메뉴 건너뛰기




Volumn 56, Issue 3, 2009, Pages 231-241

Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations

Author keywords

Combined harmonic and white noise excitations; First passage failure; Fractional derivative damping; Stochastic averaging method; Strongly nonlinear oscillator

Indexed keywords

COMBINED HARMONIC AND WHITE NOISE EXCITATIONS; FIRST PASSAGE FAILURE; FRACTIONAL DERIVATIVE DAMPING; STOCHASTIC AVERAGING METHOD; STRONGLY NONLINEAR OSCILLATOR;

EID: 63949084398     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-008-9395-6     Document Type: Article
Times cited : (59)

References (37)
  • 4
    • 0020765202 scopus 로고
    • A theoretical basis for the application of fractional calculus to viscoelasticity
    • R.L. Bagley P.J. Torvik 1983 A theoretical basis for the application of fractional calculus to viscoelasticity J. Rheol. 27 201 210
    • (1983) J. Rheol. , vol.27 , pp. 201-210
    • Bagley, R.L.1    Torvik, P.J.2
  • 5
    • 0020751558 scopus 로고
    • Fractional calculus-a different approach to the analysis of viscoelastically damped structures
    • R.L. Bagley P.J. Torvik 1983 Fractional calculus-a different approach to the analysis of viscoelastically damped structures AIAA J. 21 741 748
    • (1983) AIAA J. , vol.21 , pp. 741-748
    • Bagley, R.L.1    Torvik, P.J.2
  • 6
    • 0022076968 scopus 로고
    • Fractional calculus in the transient analysis of viscoelastically damped structures
    • R.L. Bagley P.J. Torvik 1985 Fractional calculus in the transient analysis of viscoelastically damped structures AIAA J. 23 6 918 925
    • (1985) AIAA J. , vol.23 , Issue.6 , pp. 918-925
    • Bagley, R.L.1    Torvik, P.J.2
  • 7
    • 0025387251 scopus 로고
    • Application of fractional derivatives to seismic analysis of base-isolated models
    • C.G. Koh J.M. Kelly 1990 Application of fractional derivatives to seismic analysis of base-isolated models Earthq. Eng. Struct. Dyn. 19 229 241
    • (1990) Earthq. Eng. Struct. Dyn. , vol.19 , pp. 229-241
    • Koh, C.G.1    Kelly, J.M.2
  • 8
    • 0026613651 scopus 로고
    • Spring-viscous damper systems of combined seismic and vibration isolation
    • N. Makris M.C. Constantinou 1992 Spring-viscous damper systems of combined seismic and vibration isolation Earthq. Eng. Struct. Dyn. 21 649 664
    • (1992) Earthq. Eng. Struct. Dyn. , vol.21 , pp. 649-664
    • Makris, N.1    Constantinou, M.C.2
  • 9
    • 0000400568 scopus 로고
    • Modeling of viscoelastic dampers for structural applications
    • K.L. Shen T.T. Soong 1995 Modeling of viscoelastic dampers for structural applications ASCE J. Eng. Mech. 121 694 701
    • (1995) ASCE J. Eng. Mech. , vol.121 , pp. 694-701
    • Shen, K.L.1    Soong, T.T.2
  • 10
    • 0030575463 scopus 로고    scopus 로고
    • Analysis of four-parameter fractional derivative model of real solid materials
    • T. Pritz 1996 Analysis of four-parameter fractional derivative model of real solid materials J. Sound Vib. 195 103 115
    • (1996) J. Sound Vib. , vol.195 , pp. 103-115
    • Pritz, T.1
  • 11
    • 0031191268 scopus 로고    scopus 로고
    • Visco-hyperelastic model for filled rubbers used in vibration isolation
    • K.D. Papoulia J.M. Kelly 1997 Visco-hyperelastic model for filled rubbers used in vibration isolation ASME J. Eng. Mater. Technol. 119 292 297
    • (1997) ASME J. Eng. Mater. Technol. , vol.119 , pp. 292-297
    • Papoulia, K.D.1    Kelly, J.M.2
  • 12
    • 0029369995 scopus 로고
    • Analysis of nonlinear free vibrations of suspension bridges
    • Y.A. Rossikhin M.V. Shitikova 1995 Analysis of nonlinear free vibrations of suspension bridges J. Sound Vib. 186 369 393
    • (1995) J. Sound Vib. , vol.186 , pp. 369-393
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 13
    • 0030867045 scopus 로고    scopus 로고
    • Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids
    • Y.A. Rossikhin M.V. Shitikova 1997 Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids Appl. Mech. Rev. 50 15 67
    • (1997) Appl. Mech. Rev. , vol.50 , pp. 15-67
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 14
    • 0034024993 scopus 로고    scopus 로고
    • Analysis of nonlinear vibrations of a two-degree-of-freedom mechanical system with damping modeled by a fractional derivative
    • Y.A. Rossikhin M.V. Shitikova 2000 Analysis of nonlinear vibrations of a two-degree-of-freedom mechanical system with damping modeled by a fractional derivative J. Eng. Math. 37 343 362
    • (2000) J. Eng. Math. , vol.37 , pp. 343-362
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 15
    • 30344479191 scopus 로고    scopus 로고
    • Analysis of free non-linear vibrations of a viscoelastic plate under the condition of different internal resonances
    • Y.A. Rossikhin M.V. Shitikova 2006 Analysis of free non-linear vibrations of a viscoelastic plate under the condition of different internal resonances Int. J. Non-Linear Mech. 41 313 325
    • (2006) Int. J. Non-Linear Mech. , vol.41 , pp. 313-325
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 16
    • 0032141482 scopus 로고    scopus 로고
    • Nonlinear vibrations of fractionally damped systems
    • J. Padovan J.T. Sawicki 1998 Nonlinear vibrations of fractionally damped systems Nonlinear Dyn. 16 321 336
    • (1998) Nonlinear Dyn. , vol.16 , pp. 321-336
    • Padovan, J.1    Sawicki, J.T.2
  • 17
    • 0033502032 scopus 로고    scopus 로고
    • Fractional calculus approach to dynamic problems of viscoelastic materials
    • N. Shimizu W. Zhang 1999 Fractional calculus approach to dynamic problems of viscoelastic materials JSME Int. J. Ser. C 42 825 837
    • (1999) JSME Int. J. Ser. C , vol.42 , pp. 825-837
    • Shimizu, N.1    Zhang, W.2
  • 18
    • 0036650866 scopus 로고    scopus 로고
    • Fractional calculus via functional calculus: Theory and applications
    • S. Kempfle I. Schafer H. Beyer 2002 Fractional calculus via functional calculus: theory and applications Nonlinear Dyn. 29 99 127
    • (2002) Nonlinear Dyn. , vol.29 , pp. 99-127
    • Kempfle, S.1    Schafer, I.2    Beyer, H.3
  • 19
    • 15544369618 scopus 로고    scopus 로고
    • Impulse responses of fractional damped system
    • I. Schafer S. Kempfle 2004 Impulse responses of fractional damped system Nonlinear Dyn. 38 61 68
    • (2004) Nonlinear Dyn. , vol.38 , pp. 61-68
    • Schafer, I.1    Kempfle, S.2
  • 20
    • 33845466254 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractionally damped Duffing equation
    • L.J. Sheu H.K. Chen J.H. Chen L.M. Tam 2007 Chaotic dynamics of the fractionally damped Duffing equation Chaos Solitons Fractals 32 1459 1468
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 1459-1468
    • Sheu, L.J.1    Chen, H.K.2    Chen, J.H.3    Tam, L.M.4
  • 21
    • 34548530905 scopus 로고    scopus 로고
    • Chaotic dynamics of the fractionally damped van del Pol equation
    • J.H. Chen W.C. Chen 2008 Chaotic dynamics of the fractionally damped van del Pol equation Chaos Solitons Fractals 35 188 198
    • (2008) Chaos Solitons Fractals , vol.35 , pp. 188-198
    • Chen, J.H.1    Chen, W.C.2
  • 22
    • 0010970550 scopus 로고
    • Impulse response function of an oscillator with fractional derivative in damping description
    • L. Gaul P. Klein S. Kemple 1989 Impulse response function of an oscillator with fractional derivative in damping description Mech. Res. Commun. 16 5 4447 4472
    • (1989) Mech. Res. Commun. , vol.16 , Issue.5 , pp. 4447-4472
    • Gaul, L.1    Klein, P.2    Kemple, S.3
  • 24
    • 0033471671 scopus 로고    scopus 로고
    • A comparison of numerical methods applied to a fractional model of damping materials
    • A. Shokooh L. Suarez 1999 A comparison of numerical methods applied to a fractional model of damping materials J. Vib. Control 5 331 354
    • (1999) J. Vib. Control , vol.5 , pp. 331-354
    • Shokooh, A.1    Suarez, L.2
  • 25
    • 0042026660 scopus 로고    scopus 로고
    • A numerical method for fractional integral with application
    • Z.Y. Zhu G.G. Li C.J. Cheng 2003 A numerical method for fractional integral with application Appl. Math. Mech. 24 373 384
    • (2003) Appl. Math. Mech. , vol.24 , pp. 373-384
    • Zhu, Z.Y.1    Li, G.G.2    Cheng, C.J.3
  • 26
    • 0003001893 scopus 로고    scopus 로고
    • An eigenvector expansion method for the solution of motion containing fractional derivatives
    • L. Suarez A. Shokooh 1997 An eigenvector expansion method for the solution of motion containing fractional derivatives ASME J. App. Mech. 64 629 635
    • (1997) ASME J. App. Mech. , vol.64 , pp. 629-635
    • Suarez, L.1    Shokooh, A.2
  • 27
    • 0034889708 scopus 로고    scopus 로고
    • Dynamical stability of viscoelastic column with fractional derivative constitutive relation
    • G.G. Li Z.Y. Zhu C.J. Cheng 2001 Dynamical stability of viscoelastic column with fractional derivative constitutive relation Appl. Math. Mech. 22 294 303
    • (2001) Appl. Math. Mech. , vol.22 , pp. 294-303
    • Li, G.G.1    Zhu, Z.Y.2    Cheng, C.J.3
  • 29
    • 15544373277 scopus 로고    scopus 로고
    • Averaging oscillations with small fractional damping and delayed terms
    • P. Wahi A. Chatterjee 2004 Averaging oscillations with small fractional damping and delayed terms Nonlinear Dyn. 38 3 22
    • (2004) Nonlinear Dyn. , vol.38 , pp. 3-22
    • Wahi, P.1    Chatterjee, A.2
  • 30
    • 0000725994 scopus 로고    scopus 로고
    • Random vibration of systems with frequency-dependent parameters or fractional derivatives
    • P.D. Spanos B.A. Zeldin 1997 Random vibration of systems with frequency-dependent parameters or fractional derivatives ASCE J. Eng. Mech. 123 290 292
    • (1997) ASCE J. Eng. Mech. , vol.123 , pp. 290-292
    • Spanos, P.D.1    Zeldin, B.A.2
  • 31
    • 33750605555 scopus 로고    scopus 로고
    • Tuned mass damper with fractional derivative damping
    • F. Rüdinger 2006 Tuned mass damper with fractional derivative damping Eng. Struct. 28 1774 1779
    • (2006) Eng. Struct. , vol.28 , pp. 1774-1779
    • Rüdinger, F.1
  • 32
    • 85100989863 scopus 로고    scopus 로고
    • An analytical scheme for stochastic dynamic systems containing fractional derivatives
    • Las Vegas, NV
    • Agrawal, O.P.: An analytical scheme for stochastic dynamic systems containing fractional derivatives. In: Proceedings of the 1999 ASME Design Engineering Technical Conferences, pp. 12-15. Las Vegas, NV (1999)
    • (1999) Proceedings of the 1999 ASME Design Engineering Technical Conferences , pp. 12-15
    • Agrawal, O.P.1
  • 33
    • 0036660797 scopus 로고    scopus 로고
    • Stochastic analysis of a 1-D system with fractional damping of order 1/2
    • O.P. Agrawal 2002 Stochastic analysis of a 1-D system with fractional damping of order 1/2 J. Vib. Acoust. 124 454 460
    • (2002) J. Vib. Acoust. , vol.124 , pp. 454-460
    • Agrawal, O.P.1
  • 34
    • 13244251229 scopus 로고    scopus 로고
    • Analytical solution for stochastic response of a fractionally damped beam
    • O.P. Agrawal 2004 Analytical solution for stochastic response of a fractionally damped beam J. Vib. Acoust. 126 561 566
    • (2004) J. Vib. Acoust. , vol.126 , pp. 561-566
    • Agrawal, O.P.1
  • 35
    • 4544343478 scopus 로고    scopus 로고
    • Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative
    • K. Ye L. Li J.X. Tang 2003 Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative Earthq. Eng. Eng. Vib. 2003 2 133 139
    • (2003) Earthq. Eng. Eng. Vib. , vol.2003 , Issue.2 , pp. 133-139
    • Ye, K.1    Li, L.2    Tang, J.X.3
  • 36
    • 0028466109 scopus 로고
    • Averaging method using generalized harmonic functions for strongly non-linear oscillators
    • Z. Xu Y.K. Chung 1994 Averaging method using generalized harmonic functions for strongly non-linear oscillators J. Sound Vib. 174 563 576
    • (1994) J. Sound Vib. , vol.174 , pp. 563-576
    • Xu, Z.1    Chung, Y.K.2
  • 37
    • 0000182826 scopus 로고
    • On the averaging principle for Itô stochastic differential equations
    • (in Russian)
    • R.Z. Khasminskii 1968 On the averaging principle for Itô stochastic differential equations Kibernetika 3 260 279 (in Russian)
    • (1968) Kibernetika , vol.3 , pp. 260-279
    • Khasminskii, R.Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.