On the interaction of exponential non-viscous damping with symmetric nonlinearities

Journal of Sound and Vibration

Volumn 314, Issue 1-2, 2008, Pages 1-11

  Sieber, J ^a   Wagg, D J ^b   Adhikari, S ^c  

^a UNIVERSITY OF ABERDEEN   (United Kingdom)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONTROL NONLINEARITIES; DAMPING; FREQUENCY RESPONSE; MATHEMATICAL MODELS; OSCILLATORS (MECHANICAL);

EXPONENTIAL DAMPING MODEL; NON-VISCOUS DAMPING PARAMETER; NONLINEAR OSCILLATORS;

ASYMPTOTIC STABILITY;

EID: 42049103853     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2007.12.017     Document Type: Article

References (32)

1. J.W.S. Rayleigh, Theory of Sound (two volumes), Dover Publications, 1877.
2. Cremer L., and Heckl M. Structure-borne Sound (1973), Springer, Berlin, Germany
3. Wagner N., and Adhikari S. Symmetric state-space formulation for a class of non-viscously damped systems. AIAA Journal 41 (2003) 951-956
4. McTavish D.J., and Hughes P.C. Modelling of linear viscoelastic space structures. Transactions of ASME, Journal of Vibration and Acoustics 115 (1993) 103-110
5. Muravyov A., and Hutton S.G. Closed-form solutions and the eigenvalue problem for vibration of discrete viscoelastic systems. Transactions of ASME, Journal of Applied Mechanics 64 (1997) 684-691
6. Muravyov A., and Hutton S.G. Free vibration response characteristics of a simple elasto-hereditary system. Transactions of ASME, Journal of Vibration and Acoustics 120 (1998) 628-632
7. Biot M.A. Variational principles in irreversible thermodynamics with application to viscoelasticity. Physical Review 97 (1955) 1463-1469
8. M.A. Biot, Linear thermodynamics and the mechanics of solids, Proceedings of the Third U. S. National Congress on Applied Mechanics, 1958, pp. 1-18.
9. Golla D.F., and Hughes P.C. Dynamics of viscoelastic structures-a time domain finite element formulation. Journal of Applied Mechanics, ASME 52 (1985) 897-906
10. Bishop R.E.D., and Price W.G. An investigation into the linear theory of ship response to waves. Journal of Sound and Vibration 62 (1979) 353-363
11. Bagley R.L., and Torvik P.J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures. AIAA Journal 21 (1983) 741-748
12. Sheu L.J., Chen H.K., Chen J.H., and Tam L.M. Chaotic dynamics of the fractionally damped Duffing equation. Chaos Solitons & Fractals 32 (2007) 1459-1468
13. P.J. Torvik, R.L. Bagley, Fractional derivatives in the description of damping: materials and phenomena, The Role of Damping in Vibration and Noise Control (1987) 125-135.
14. Gaul L., Klein P., and Kemple S. Damping description involving fractional operators. Mechanical Systems and Signal Processing 5 (1991) 81-88
15. Maia N.M.M., Silva J.M.M., and Ribeiro A.M.R. On a general model for damping. Journal of Sound and Vibration 218 (1998) 749-767
16. Papoulia K.D., and Kelly J.M. Visco-hyperelastic model for filled rubbers used in vibration isolation. Journal of Engineering Materials and Technology-Transactions of the ASME 119 (1997) 292-297
17. Koh C.G., and Kelly J.M. Application of fractional derivatives to seismic analysis of base-isolated models. Earthquake Engineering and Structural Dynamics 19 (1990) 229-241
18. Adhikari S. Dynamics of non-viscously damped linear systems ASCE. Journal of Engineering Mechanics 128 (2002) 328-339
19. Woodhouse J. Linear damping models for structural vibration. Journal of Sound and Vibration 215 (1998) 547-569
20. Adhikari S. Qualitative dynamic characteristics of a non-viscously damped oscillator. Proceedings of the Royal Society A 461 (2005) 2269-2288
21. S. Adhikari, Dynamic response characteristics of a non-viscously damped oscillator, Transactions of ASME, Journal of Applied Mechanics (2007), in press.
22. Adhikari S., and Woodhouse J. Identification of damping: part 1, viscous damping. Journal of Sound and Vibration 243 (2001) 43-61
23. Adhikari S., and Woodhouse J. Identification of damping: part 2, non-viscous damping. Journal of Sound and Vibration 243 (2001) 63-88
24. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer: New York, (1983).
25. Moon F.C. Chaotic Vibrations: An Introduction for Applied Scientists and Engineers (1987), Wiley, New York
26. Thompson J.M.T., and Stewart H.B. Nonlinear Dynamics and Chaos (2002), Wiley, Chichester
27. Nayfeh A.H., and Mook D.T. Nonlinear Oscillations (1979), Wiley, New York
28. Ravindra B., and Mallik A.K. Hard Duffing type vibration isolator with combined Coulomb and viscous damping. International Journal of Non-linear Mechanics 28 (1993) 427-440
29. Borowiec M., Litak G., and Syta A. Vibration of the Duffing oscillator: Effect of fractional damping. Shock and Vibration 14 (2007) 29-36
30. D.J. Wagg, S. Adhikari, On the dynamics of a Duffing oscillator with an exponential non-viscous damping model, in: B.H.V. Topping, G. Montero, R. Montenegro, (Eds.), Proceedings of the Eighth International Conference on Computational Structures Technology, Civil-Comp Press, UK, 2006.
31. E.J. Doedel, A.R. Champneys, T.F. Fairgrieve, Y.A. Kuznetsov, B. Sandstede, X. Wang, AUTO97, Continuation and bifurcation software for ordinary differential equations, Concordia University, 1998.
32. F. Schilder, RAUTO: running AUTO more efficiently, 2007. 〈http://www.dynamicalsystems.org/sw/sw/〉.