메뉴 건너뛰기




Volumn 2010, Issue , 2010, Pages

On the selection and meaning of variable order operators for dynamic modeling

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84862843990     PISSN: 16879643     EISSN: 16879651     Source Type: Journal    
DOI: 10.1155/2010/846107     Document Type: Article
Times cited : (134)

References (28)
  • 1
    • 0346897985 scopus 로고    scopus 로고
    • Mechanics with variable-order differential operators
    • 10.1002/andp.200310032 MR2020716 ZBL1103.26301
    • Coimbra C. F. M., Mechanics with variable-order differential operators. Annalen der Physik 2003 12 11-12 692 703 10.1002/andp.200310032 MR2020716 ZBL1103.26301
    • (2003) Annalen der Physik , vol.12 , Issue.11-12 , pp. 692-703
    • Coimbra, C.F.M.1
  • 2
    • 10144243375 scopus 로고    scopus 로고
    • Control of damping oscillations by fractional differential operator with time-dependent order
    • DOI 10.1016/j.cma.2004.06.029, PII S0045782504002944
    • Ingman D., Suzdalnitsky J., Control of damping oscillations by fractional differential operator with time-dependent order. Computer Methods in Applied Mechanics and Engineering 2004 193 52 5585 5595 10.1016/j.cma.2004.06.029 MR2103155 ZBL1079.70020 (Pubitemid 39615630)
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , Issue.52 , pp. 5585-5595
    • Ingman, D.1    Suzdalnitsky, J.2
  • 3
    • 25444483399 scopus 로고    scopus 로고
    • The variable viscoelasticity oscillator
    • DOI 10.1002/andp.200410140
    • Soon C. M., Coimbra C. F. M., coimbra@hawaii.edu Kobayashi M. H., The variable viscoelasticity oscillator. Annalen der Physik 2005 14 6 378 389 2-s2.0-25444442673 10.1002/andp.200410140 ZBL1125.74316 (Pubitemid 41359363)
    • (2005) Annalen der Physik (Leipzig) , vol.14 , Issue.6 , pp. 378-389
    • Soon, C.M.1    Coimbra, C.F.M.2    Kobayashi, M.H.3
  • 4
    • 36249022993 scopus 로고    scopus 로고
    • San Diego, Calif, USA Academic Press Mathematics in Science and Engineering MR1658022
    • Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering MR1658022
    • (1999) Fractional Differential Equations , vol.198
    • Podlubny, I.1
  • 9
    • 0032162662 scopus 로고    scopus 로고
    • General solution of the particle momentum equation in unsteady Stokes flows
    • Coimbra C. F. M., Rangel R. H., General solution of the particle momentum equation in unsteady Stokes flows. Journal of Fluid Mechanics 1998 370 53 72 10.1017/S0022112098001967 MR1647206 ZBL0935.76018 (Pubitemid 128490023)
    • (1998) Journal of Fluid Mechanics , vol.370 , pp. 53-72
    • Coimbra, C.F.M.1    Rangel, R.H.2
  • 10
    • 0035448047 scopus 로고    scopus 로고
    • Spherical particle motion in harmonic Stokes flows
    • Coimbra C. F. M., Rangel R. H., Spherical particle motion in harmonic Stokes flows. AIAA Journal 2001 39 9 1673 1682 2-s2.0-0026792388 10.2514/2.1524 (Pubitemid 32866590)
    • (2001) AIAA Journal , vol.39 , Issue.9 , pp. 1673-1682
    • Coimbra, C.F.M.1    Rangel, R.H.2
  • 11
    • 0037174898 scopus 로고    scopus 로고
    • On the viscous motion of a small particle in a rotating cylinder
    • DOI 10.1017/S0022112002001829
    • Coimbra C. F. M., Kobayashi M. H., On the viscous motion of a small particle in a rotating cylinder. Journal of Fluid Mechanics 2002 469 257 286 10.1017/S0022112002001829 MR1932831 ZBL1043.76059 (Pubitemid 35225120)
    • (2002) Journal of Fluid Mechanics , vol.469 , pp. 257-286
    • Coimbra, C.F.M.1    Kobayashi, M.H.2
  • 12
    • 0141867815 scopus 로고    scopus 로고
    • On the dynamics of a spherical scaffold in rotating bioreactors
    • DOI 10.1002/bit.10778
    • Ramirez L. E. S., Lim E. A., Coimbra C. F. M., coimbra@hawaii.edu Kobayashi M. H., On the dynamics of a spherical scaffold in rotating bioreactors. Biotechnology and Bioengineering 2003 84 3 382 389 2-s2.0-34547210645 10.1002/bit.10778 (Pubitemid 37221539)
    • (2003) Biotechnology and Bioengineering , vol.84 , Issue.3 , pp. 382-389
    • Ramirez, L.E.S.1    Lim, E.A.2    Coimbra, C.F.M.3    Kobayashi, M.H.4
  • 13
    • 0020765202 scopus 로고
    • Theoretical Basis for The Application of Fractional Calculus to Viscoelasticity
    • DOI 10.1122/1.549724
    • Bagley R. L., Torvik P. J., A theoretical basis for the application of fractional calculus to viscoelasticity. Journal of Rheology 1983 27 3 201 210 2-s2.0-0020765202 10.1122/1.549724 ZBL0515.76012 (Pubitemid 13540406)
    • (1983) Journal of Rheology , vol.27 , Issue.3 , pp. 201-210
    • Bagley, R.L.1    Torvik, P.J.2
  • 14
    • 0022660581 scopus 로고
    • On The Fractional Calculus Model of Viscoelastic Behavior
    • DOI 10.1122/1.549887
    • Bagley R. L., Torvik P. J., On the fractional calculus model of viscoelastic behavior. Journal of Rheology 1986 30 1 133 155 2-s2.0-0022660581 10.1122/1.549887 ZBL0613.73034 (Pubitemid 16535851)
    • (1986) Journal of Rheology , vol.30 , Issue.1 , pp. 133-155
    • Bagley, R.L.1    Torvik, P.J.2
  • 15
    • 0001488637 scopus 로고
    • Fractal rheological models and fractional differential equations for viscoelastic behavior
    • 2-s2.0-0001488637 10.1007/BF00437306
    • Heymans N., Bauwens J.-C., Fractal rheological models and fractional differential equations for viscoelastic behavior. Rheologica Acta 1994 33 3 210 219 2-s2.0-0001488637 10.1007/BF00437306
    • (1994) Rheologica Acta , vol.33 , Issue.3 , pp. 210-219
    • Heymans, N.1    Bauwens, J.-C.2
  • 16
    • 0042884059 scopus 로고    scopus 로고
    • Five-parameter fractional derivative model for polymeric damping materials
    • 2-s2.0-0020805145 10.1016/S0022-460X(02)01530-4
    • Pritz T., Five-parameter fractional derivative model for polymeric damping materials. Journal of Sound and Vibration 2003 265 5 935 952 2-s2.0-0020805145 10.1016/S0022-460X(02)01530-4
    • (2003) Journal of Sound and Vibration , vol.265 , Issue.5 , pp. 935-952
    • Pritz, T.1
  • 17
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • 10.1016/S0370-1573(00)00070-3 MR1809268 ZBL0984.82032
    • Metzler R., Klafter J., The random walk's guide to anomalous diffusion: a fractional dynamics approach. Physics Reports 2000 339 1 1 77 10.1016/S0370-1573(00)00070-3 MR1809268 ZBL0984.82032
    • (2000) Physics Reports , vol.339 , Issue.1 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 18
    • 0032653954 scopus 로고    scopus 로고
    • Fractional-order systems and PIλDμ -controllers
    • 10.1109/9.739144 MR1666937
    • Podlubny I., Fractional-order systems and PIλDμ -controllers. IEEE Transactions on Automatic Control 1999 44 1 208 214 10.1109/9.739144 MR1666937
    • (1999) IEEE Transactions on Automatic Control , vol.44 , Issue.1 , pp. 208-214
    • Podlubny, I.1
  • 19
    • 0034206621 scopus 로고    scopus 로고
    • Constitutive dynamic-order model for nonlinear contact phenomena
    • 2-s2.0-0022774313 10.1115/1.1304916 ZBL1110.74493
    • Ingman D., qadov@tx.technion.ac.il Suzdalnitsky J., isosef@tx.technion. ac.il Zeifman M., zmicael@tx.technion.ac.il Constitutive dynamic-order model for nonlinear contact phenomena. Journal of Applied Mechanics 2000 67 2 383 390 2-s2.0-0022774313 10.1115/1.1304916 ZBL1110.74493
    • (2000) Journal of Applied Mechanics , vol.67 , Issue.2 , pp. 383-390
    • Ingman, D.1
  • 20
    • 23044492109 scopus 로고    scopus 로고
    • Application of differential operator with servo-order function in model of viscoelastic deformation process
    • DOI 10.1061/(ASCE)0733-9399(2005)131:7(763)
    • Ingman D., qadov@tx.technion.ac.il Suzdalnitsky J., iosef@tx.technion.ac. il Application of differential operator with servo-order function in model of viscoelastic deformation process. Journal of Engineering Mechanics 2005 131 7 763 767 2-s2.0-0021439912 10.1061/(ASCE)0733-9399(2005)131:7(763) (Pubitemid 41065463)
    • (2005) Journal of Engineering Mechanics , vol.131 , Issue.7 , pp. 763-767
    • Ingman, D.1    Suzdalnitsky, J.2
  • 21
    • 34547624283 scopus 로고    scopus 로고
    • A variable order constitutive relation for viscoelasticity
    • DOI 10.1002/andp.200710246
    • Ramirez L. E. S., Coimbra C. F. M., A variable order constitutive relation for viscoelasticity. Annalen der Physik 2007 16 7-8 543 552 10.1002/andp.200710246 MR2320863 ZBL1159.74008 (Pubitemid 47203902)
    • (2007) Annalen der Physik (Leipzig) , vol.16 , Issue.7-8 , pp. 543-552
    • Ramirez, L.E.S.1    Coimbra, C.F.M.2
  • 22
    • 45249108860 scopus 로고    scopus 로고
    • Response of viscoelastic plate to impact
    • 011010 2-s2.0-25444483399 10.1115/1.2731416
    • Ingman D., qadov@tx.technion.ac.il Suzdalnitsky J., iosef@tx.technion.ac. il Response of viscoelastic plate to impact. Journal of Vibration and Acoustics 2008 130 1 8 011010 2-s2.0-25444483399 10.1115/1.2731416
    • (2008) Journal of Vibration and Acoustics , vol.130 , Issue.1 , pp. 8
    • Ingman, D.1
  • 23
    • 84948882036 scopus 로고
    • Integration and differentiation to a variable fractional order
    • 10.1080/10652469308819027 MR1421643 ZBL0820.26003
    • Samko S. G., Ross B., Integration and differentiation to a variable fractional order. Integral Transforms and Special Functions 1993 1 4 277 300 10.1080/10652469308819027 MR1421643 ZBL0820.26003
    • (1993) Integral Transforms and Special Functions , vol.1 , Issue.4 , pp. 277-300
    • Samko, S.G.1    Ross, B.2
  • 24
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • DOI 10.1023/A:1016586905654, Fractional Order Calculus and Its Applications
    • Lorenzo C. F., Hartley T. T., Variable order and distributed order fractional operators. Nonlinear Dynamics 2002 29 1-4 57 98 10.1023/A: 1016586905654 MR1926468 ZBL1018.93007 (Pubitemid 34945393)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 25
    • 33244459920 scopus 로고    scopus 로고
    • Initialization, conceptualization, and application in the generalized fractional calculus
    • Cleveland, Ohio, USA Lewis Research Center, NASA
    • Lorenzo C. F., Hartley T. T., Initialization, conceptualization, and application in the generalized fractional calculus. NASA Technical Publication 1998 98-208415 Cleveland, Ohio, USA Lewis Research Center, NASA
    • (1998) NASA Technical Publication , Issue.98 , pp. 208415
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 26
    • 10644238068 scopus 로고    scopus 로고
    • Algorithms for the fractional calculus: A selection of numerical methods
    • DOI 10.1016/j.cma.2004.06.006, PII S0045782504002981
    • Diethelm K., Ford N. J., Freed A. D., Luchko Y., Algorithms for the fractional calculus: a selection of numerical methods. Computer Methods in Applied Mechanics and Engineering 2005 194 6-8 743 773 10.1016/j.cma.2004.06.006 MR2105648 ZBL1119.65352 (Pubitemid 39660444)
    • (2005) Computer Methods in Applied Mechanics and Engineering , vol.194 , Issue.6-8 , pp. 743-773
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3    Luchko, Yu.4
  • 27
    • 0030867045 scopus 로고    scopus 로고
    • Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids
    • Rossikhin Y. A., Shitikova M. V., Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Applied Mechanics Reviews 1997 50 1 15 67 2-s2.0-6144263023 (Pubitemid 127645586)
    • (1997) Applied Mechanics Reviews , vol.50 , Issue.1 , pp. 15-67
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 28
    • 0030736195 scopus 로고    scopus 로고
    • Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems
    • Rossikhin Y. A., Shitikova M. V., Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems. Acta Mechanica 1997 120 1-4 109 125 MR1436471 10.1007/BF01174319 ZBL0901.73030 (Pubitemid 127544483)
    • (1997) Acta Mechanica , vol.120 , pp. 109-125
    • Rossikhin, Y.A.1    Shitikova, M.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.