Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach

Probabilistic Engineering Mechanics

Volumn 26, Issue 1, 2011, Pages 101-108

  Cottone, Giulio ^a,b   Di Paola, Mario ^a   Butera, Salvatore ^a  

^a UNIVERSITY OF PALERMO   (Italy)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Characteristic function; Fractional calculus; Fractional differential equations; Nonlinear viscouselastic damper; Power law drift; Stochastic differential equations

Indexed keywords

CHARACTERISTIC FUNCTIONS; FRACTIONAL CALCULUS; FRACTIONAL DIFFERENTIAL EQUATIONS; NONLINEAR VISCOUSELASTIC DAMPER; POWER-LAW; STOCHASTIC DIFFERENTIAL EQUATIONS;

CALCULATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); MATHEMATICAL OPERATORS; MEASUREMENT THEORY; NONLINEAR SYSTEMS; STOCHASTIC SYSTEMS; WHITE NOISE;

NONLINEAR EQUATIONS;

EID: 77957750670     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.probengmech.2010.06.010     Document Type: Article

References (21)

1. M. Nicos Makris, and A.M. Jian Zhang Seismic response analysis of a highway overcrossing equipped with elastomeric bearings and fluid dampers J Struct Eng 130 2004 830
2. N. Makris Viscous heating of fluid dampers. I: small-amplitude motions J Eng Mech 124 11 1998 1210 1216 (Pubitemid 29041104)
3. N. Makris, G.F. Dargush, and M.C. Constantinou Dynamic analysis of viscoelastic-fluid dampers J Eng Mech 121 1995 1114
4. N. Makris, Y. Roussos, and A.S. Whittaker Viscous heating of fluid dampers. II: large-amplitude motions J Eng Mech 124 1998 1217
5. A. Bruckner, and Y.K. Lin Generalization of the equivalent linearization method for non-linear random vibration problems Int J Non-linear Mech. 22 3 1987 227 235 (Pubitemid 17636345)
6. C. Proppe, H.J. Pradlwarter, and G.I. Schuller Equivalent linearization and Monte Carlo simulation in stochastic dynamics Probabilistic Engineering Mech. 18 1 2003 1 15
7. J.B. Roberts, and P.D. Spanos Random vibration and statistical linearization 2003 Dover Publications
8. P.D. Spanos, and W.D. Iwan On the existence and uniqueness of solutions generated by equivalent linearization (for harmonic or Gaussian random excitation) Int J Non-Linear Mech. 13 2 1978 71 78
9. W.F. Wu, and Y.K. Lin Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations Int J Non-linear Mech. 19 4 1984 349 362
10. A. Masud, and L.A. Bergman Application of multi-scale finite element methods to the solution of the FokkerPlanck equation Comput Methods Appl Mech Eng 194 1216 2005 1513 1526
11. M. Grigoriu Stochastic calculus: application in science and engineering 2002 Birkuser
12. Iwankiewicz R, Nielsen SRK. Advanced methods in stochastic dynamics of non-linear systems. Aalborg tekniske Universitetsforlag; 1999.
13. G.I. Schueller A state-of-the-art report on computational stochastic mechanics Probabilistic Engineering Mech. 12 4 1997 197 321
14. K. Sobczyk Stochastic differential equations with applications to physics and engineering Mathematics and its applications vol. 40 2002 Kluwer Academic Publishers
15. I. Podlubny Fractional differential equations: an introduction to fractional derivatives 1999 Academic Press
16. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional integrals and derivatives: theory and applications 1993 Gordon and Breach New York (NY) Transl. from the Russian
17. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and applications of fractional differential equations 2006 Elsevier Science Ltd.
18. A.V. Chechkin, V.Y. Gonchar, J. Klafter, R. Metzler, and L.V. Tanatarov Lvy flights in a steep potential well J Statist Phys 115 2004 1505 1535
19. C. Lubich Convolution quadrature and discretized operational calculus. I Numer Math 52 2 1988 129 145
20. M.B. Allen, and E.L. Isaacson Numerical analysis for applied science 1997 Wiley Interscience Publication
21. B. Fornberg Calculation of weights in finite difference formulas SIAM Rev 40 1998 685 691