We present a numerical study for the suppression of self-excited vibrations represented by a Rayleigh oscillator using an impact viscous damper. A systematic approach based on a univariate search optimization method is used to determine the best design parameters for suppressing self-excited vibrations. The suggested system is found to be effective in suppressing this type of vibration. Optimum parameters for complete quenching of such vibrations are obtained. We investigate quasi-static as well as dynamic variations of the bifurcation parameter for both supercritical and subcritical Hopf bifurcation.
Anderson, K. and Hagedorn, P. , 1995, “On the energy dissipation in spacer dampers in bundled conductors of overhead transmission lines,”Journal of Sound and Vibration180 (4), 539-556 .
2.
Asfar, K. , 1989, “Quenching of self-excited vibrations,”ASME Journal of Vibration, Acoustics, Stress and Reliability in Design111, 130-133 .
3.
Bapat, C.N. , and Sankar, S. , 1984, “Single unit impact damper in free and forced vibration,”Journal of Sound and Vibration99 (1), 85-94 .
4.
Chapra, S. and Canale R. , 1998, Numerical Methods for Engineers, 3rd edition, McGraw-Hill, New York .
5.
Chatterjee, S. and Mallik, A. K. , 1996, “Bifurcations and chaos in autonomous self-excited oscillators with impact damping,”Journal of Sound and Vibration191 (4), 539-562 .
6.
Chatterjee, S. , Mallik, A. K. , and Ghosh, A. , 1996, “Impact dampers for controlling self-excited oscillation,”Journal of Sound and Vibration193 (5), 1003-1014 .
7.
Chen, L. and Semercigil, S. , 1993, “A beam-like damper for attenuating transient vibrations of light structures,”Journal of Sound and Vibration164 (1), 53-65 .
8.
Chunlin, S. , Chunru, X. , and Changsheng, J. , 2000, “Active control of self-excited vibrations for a high-speed rotating machinery,” in Proceedings of the 4th Asia-Pacific Conference on Control and Measurement, Beijing, China, China Aviation Industry Press, Vol. 383, pp. 288-293 .
9.
Cveticanin, L. , 1998, “Self-excited vibrations of the variable mass rotor/fluid system,”Journal of Sound and Vibration212 (4), 685-702 .
10.
Ema, S. and Marui, E. , 2000, “Suppression of chatter vibration of boring tools using impact dampers,”International Journal of Machine Tools and Manufacture40, 1141-1156 .
11.
Grubin, C. , 1956, “On the theory of acceleration damper,”ASME Journal of Applied Mechanics23, 373-378 .
12.
Hagedorn, P. , 1978, “Damping of self excited vibrations,”Zeitschrift fur Angewandte Mathematik und Physik29 (5), 815-821 .
13.
Jansen, J. D. and Van Den Steen, L. , 1995, “Active damping of self-excited torsional vibrations in oil well drill-strings,”Journal of Sound and Vibration179 (4), 647-668 .
14.
Jinhao Q. , Junji, T. , and Taekyu, K. , 2003, “Control of self-excited vibration of a rotor system with active gas bearings,”Journal of Vibration and Acoustics125, 328-334 .
15.
McMillan, J. , 1997, “A non-linear friction model for self-excited vibrations,”Journal of Sound and Vibration205 (3), 323-335 .
16.
Mansour, W. M. , 1972, “Quenching of limit cycles of a van der Pol oscillator,”Journal of Sound and Vibration25, 325-405 .
17.
Natsiavas, S. , 1993, “Vibration absorbers for a class of self-excited mechanical systems,”Journal of Applied Mechanics60, 382-387 .
18.
Nayfeh, A. H. , 1981, Introduction to Perturbation Techniques, Wiley, NewYork .
19.
Paget, L. , 1937, “Vibration in steam turbine buckets and damping by impacts,”Engineering143, 305-307 .
20.
Reed, H. H. , 1967, “Hanging chain impact dampers: A simple method of damping tall, flexible structures,” in Wind Effects on Buildings and Structures, Proceedings of Internal Research Seminar, Ottawa, Canada.
21.
Sadek, M. M. , 1972, “Impact dampers for controlling vibration in machine tools,”Machinery120, 152-161 .
22.
Sinha, A. , 1988, “Optimal vibration control of flexible structures for specified modal decay rates,”Journal of Sound and Vibration123, 185-188 .
23.
Tarng, Y. S. and Li, T. C. , 1994, “On-line monitoring and suppression of self-excited vibration in end milling,”Mechanical Systems and Signal Processing8 (5), 597-606 .
24.
Tondl, A. , 1975, “Quenching of self-excited vibrations; equilibrium aspects,”Journal of Sound and Vibration42, 251-260 .
25.
Yamuara, H. and Ono, K. , 1989, “Vibrationless starting and stopping control for a flexible arm,”Japanese Society of Mechanical Engineers (JSME), Series III32, 413-420 .
26.
Yigit, S. and Christoforou, A. P. , 1998, “Coupled torsional and bending vibrations of drillstrings subjected to impact with friction,”Journal of Sound and Vibration215 (1), 167-181 .
27.
Yoshitake, Y. and Sueoka, A. , 1994, “Quenching of self-excited vibrations by impact damper,”Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C60 (569), pp 50-56 .
