On simulation of a bistable system with fractional damping in the presence of stochastic coherence resonance

Nonlinear Dynamics

Volumn 77, Issue 3, 2014, Pages 681-686

  Litak, Grzegorz ^a   Borowiec, Marek ^a  

^a LUBLIN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Fractional derivative; Nonlinear dynamics; Stochastic process

Indexed keywords

DAMPING; DYNAMICAL SYSTEMS; DYNAMICS; MAGNETIC RESONANCE; RANDOM PROCESSES;

BISTABLE SYSTEM; COHERENCE RESONANCE; CRITICAL VALUE; DAMPING ENHANCEMENT; FRACTIONAL DERIVATIVES; RANDOM EXCITATIONS; STOCHASTIC FORCES; STOCHASTIC RESONANCES;

STOCHASTIC SYSTEMS;

EID: 84905086674     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-014-1330-4     Document Type: Article

References (26)

1. Rossikhin, Y.A.; Shitikova, M.V.: Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results. Appl. Mech. Rev. 63, 010801 (2010)
2. Bagley, R.L.; Torvik, P.J.: Fractional calculus: A different approach to the analysis of viscoelastically damped structures. AIAA J. 21, 741-748 (1983)
3. Adolfsson, K.; Enelund, M.: Fractional derivative viscoelasticity at large deformations. Nonlinear Dyn. 33, 301-321 (2003)
4. Adolfsson, K.; Enelund, M.; Olsson, P.: On the fractional order model of viscoelasticity. Mech. Time Depend. Mater. 9, 15-34 (2005) (Pubitemid 41202455)
5. Müller, S.; Kästner, M.; Brummund, J.; Ulbricht, V.: On the numerical handling of fractional viscoelastic material models in a FE analysis. Comput. Mech. 51, 999-1012 (2013)
6. Sieber, J.; Wagg, D.J.; Adhikari, S.: On the interaction of exponential non-viscous damping with symmetric nonlinearities. J. Sound Vibr. 314, 1-11 (2008)
7. Ruzziconi, L.; Litak, G.; Lenci, S.: Nonlinear oscillations, transition to chaos and escape in the Duffing system with non-classical damping. J. Vibroeng. 13, 22-38 (2011)
8. Cao, J.; Ma, C.; Jiang, Z.; Liu, S.: Nonlinear dynamic analysis of fractional order rub-impact rotor system. Commun. Nonlin. Sci. Numer. Simul. 16, 1443-1463 (2011)
9. Cao, J.; Xue, S.; Lin, J.; Chen, Y.: Nonlinear dynamic analysis of a cracked rotor-bearing system with fractional order damping. J. Comput. Nonlinear Dyn. 8, 031008 (2013)
10. Zhu, W.Q.; Huang, Z.L.: Stochastic Hopf bifurcation of quasi-nonintegrable Hamiltonian systems. Int. J. Nonlinear Mech. 34, 437-447 (1999) (Pubitemid 128396187)
11. Ni, F.; Xu, W.; Fang, T.; Yue, X.L.: Stochastic period-doubling bifurcation analysis of a Rössler system with a bounded random parameter. Chin. Phys. B 19, 010510 (2010)
12. Gammaitoni, L.; Hanggi, P.; Jung, P.; Marchesoni, F.: Stochastic resonance. Rev. Mod. Phys. 70, 223 (1998) (Pubitemid 128022013)
13. Pikovsky, A.S.; Kurths, J.: Coherence resonance in a noise-driven excitable system Phys. Rev. Lett. 78, 775-778 (1997) (Pubitemid 127648034)
14. Padowan, J.; Sawicki, J.T.: Nonlinear vibrations of fractionally damped systems. Nonlinear Dyn. 16, 321-336 (1998) (Pubitemid 128513984)
15. Borowiec, M.; Litak, G.; Syta, A.: Vibration of the Duffing oscillator: effect of fractional damping. Shock Vibr. 14, 29 (2007)
16. Shen, Y.J.; Yang, S.P.; Xing, H.J.; Gao, G.S.: Primary resonance of Duffing oscillator with fractional-order derivative. Commun. Nonlinear Sci. Numer. Simul. 17, 3092-3100 (2012)
17. Machado, J.A.T.; Silvia, M.F.; Barbosa, R.S.; Jesus, I.S.; Reis, C.M.; Marcos, M.G.; Galhano, A.F.: Some applications of fractional calculus in engineering. Math. Probl. Eng. 2010, 639801 (2010)
18. Yang, J.H.; Zhu, H.: Vibrational resonance in Duffing systems with fractional-order damping. Chaos 22, 013112 (2012)
19. Cao, J.; Ma, C.; Xie, H.; Jiang, Z.: Nonlinear dynamics of Duffing system with fractional order damping. J. Comput. Nonlinear Dyn. 5, 041012 (2010)
20. Chen, L.C.; Zhu, W.Q.: Stochastic jump and bifurcation of Duffing oscillator with fractional derivative damping under combined harmonic and white noise excitations. Int. J. Nonlinear Mech. 46, 1324-1329 (2011)
21. Hu, F.; Chen, L.C.; Zhu, W.Q.: Stationary response of strongly non-linear oscillator with fractional derivative damping under bounded noise excitation Int. J. Nonlinear Mech. 47, 1081-1087 (2012)
22. Petras, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Springer, Berlin (2011)
23. Naess, A.; Moe, V.: Efficient path integration method for nonlinear dynamic systems. Probalist. Eng. Mech. 15, 221-231 (2000) (Pubitemid 30558273)
24. Litak, G.; Borowiec, M.; Wiercigroch, M.: Phase locking and rotational motion of a parametric pendulum in noisy and chaotic conditions. Dyn. Syst. 23, 259-265 (2008)
25. Papoulis, A.; Pillai, S.U.: Probability, Random Variables, and Stochastic Processes, 4th edn. McGraw-Hill, Boston (2002)
26. Litak, G.; Friswell, M.I.; Adhikari, S.: Magnetopiezoelastic energy harvesting driven by random excitations. App. Phys. Lett. 96, 214103 (2010)