As the forcing amplitude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitude of the indirectly excited mode (absorber) increases. We obtain an approximate solution to the governing equations using the method of multiple scales and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that the system exhibits complicated dynamics, such as Hopf bifurcations, intermittency, and chaotic responses.
Similar content being viewed by others
References
Sethna, P. R., 'Vibrations of dynamical systems with quadratic nonlinearities', Journal of Applied Mechanics 32, 1965, 576–582.
Nayfeh, A. H., Mook, D. T., and Marshall, L. R., 'Nonlinear coupling of pitch and roll modes in ship motion', Journal of Hydronautics 7, 1973, 145–152.
Haddow, A. G., Barr, A. D. S., and Mook, D. T., 'Theoretical and experimental study of modal interaction in a two degree-of-freedom structure', Journal of Sound and Vibration 97, 1984, 451–473.
Balachandran, B. and Nayfeh, A. H., 'Observations of modal interactions in resonantly forced beam-mass structures', Nonlinear Dynamics 2, 1991, 77–117.
Bajaj, A. K., Chang, S. I., and Johnson, J. M., 'Amplitude modulated dynamics of a resonantly excited autoparametric two degree-of-freedom system', Nonlinear Dynamics 5, 1994, 433–457.
Banerjee, B., Bajaj, A. K., and Davies, P., 'Resonant dynamics of an autoparametric system: A study using higher order averaging', International Journal of Non-Linear Mechanics 31, 1993, 21–39.
Oueini, S. S., Nayfeh, A. H., and Pratt, J. R., 'A nonlinear vibration absorber for flexible structures', Nonlinear Dynamics 15, 1998, 259–282.
Pratt, J. R., Oueini, S. S., and Nayfeh, A. H., 'A Terfenol-D nonlinear vibration absorber', Journal of Intelligent Material Systems and Structures, 1999, to appear.
Nayfeh, A. H., Perturbation Methods, Wiley, New York, 1973.
Nayfeh, A. H. and Balachandran, B., Applied Nonlinear Dynamics, Wiley, New York, 1995.
Seydel, R., Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos, Springer-Verlag, New York, 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oueini, S.S., Chin, CM. & Nayfeh, A.H. Dynamics of a Cubic Nonlinear Vibration Absorber. Nonlinear Dynamics 20, 283–295 (1999). https://doi.org/10.1023/A:1008358825502
Issue Date:
DOI: https://doi.org/10.1023/A:1008358825502