On the jump-up and jump-down frequencies of the Duffing oscillator

Journal of Sound and Vibration

Volumn 318, Issue 4-5, 2008, Pages 1250-1261

  Brennan, M J ^a   Kovacic, I ^b   Carrella, A ^a   Waters, T P ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; NUMERICAL METHODS; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES;

ANALYTICAL EXPRESSIONS; DEGREE OF NON-LINEARITY; DISPLACEMENT AMPLITUDES; EQUATION OF MOTION; HARMONIC BALANCE APPROACH; NON-DIMENSIONAL EXPRESSIONS; NUMERICAL INTEGRATIONS; PERTURBATION METHOD;

DAMPING;

EID: 55349122939     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2008.04.032     Document Type: Article

References (11)

1. A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations, Wiley, New York, 1979.
2. G. Duffing, Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung, Vieweg Braunschweig, 1918.
3. J. Kevorkian, J.D. Cole, Perturbation Methods in Applied Mathematics, Springer, New York, 1981.
4. K. Magnus, Vibrations, Blackie and Son, London, 1965.
5. K. Peleg, Frequency response of non-linear single degree-of-freedom systems, International Journal of Mechanical Science 21 (1979) 75-84.
6. A. Murata, Y. Kume, F. Hashimoto, Application of catastrophe theory to the forced vibration of a diaphragm air spring, Journal of Sound and Vibration 112 (1) (1987) 31-44.
7. M.I. Friswell, J.E.T. Penny, The accuracy of jump frequencies in series solutions of the response of a Duffing oscillator, Journal of Sound and Vibration 169 (2) (1994) 261-269.
8. K. Worden, On jump frequencies in the response of a Duffing oscillator, Journal of Sound and Vibration 198 (4) (1996) 522-525.
9. A. Carrella, Passive Vibration Isolators with High-Static-Low-Dynamic- Stiffness, PhD Thesis, University of Southampton, 2008.
10. P. Malatkar, A.H. Nayfeh, Calculation of the jump frequencies in the response of a s.d.o.f. non-linear systems, Journal of Sound and Vibration 254 (5) (2002) 1005-1011.
11. P. Hagedorn, Non-linear Oscillations ( Translated and edited by Wolfram Stadler), Clarendon Press, Oxford, 1981.