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Volumn 50, Issue 1, 1997, Pages 15-67

Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; ELASTICITY; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; MECHANICAL WAVES; PERTURBATION TECHNIQUES; SECOND HARMONIC GENERATION; SOLIDS; VIBRATIONS (MECHANICAL); VISCOELASTICITY;

EID: 0030867045     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.3101682     Document Type: Article
Times cited : (732)

References (173)
  • 1
    • 0039638036 scopus 로고
    • Note on wave propagation in linearly viscoelastic media
    • Achenbach JD and Reddy DP (1967), Note on wave propagation in linearly viscoelastic media, ZAngew Math Phys 18(1), 141-144.
    • (1967) Zangew Math Phys , vol.18 , Issue.1 , pp. 141-144
    • Achenbach, J.D.1    Reddy, D.P.2
  • 2
    • 3242843717 scopus 로고
    • Asymptotic expansion of an exponential function of fractional order (Russian)
    • Annin VD (1961), Asymptotic expansion of an exponential function of fractional order (Russian), Prikl Matem i Mekh 25(4), 796-798.
    • (1961) Prikl Matem I Mekh , vol.25 , Issue.4 , pp. 796-798
    • Annin, V.D.1
  • 3
    • 85008018985 scopus 로고
    • Uniaxial wave propagation in realistic viscoelastic materials
    • Arenz RJ (1964), Uniaxial wave propagation in realistic viscoelastic materials, J Appi Mech 31(1), 17-21.
    • (1964) J Appi Mech , vol.31 , Issue.1 , pp. 17-21
    • Arenz, R.J.1
  • 4
    • 84889553985 scopus 로고
    • Forced vibrations of a semi-infinite rod from a nonlinear hereditarily elastic material (Russian)
    • Astafyev VI and Meshkov SI (1970), Forced vibrations of a semi-infinite rod from a nonlinear hereditarily elastic material (Russian), Izv Akad Nauk SSSR. Mekh Tverdogo Tela (4), 93-98.
    • (1970) Izv Akad Nauk SSSR. Mekh Tverdogo Tela , Issue.4 , pp. 93-98
    • Astafyev, V.I.1    Meshkov, S.I.2
  • 6
    • 0343892055 scopus 로고
    • Fractional order state equations for the control of viscoelastically damped structures
    • DAB-i - DAB-26
    • Bagley RL and Calico RA (1989), Fractional order state equations for the control of viscoelastically damped structures, Proc of Damping '89 1, DAB-i - DAB-26.
    • (1989) Proc of Damping '89 , vol.1
    • Bagley, R.L.1    Calico, R.A.2
  • 7
    • 0000242586 scopus 로고
    • Generalized derivative model for an elastomer damper
    • Bagley RL and Torvik PJ (1979), Generalized derivative model for an elastomer damper, Shock Vibr Bull 49(2), 135-143.
    • (1979) Shock Vibr Bull , vol.49 , Issue.2 , pp. 135-143
    • Bagley, R.L.1    Torvik, P.J.2
  • 8
    • 0020765202 scopus 로고
    • Theoretical basis for the application of fractional calculus to viscoelasticity
    • Bagley RL and Torvik PJ (1983a), Theoretical basis for the application of fractional calculus to viscoelasticity, J Rheol 27(3), 201-210.
    • (1983) J Rheol , vol.27 , Issue.3 , pp. 201-210
    • Bagley, R.L.1    Torvik, P.J.2
  • 9
    • 0020751558 scopus 로고
    • Fractional calculus - A different approach to the analysis of viscoelastically damped structures
    • Bagley RL and Torvik PJ (1983b), Fractional calculus - A different approach to the analysis of viscoelastically damped structures, ALAA J 21(5), 741-748.
    • (1983) ALAA J , vol.21 , Issue.5 , pp. 741-748
    • Bagley, R.L.1    Torvik, P.J.2
  • 10
    • 0022076968 scopus 로고
    • Fractional calculus in the transient analysis of viscoelastically damped structures
    • Bagley RL and Torvik PJ (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
  • 11
    • 0022660581 scopus 로고
    • Fractional calculus model of viscoelastic behavior
    • Bagley RL and Torvik PJ (1986), Fractional calculus model of viscoelastic behavior, J Rheol 30(1), 133-155.
    • (1986) J Rheol , vol.30 , Issue.1 , pp. 133-155
    • Bagley, R.L.1    Torvik, P.J.2
  • 12
    • 0000511921 scopus 로고
    • Material damping: An introductory review of mathematical models, measures, and experimental techniques
    • Bert CW (1973), Material damping: An introductory review of mathematical models, measures, and experimental techniques. J Sound Vib 29(2), 129-153.
    • (1973) J Sound Vib , vol.29 , Issue.2 , pp. 129-153
    • Bert, C.W.1
  • 13
    • 0040328035 scopus 로고
    • Propagation of dynamic stresses in viscoelastic rods
    • Berry DS and Hunter SC (1956). Propagation of dynamic stresses in viscoelastic rods, J Mech Phys Solids 4(2), 72.
    • (1956) J Mech Phys Solids , vol.4 , Issue.2 , pp. 72
    • Berry, D.S.1    Hunter, S.C.2
  • 14
    • 0000480754 scopus 로고
    • Generalized Burgers equation for plane waves
    • Blackstock DT (1985), Generalized Burgers equation for plane waves, J Acoust Soc Am 77, 2050-2053.
    • (1985) J Acoust Soc Am , vol.77 , pp. 2050-2053
    • Blackstock, D.T.1
  • 16
    • 84889502697 scopus 로고
    • Determination of relaxation spectrum parameters during forced vibrations of a nonlinear hereditarily elastic oscillator (Russian)
    • Andrunakievich VA (ed), Shtiintsa, Kishinev
    • Blitshtein YuM, Meshkov SI, and Cheban VG (1970), Determination of relaxation spectrum parameters during forced vibrations of a nonlinear hereditarily elastic oscillator (Russian), AN Moldavskoi SSR Prikl Matem i Programmirovanie 3, Andrunakievich VA (ed), Shtiintsa, Kishinev, 3-12.
    • (1970) AN Moldavskoi SSR Prikl Matem I Programmirovanie , vol.3 , pp. 3-12
    • Blitshtein, Y.1    Meshkov, S.I.2    Cheban, V.G.3
  • 20
    • 85025238107 scopus 로고
    • Phenomenon of after-effect in solids (Russian)
    • Bronski AP (1941), Phenomenon of after-effect in solids (Russian), Prikl Mat i Mekh 5(1).
    • (1941) Prikl Mat I Mekh , vol.5 , Issue.1
    • Bronski, A.P.1
  • 21
    • 3042863742 scopus 로고
    • Effect of viscosity on the character of the propagation of a plane longitudinal shock wave
    • (Engl transl)
    • Burenin AA and Rossikhin YuA (1990), Effect of viscosity on the character of the propagation of a plane longitudinal shock wave, Appl Mech Tech Phys (Engl transl) 31(6), 807-810.
    • (1990) Appl Mech Tech Phys , vol.31 , Issue.6 , pp. 807-810
    • Burenin, A.A.1    Rossikhin, Y.2
  • 22
    • 0002217735 scopus 로고
    • Access to fractional differentiation via fractional difference quotients
    • Butzer PL and Westphal U (1975), Access to fractional differentiation via fractional difference quotients, Led Notes Math 457, 116-145.
    • (1975) Led Notes Math , vol.457 , pp. 116-145
    • Butzer, P.L.1    Westphal, U.2
  • 23
    • 84889548330 scopus 로고
    • About energy dissipation under periodic excitation of nonlinear hereditarily elastic systems (Russian)
    • Kuibushev State Univ, Kuibushev
    • Byrdin AP and Rossikhin YuA (1979), About energy dissipation under periodic excitation of nonlinear hereditarily elastic systems (Russian), Physics of Structure and Properties of Solids 3, Kuibushev State Univ, Kuibushev, 200-204.
    • (1979) Physics of Structure and Properties of Solids , vol.3 , pp. 200-204
    • Byrdin, A.P.1    Rossikhin, Y.2
  • 24
    • 84889535644 scopus 로고
    • Deformation waves in a nonlinear hereditarily elastic medium (Russian)
    • Byrdin AP and Rozovski MI (1984), Deformation waves in a nonlinear hereditarily elastic medium (Russian), Izv AN SSSR Mekh Tverdogo Tela (4), 100-104.
    • (1984) Izv AN SSSR Mekh Tverdogo Tela , Issue.4 , pp. 100-104
    • Byrdin, A.P.1    Rozovski, M.I.2
  • 25
    • 0017002154 scopus 로고
    • Vibrations of an infinite plate with a frequency independent Q
    • Caputo M (1976), Vibrations of an infinite plate with a frequency independent Q, J Acoust Soc Am 60(3), 634-639.
    • (1976) J Acoust Soc Am , vol.60 , Issue.3 , pp. 634-639
    • Caputo, M.1
  • 26
    • 0343892052 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent
    • Caputo M (1966), Linear models of dissipation whose Q is almost frequency independent, Annales di Geoflsica 19(4), 383-393.
    • (1966) Annales Di Geoflsica , vol.19 , Issue.4 , pp. 383-393
    • Caputo, M.1
  • 27
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent - II
    • Caputo M (1967), Linear models of dissipation whose Q is almost frequency independent - II, Geophys JR Astr Soc 13, 529-539.
    • (1967) Geophys JR Astr Soc , vol.13 , pp. 529-539
    • Caputo, M.1
  • 28
    • 0000930143 scopus 로고
    • New dissipation model based on memory mechanism
    • Caputo M and Mainardi F (1971), New dissipation model based on memory mechanism, Pure Appl Geophys 91, 134-147.
    • (1971) Pure Appl Geophys , vol.91 , pp. 134-147
    • Caputo, M.1    Mainardi, F.2
  • 30
    • 0344703525 scopus 로고
    • Stress waves in isotropic linear viscoelastic materials
    • Chu BT (1962), Stress waves in isotropic linear viscoelastic materials, J de Mec 1(4), 439-461.
    • (1962) J De Mec , vol.1 , Issue.4 , pp. 439-461
    • Chu, B.T.1
  • 31
    • 33748565282 scopus 로고
    • Dispersion and absorption in dielectrics
    • Cole KS and Cole RH (1941), Dispersion and absorption in dielectrics, J Chem Phys 9(4), 341-351.
    • (1941) J Chem Phys , vol.9 , Issue.4 , pp. 341-351
    • Cole, K.S.1    Cole, R.H.2
  • 32
    • 3242832315 scopus 로고
    • Singular kernels of heredity and relaxation and retardation spectra (Russian)
    • Darinsky BM and Meshkov SI (1969), Singular kernels of heredity and relaxation and retardation spectra (Russian), Izv Akad Nauk SSSR. Mekh Tverdogo Tela (3), 134-140.
    • (1969) Izv Akad Nauk SSSR. Mekh Tverdogo Tela , Issue.3 , pp. 134-140
    • Darinsky, B.M.1    Meshkov, S.I.2
  • 33
    • 0345263918 scopus 로고
    • Dielectric relaxation in glycerol, propylene glycole and n-propanol
    • Davidson DW and Cole RH (1951), Dielectric relaxation in glycerol, propylene glycole and n-propanol, J Chem Phys 19(12), 1484-1490.
    • (1951) J Chem Phys , vol.19 , Issue.12 , pp. 1484-1490
    • Davidson, D.W.1    Cole, R.H.2
  • 38
    • 3543078448 scopus 로고
    • Wave propagation in the linear theory of viscoelasticity
    • Fisher GMC and Gurtin ME (1965), Wave propagation in the linear theory of viscoelasticity, Quart Appl Math 23(3), 257-263.
    • (1965) Quart Appl Math , vol.23 , Issue.3 , pp. 257-263
    • Fisher, G.1    Gurtin, M.E.2
  • 39
    • 85116260103 scopus 로고
    • Improved solution techniques for the eigenstructure of fractional order systems
    • DAC-1 - DAC-19
    • Gaudrealt M and Bagley RL (1989), Improved solution techniques for the eigenstructure of fractional order systems, Proc of Damping '89 1, DAC-1 - DAC-19.
    • (1989) Proc of Damping '89 , vol.1
    • Gaudrealt, M.1    Bagley, R.L.2
  • 40
    • 0010970550 scopus 로고
    • Impulse response function of an oscillator with fractional derivative in damping description
    • Gaul L, Klein P, and Kempfle S (1989), Impulse response function of an oscillator with fractional derivative in damping description, Mech Res Comm 16(5), 297-305.
    • (1989) Mech Res Comm , vol.16 , Issue.5 , pp. 297-305
    • Gaul, L.1    Klein, P.2    Kempfle, S.3
  • 42
    • 0003149207 scopus 로고
    • Dynamics of viscoelastic solids treated by boundary element approaches in time domain
    • Gaul L and Schanz M (1994), Dynamics of viscoelastic solids treated by boundary element approaches in time domain, Eur J Mech, A Solids 13(4-suppl), 43-59.
    • (1994) Eur J Mech, a Solids , vol.13 , pp. 43-59
    • Gaul, L.1    Schanz, M.2
  • 44
    • 0345218900 scopus 로고
    • Method for analyzing experimental results obtained from elasto-viscous bodies
    • Gemant A (1936). Method for analyzing experimental results obtained from elasto-viscous bodies. Physics 7, 311-317.
    • (1936) Physics , vol.7 , pp. 311-317
    • Gemant, A.1
  • 45
    • 0001552054 scopus 로고
    • Fractional differentials
    • Gemant A (1938), Fractional differentials, Phil Mag 25, 540-549.
    • (1938) Phil Mag , vol.25 , pp. 540-549
    • Gemant, A.1
  • 46
    • 84889554540 scopus 로고
    • Investigation of roots of the characteristic equation connected with damping vibrations of elastic hereditary systems (Russian)
    • GS Pisarenko (ed), Naukova Dumka, Kiev
    • Gonsovski VL, Meshkov SI, and Rossikhin YuA (1972a), Investigation of roots of the characteristic equation connected with damping vibrations of elastic hereditary systems (Russian), Energy Scattering under Vibrations of Mechanical Systems, GS Pisarenko (ed), Naukova Dumka, Kiev, 101-107.
    • (1972) Energy Scattering under Vibrations of Mechanical Systems , pp. 101-107
    • Gonsovski, V.L.1    Meshkov, S.I.2    Rossikhin, Y.3
  • 47
    • 34250418148 scopus 로고
    • Impact of a viscoelastic bar on a rigid barrier (Russian)
    • Gonsovski VL, Meshkov SI, and Rossikhin YuA (1972b), Impact of a viscoelastic bar on a rigid barrier (Russian), Prikl Mekh 8(10), 71-76.
    • (1972) Prikl Mekh , vol.8 , Issue.10 , pp. 71-76
    • Gonsovski, V.L.1    Meshkov, S.I.2    Rossikhin, Y.3
  • 48
    • 6144258731 scopus 로고
    • Propagation of impulse load in a viscoelastic medium (Russian)
    • Ivlev DD (ed), Voronezh State Univ
    • Gonsovski VL and Rossikhin YuA (1972), Propagation of impulse load in a viscoelastic medium (Russian), Trans of Math Res Inst at Voronezh State Univ 6, Ivlev DD (ed), Voronezh State Univ, 63-66.
    • (1972) Trans of Math Res Inst at Voronezh State Univ , vol.6 , pp. 63-66
    • Gonsovski, V.L.1    Rossikhin, Y.2
  • 49
    • 6144257031 scopus 로고
    • Stress waves in a viscoelastic medium with a singular hereditary kernel
    • Engl transl
    • Gonsovski VL and Rossikhin YuA (1975), Stress waves in a viscoelastic medium with a singular hereditary kernel, J Appl Mech Tech Phvs (Engl transl) 14(4), 595-597.
    • (1975) J Appl Mech Tech Phvs , vol.14 , Issue.4 , pp. 595-597
    • Gonsovski, V.L.1    Rossikhin, Y.2
  • 51
    • 0000238491 scopus 로고
    • Ueber “begrenzte” Derivationen und deren Anwendung
    • Grünvald AK (1867), Ueber “begrenzte” Derivationen und deren Anwendung, Z angew Math und Phys 12,441-480.
    • (1867) Z Angew Math Und Phys , vol.12 , pp. 441-480
    • Grünvald, A.K.1
  • 52
    • 0001785405 scopus 로고
    • Analysis of a-dispersion in some polymer systems by the complex variables method
    • Havriliak S and Negami S (1966), Analysis of a-dispersion in some polymer systems by the complex variables method, J Polymer Sci (c) 14, 99-117.
    • (1966) J Polymer Sci (C) , vol.14 , pp. 99-117
    • Havriliak, S.1    Negami, S.2
  • 53
    • 0014595630 scopus 로고
    • Equivalence of dielectric and mechanical dispersions in some polymers; eg, poly (N-octyl methacrylate)
    • Havriliak S and Negami S (1969), Equivalence of dielectric and mechanical dispersions in some polymers; eg, poly (n-octyl methacrylate), Polymer 10(10), 859-872.
    • (1969) Polymer , vol.10 , Issue.10 , pp. 859-872
    • Havriliak, S.1    Negami, S.2
  • 54
    • 84889533398 scopus 로고
    • Evolution of the nonstationary wave in a hereditarily elastic medium (Russian)
    • Itskovich MA and Nigul UK (1984), Evolution of the nonstationary wave in a hereditarily elastic medium (Russian), Izv AN SSSR Mekharika Tverdogo Tela (1), 72-77.
    • (1984) Izv AN SSSR Mekharika Tverdogo Tela , Issue.1 , pp. 72-77
    • Itskovich, M.A.1    Nigul, U.K.2
  • 55
    • 84889513099 scopus 로고
    • Energy dissipation during vibrations of nonlinear hereditarily elastic systems (Russian)
    • Meshkov SI (ed), Kuibyshev State Univ, Kuibyshev
    • Karkovski Yul and Meshkov SI (1976a), Energy dissipation during vibrations of nonlinear hereditarily elastic systems (Russian), Mechanics of Deformable Solids 2, Meshkov SI (ed), Kuibyshev State Univ, Kuibyshev, 105-112.
    • (1976) Mechanics of Deformable Solids , vol.2 , pp. 105-112
    • Yul, K.1    Meshkov, S.I.2
  • 56
    • 84889552336 scopus 로고
    • Propagation of monoharmonic excitation in a unidimensional nonlinear hereditarily elastic medium (Russian)
    • Meshkov SI (ed), Kuibyshev State Univ, Kuibyshev
    • Karkovski Yul and Meshkov SI (1976b), Propagation of monoharmonic excitation in a unidimensional nonlinear hereditarily elastic medium (Russian), Mechanics of Deformable Solids 2, Meshkov SI (ed), Kuibyshev State Univ, Kuibyshev, 10-15.
    • (1976) Mechanics of Deformable Solids , vol.2 , pp. 10-15
    • Yul, K.1    Meshkov, S.I.2
  • 57
    • 0003223705 scopus 로고
    • Generalized fractional calculus and applications
    • Harlow; Longman Sci and Tech
    • Kiryakova V (1994), Generalized fractional calculus and applications, Pitman Research Notes in Mathematics 301, Harlow; Longman Sci and Tech.
    • (1994) Pitman Research Notes in Mathematics , vol.301
    • Kiryakova, V.1
  • 59
    • 0021440218 scopus 로고
    • Applications of fractional calculus to the theory of viscoelasticity
    • Koeller RC (1984), Applications of fractional calculus to the theory of viscoelasticity, Trans ASME JAppl Mech 51(2), 299-307.
    • (1984) Trans ASME Jappl Mech , vol.51 , Issue.2 , pp. 299-307
    • Koeller, R.C.1
  • 60
    • 0022700808 scopus 로고
    • Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics
    • Koeller RC (1986), Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics, Acta Mech 58(3-4), 251-264.
    • (1986) Acta Mech , vol.58 , Issue.3-4 , pp. 251-264
    • Koeller, R.C.1
  • 61
    • 0025387251 scopus 로고
    • Application of fractional derivatives to seismic response analysis of base-isolated models
    • Koh CG and Kelly JM (1990), Application of fractional derivatives to seismic response analysis of base-isolated models. Earthquake Eng Struct Dyn 19(2), 229-241.
    • (1990) Earthquake Eng Struct Dyn , vol.19 , Issue.2 , pp. 229-241
    • Koh, C.G.1    Kelly, J.M.2
  • 63
    • 84996179319 scopus 로고
    • Propagation of stress pulses in viscoelastic solids
    • Kolsky H (1956) Propagation of stress pulses in viscoelastic solids, Phil Mag H 1(8), 693-709.
    • (1956) Phil Mag H , vol.1 , Issue.8 , pp. 693-709
    • Kolsky, H.1
  • 64
    • 6144250803 scopus 로고
    • Question is how to choose the kernels when solving problems with due account for creep and relaxation (Russian)
    • Koltynov MA (1966), Question is how to choose the kernels when solving problems with due account for creep and relaxation (Russian), Mekh Polimerov (4), 483-497.
    • (1966) Mekh Polimerov , Issue.4 , pp. 483-497
    • Koltynov, M.A.1
  • 65
    • 84889558804 scopus 로고
    • Integro-operator method of investigating of damping properties of elastic hereditary systems (Russian)
    • Krush II (1965), Integro-operator method of investigating of damping properties of elastic hereditary systems (Russian), Izv Akad Nauk SSSR Mekhanika (6), 90-94.
    • (1965) Izv Akad Nauk SSSR Mekhanika , Issue.6 , pp. 90-94
    • Krush, I.I.1
  • 66
    • 84889509763 scopus 로고
    • Solution to the equation of nonlinear vibrations in the presence of elastic after-effect (Russian)
    • Krush II and Rozovski MI (1965), Solution to the equation of nonlinear vibrations in the presence of elastic after-effect (Russian), Izv Akad Nauk SSSR Mekhanika (5), 127-129.
    • (1965) Izv Akad Nauk SSSR Mekhanika , Issue.5 , pp. 127-129
    • Krush, I.I.1    Rozovski, M.I.2
  • 69
    • 6144229662 scopus 로고
    • Wave propagation in finite rods of viscoelastic material
    • Lee EH and Kanter I (1953), Wave propagation in finite rods of viscoelastic material, JAppl Phys 24(9), 1115-1122.
    • (1953) Jappl Phys , vol.24 , Issue.9 , pp. 1115-1122
    • Lee, E.H.1    Kanter, I.2
  • 70
    • 0001936243 scopus 로고
    • Theory of differentiation with an arbitrary indicator (Russian)
    • Letnikov AV (1868), Theory of differentiation with an arbitrary indicator (Russian), Matem Sbomik 3, 1-68.
    • (1868) Matem Sbomik , vol.3 , pp. 1-68
    • Letnikov, A.V.1
  • 71
    • 84889527990 scopus 로고
    • Recherches relatives a la théorie des intégrales de la forme i, x(X-u)p’f(u)du
    • p’f(u)du, Bull Sci Math Astron J 7, 233-238.
    • (1874) Bull Sci Math Astron J , vol.7 , pp. 233-238
    • Letnikov, A.V.1
  • 72
    • 0010071336 scopus 로고
    • Mémore sur quelques questions de géométrie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces questions
    • Liouville J (1832), Mémore sur quelques questions de géométrie et de mécanique, et sur un nouveau genre de calcul pour résoudre ces questions, Jl 'Ecole Roy Polytèch 13(21), 1-69.
    • (1832) Jl 'Ecole Roy Polytèch , vol.13 , Issue.21 , pp. 1-69
    • Liouville, J.1
  • 73
    • 0028427594 scopus 로고
    • Damping of beam vibrations by means of a thin constrained viscoelastic layer: Evaluation of a new theory
    • Mace M (1994), Damping of beam vibrations by means of a thin constrained viscoelastic layer: Evaluation of a new theory, J Sound Vib 172(5), 577-591.
    • (1994) J Sound Vib , vol.172 , Issue.5 , pp. 577-591
    • Mace, M.1
  • 74
    • 0010953458 scopus 로고
    • Special function arising in the time fractional diffusion-wave equation
    • 12-17 Aug 1994, Rusev P, Dimovski I, and Kiryakova V (eds)
    • Mainardi F and Tomirotti M (1994), Special function arising in the time fractional diffusion-wave equation, Proc of 1st Int Workshop Transform Methods and Special Functions, Sofia ‘94, 12-17 Aug 1994, Rusev P, Dimovski I, and Kiryakova V (eds), 171-183.
    • (1994) Proc of 1St Int Workshop Transform Methods and Special Functions, Sofia ‘94 , pp. 171-183
    • Mainardi, F.1    Tomirotti, M.2
  • 75
    • 0027625617 scopus 로고
    • Models of viscoelasticity with complex-order derivatives
    • Makris N and Constantinou MC (1993), Models of viscoelasticity with complex-order derivatives, J Eng Mech 119(20), 1453-1464.
    • (1993) J Eng Mech , vol.119 , Issue.20 , pp. 1453-1464
    • Makris, N.1    Constantinou, M.C.2
  • 76
    • 0004285788 scopus 로고
    • Fractional Calculus and Integral Transforms of Generalized Functions
    • San Francisco, London: Pitman
    • McBride AC (1979), Fractional Calculus and Integral Transforms of Generalized Functions, Research Notes in Mathematics 31, San Francisco, London: Pitman.
    • (1979) Research Notes in Mathematics , pp. 31
    • McBride, A.C.1
  • 77
    • 6144263023 scopus 로고
    • Dynamic mechanical studies of irradiated polyethylene
    • Merrill SJ, Sauer JA, and Woodward AE (1960), Dynamic mechanical studies of irradiated polyethylene, Polymer 1(3), 351.
    • (1960) Polymer , vol.1 , Issue.3 , pp. 351
    • Merrill, S.J.1    Sauer, J.A.2    Woodward, A.E.3
  • 78
    • 84889506829 scopus 로고
    • Description of internal friction in hereditary theory of elasticity with the help of the kernels having weak singularity (Russian)
    • Meshkov SI (1967), Description of internal friction in hereditary theory of elasticity with the help of the kernels having weak singularity (Russian), Zh Prikl Mekh Tekh Fiz (4), 147-151.
    • (1967) Zh Prikl Mekh Tekh Fiz , Issue.4 , pp. 147-151
    • Meshkov, S.I.1
  • 79
    • 84889533130 scopus 로고
    • Stationary regime of a hereditarily elastic oscillator (Russian)
    • Meshkov SI (1969), Stationary regime of a hereditarily elastic oscillator (Russian), Zh Prikl Mekh Tekh Fiz (5), 104-109.
    • (1969) Zh Prikl Mekh Tekh Fiz , Issue.5 , pp. 104-109
    • Meshkov, S.I.1
  • 80
    • 84889527741 scopus 로고
    • Integral representation of fractional exponential functions and their application to dynamic problems of linear viscoelasticity (Russian)
    • Meshkov SI (1970a), Integral representation of fractional exponential functions and their application to dynamic problems of linear viscoelasticity (Russian), Zh Prikl Mekh Tekh Fiz (91), 103-110.
    • (1970) Zh Prikl Mekh Tekh Fiz , Issue.91 , pp. 103-110
    • Meshkov, S.I.1
  • 81
    • 84889527898 scopus 로고
    • Stationary regime of a nonlinear hereditarily elastic oscillator (Russian)
    • Meshkov SI (1970b), Stationary regime of a nonlinear hereditarily elastic oscillator (Russian), Zh Prikl Mekh Tekh Fiz (3), 111-116.
    • (1970) Zh Prikl Mekh Tekh Fiz , Issue.3 , pp. 111-116
    • Meshkov, S.I.1
  • 83
    • 84889525145 scopus 로고
    • Account of volume relaxation by the method of internal friction (Russian)
    • Meshkov SI and Pachevskaya GN (1967), Account of volume relaxation by the method of internal friction (Russian), Zh Prikl Mekh Tekh Fiz (2), 80-82.
    • (1967) Zh Prikl Mekh Tekh Fiz , Issue.2 , pp. 80-82
    • Meshkov, S.I.1    Pachevskaya, G.N.2
  • 84
    • 3242841182 scopus 로고
    • Material behavior under large intensity of the dissipative processes (Russian)
    • Meshkov SI, Pachevskaya GN, and Postnikov VS (1967), Material behavior under large intensity of the dissipative processes (Russian), Fiz Khim Obrabotki Materialov (2), 135-137.
    • (1967) Fiz Khim Obrabotki Materialov , Issue.2 , pp. 135-137
    • Meshkov, S.I.1    Pachevskaya, G.N.2    Postnikov, V.S.3
  • 86
    • 3242833208 scopus 로고
    • Description of internal friction in terms of fractional exponential kernels (Russian)
    • Meshkov SI, Pachevskaya GN, and Shermergor TD (1966), Description of internal friction in terms of fractional exponential kernels (Russian), Zh Prikl Mekh Tekh Fiz (3), 103-106.
    • (1966) Zh Prikl Mekh Tekh Fiz , Issue.3 , pp. 103-106
    • Meshkov, S.I.1    Pachevskaya, G.N.2    Shermergor, T.D.3
  • 87
    • 3242829752 scopus 로고
    • Temperature dependence of internal friction of a standard linear solid under intensive damping (Russian)
    • Meshkov SI, Postnikov VS, and Shermergor TD (1964), Temperature dependence of internal friction of a standard linear solid under intensive damping (Russian), Izv Akad Nauk SSSR. Mekh Mashinostroenie (3), 90-95.
    • (1964) Izv Akad Nauk SSSR. Mekh Mashinostroenie , Issue.3 , pp. 90-95
    • Meshkov, S.I.1    Postnikov, V.S.2    Shermergor, T.D.3
  • 88
    • 77955674756 scopus 로고
    • Sound wave propagation in a hereditary elastic medium (Russian)
    • Meshkov SI and Rossikhin YuA (1968a), Sound wave propagation in a hereditary elastic medium (Russian), Zh Prikl Mekh Tekh Fiz (5), 89-93.
    • (1968) Zh Prikl Mekh Tekh Fiz , Issue.5 , pp. 89-93
    • Meshkov, S.I.1    Rossikhin, Y.2
  • 90
    • 6144278855 scopus 로고
    • Ssound wave propagation in a viscoelastic medium whose hereditary properties are determined by weakly singular kernels (Russian)
    • YuN Rabotnov (ed), Kishinev
    • Meshkov SI and Rossikhin YuA (1970), Ssound wave propagation in a viscoelastic medium whose hereditary properties are determined by weakly singular kernels (Russian), Waves in Inelastic Media, YuN Rabotnov (ed), Kishinev, 162-172.
    • (1970) Waves in Inelastic Media , pp. 162-172
    • Meshkov, S.I.1    Rossikhin, Y.2
  • 91
    • 84889531655 scopus 로고
    • Temperature dependence of damping coefficients for a dynamic system with a singular kernel of heredity (Russian)
    • Meshkov SI and Rossikhin YuA (1971), Temperature dependence of damping coefficients for a dynamic system with a singular kernel of heredity (Russian), Inzh Fiz Zh 21(2), 377.
    • (1971) Inzh Fiz Zh , vol.21 , Issue.2 , pp. 377
    • Meshkov, S.I.1    Rossikhin, Y.2
  • 92
    • 3242859172 scopus 로고
    • Temperature dependence of damping coefficients (Russian)
    • Meshkov SI and Shermergor TD (1965), Temperature dependence of damping coefficients (Russian), Izv Akad Nauk SSSR Mekhanika (5), 103-106.
    • (1965) Izv Akad Nauk SSSR Mekhanika , Issue.5 , pp. 103-106
    • Meshkov, S.I.1    Shermergor, T.D.2
  • 94
    • 0004691676 scopus 로고
    • Practical design and analysis of systems with fractional derivative materials and active control
    • 13-15 Feb 1991, San Diego CA, BCA-1 - BCA-28
    • Morgenthaler DR (1991), Practical design and analysis of systems with fractional derivative materials and active control, Proc of Damping ‘91 1,13-15 Feb 1991, San Diego CA, BCA-1 - BCA-28.
    • (1991) Proc of Damping ‘91 , vol.1
    • Morgenthaler, D.R.1
  • 95
    • 0001552518 scopus 로고
    • Wave propagation in rods of Voigt material and viscoelastic materials with three parameter models
    • Morrison JA (1956), Wave propagation in rods of Voigt material and viscoelastic materials with three parameter models. Quart Appl Math 14(2), 153-169.
    • (1956) Quart Appl Math , vol.14 , Issue.2 , pp. 153-169
    • Morrison, J.A.1
  • 96
    • 0001194043 scopus 로고
    • Theory of non-linear responses
    • Nakada O (1960), Theory of non-linear responses, J Phys Soc Japan 15(12), 2280-2288.
    • (1960) J Phys Soc Japan , vol.15 , Issue.12 , pp. 2280-2288
    • Nakada, O.1
  • 97
    • 84889518816 scopus 로고
    • Model of disturbance propagation in a vapor-fluid mixture (Russian)
    • Nakotjakov VE and Shreiber IR (1979), Model of disturbance propagation in a vapor-fluid mixture (Russian), Thermophysics of High Temperatures 17(4), 798-803.
    • (1979) Thermophysics of High Temperatures , vol.17 , Issue.4 , pp. 798-803
    • Nakotjakov, V.E.1    Shreiber, I.R.2
  • 98
    • 0000266650 scopus 로고
    • New general law of deformation
    • Nutting PG (1921), New general law of deformation, J Franklin Inst 191, 679-685.
    • (1921) J Franklin Inst , vol.191 , pp. 679-685
    • Nutting, P.G.1
  • 99
    • 0343020693 scopus 로고
    • General stress-strain-time formula
    • Nutting PG (1943), General stress-strain-time formula, J Franklin Inst 235, 513-524.
    • (1943) J Franklin Inst , vol.235 , pp. 513-524
    • Nutting, P.G.1
  • 100
    • 0001504447 scopus 로고
    • Deformation in relation to time, pressure and temperature
    • Nutting PG (1946), Deformation in relation to time, pressure and temperature, J Franklin Inst 242, 449-458.
    • (1946) J Franklin Inst , vol.242 , pp. 449-458
    • Nutting, P.G.1
  • 101
    • 0027146124 scopus 로고
    • Representation of the absorption of nonlinear waves by fractional derivatives
    • Ochmann M and Makarov S (1993), Representation of the absorption of nonlinear waves by fractional derivatives, J Acoust Soc Am 94(6), 3392-3399.
    • (1993) J Acoust Soc Am , vol.94 , Issue.6 , pp. 3392-3399
    • Ochmann, M.1    Makarov, S.2
  • 103
    • 34250103892 scopus 로고
    • Computational algorithms for FE formulations involving fractional operators
    • Padovan J (1987), Computational algorithms for FE formulations involving fractional operators, Comput Mech 2,271-287.
    • (1987) Comput Mech , vol.2 , pp. 271-287
    • Padovan, J.1
  • 105
    • 84889523503 scopus 로고
    • Numerical solution of ordinary fractional differential equations by the fractional difference method
    • Veszprem, Hungary, August 711
    • Podlubny I (1995), Numerical solution of ordinary fractional differential equations by the fractional difference method, Absts of 2d Int Conf on Difference Equations and Applications, Veszprem, Hungary, August 711, 89.
    • (1995) Absts of 2D Int Conf on Difference Equations and Applications , pp. 89
    • Podlubny, I.1
  • 106
    • 6144258722 scopus 로고
    • Temperature dependence of internal friction of pure metals and alloys (Russian)
    • Postnikov VS (1958), Temperature dependence of internal friction of pure metals and alloys (Russian), Uspekhi Fiz Nauk 66(1), 43.
    • (1958) Uspekhi Fiz Nauk , vol.66 , Issue.1 , pp. 43
    • Postnikov, V.S.1
  • 108
    • 0002403135 scopus 로고
    • Equilibrium of an elastic medium with after-effect (Russian)
    • Rabotnov YuN (1948), Equilibrium of an elastic medium with after-effect (Russian), Prikl Mat Mekh 12(1), 53-62.
    • (1948) Prikl Mat Mekh , vol.12 , Issue.1 , pp. 53-62
    • Rabotnov, Y.1
  • 110
  • 112
    • 0141912610 scopus 로고
    • Versuch einer allgemeinen Auffassung der Integration und Differentiation
    • Leipzig, Teubner
    • Riemann B (1876), Versuch einer allgemeinen Auffassung der Integration und Differentiation, Gesammelte Mathematische Werke, Leipzig, Teubner, 331-344.
    • (1876) Gesammelte Mathematische Werke , pp. 331-344
    • Riemann, B.1
  • 113
    • 0020805145 scopus 로고
    • Operators and fractional derivatives for viscoelastic constitutive equations
    • Rogers L (1983), Operators and fractional derivatives for viscoelastic constitutive equations, JRheol 27(4), 351-372.
    • (1983) Jrheol , vol.27 , Issue.4 , pp. 351-372
    • Rogers, L.1
  • 114
    • 0010173982 scopus 로고
    • Brief history and exposition of the fundamental theory of fractional calculus
    • SpringerVerlag
    • Ross B (1975), Brief history and exposition of the fundamental theory of fractional calculus. Lecture Notes in Mathematics 457, SpringerVerlag, 1-36.
    • (1975) Lecture Notes in Mathematics , vol.457 , pp. 1-36
    • Ross, B.1
  • 119
    • 0742320433 scopus 로고
    • Applications of fractional calculus to the analysis of damped vibrations of viscoelastic oscillators
    • 5, part 2
    • Rossikhin YuA and Shitikova MV (1995), Applications of fractional calculus to the analysis of damped vibrations of viscoelastic oscillators, Ahsts of 130th Meeting of the Acoust Soc of Am, J Acoust SocAm 98(5, part 2), 2890.
    • (1995) Ahsts of 130Th Meeting of the Acoust Soc of Am, J Acoust Socam , vol.98 , pp. 2890
    • Rossikhin, Y.1    Shitikova, M.V.2
  • 120
    • 0030736195 scopus 로고    scopus 로고
    • Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems, accepted for publication
    • Rossikhin YuA and Shitikova MV (1996a), Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems, accepted for publication Acta Mech.
    • (1996) Acta Mech
    • Rossikhin, Y.1    Shitikova, M.V.2
  • 121
    • 0030699713 scopus 로고    scopus 로고
    • Application of fractional operators to the analysis of damped vibrations of viscoelastic single-mass systems, accepted for publication
    • Rossikhin YuA and Shitikova MV (1996b), Application of fractional operators to the analysis of damped vibrations of viscoelastic single-mass systems, accepted for publication J Sound Vib.
    • (1996) J Sound Vib
    • Rossikhin, Y.1    Shitikova, M.V.2
  • 122
    • 84889518690 scopus 로고    scopus 로고
    • Application of fractional operators based on the weakly singular Rzhanitsyn kernel to the analysis of damped vibrations of a viscoelastic oscillator
    • Crocker MJ and Ivanov NI (eds), 2427 June 1996, St Petersburg, Russia
    • Rossikhin YuA and Shitikova MV (1996c), Application of fractional operators based on the weakly singular Rzhanitsyn kernel to the analysis of damped vibrations of a viscoelastic oscillator, Proc of 4th Int Congress on Sound and Vibration 3, Crocker MJ and Ivanov NI (eds), 2427 June 1996, St Petersburg, Russia, 1803-1808.
    • (1996) Proc of 4Th Int Congress on Sound and Vibration 3 , pp. 1803-1808
    • Rossikhin, Y.1    Shitikova, M.V.2
  • 123
    • 84889508319 scopus 로고    scopus 로고
    • Analysis of damped vibrations of a viscoelastic fractional calculus oscillator
    • Nov 27-29, West Bengal Univ, India
    • Rossikhin YuA and Shitikova MV (1996d), Analysis of damped vibrations of a viscoelastic fractional calculus oscillator, Proc of 3d Int Conf on Vibration Problems, Nov 27-29, 1996, West Bengal Univ, India.
    • (1996) Proc of 3D Int Conf on Vibration Problems , pp. 1996
    • Rossikhin, Y.1    Shitikova, M.V.2
  • 125
    • 84889544255 scopus 로고    scopus 로고
    • Derivation of nonlinear evolutionary equations for a shock layer of finite thickness
    • Wei RJ (ed), Proc of the 14th Int Symp on Nonlinear Acoustics, Nanjing Univ Press: Nanjing
    • Rossikhin YuA and Shitikova MV (1996f), Derivation of nonlinear evolutionary equations for a shock layer of finite thickness. Nonlinear Acoustics in Perspective, Wei RJ (ed), Proc of the 14th Int Symp on Nonlinear Acoustics, Nanjing Univ Press: Nanjing, 270-274.
    • (1996) Nonlinear Acoustics in Perspective , pp. 270-274
    • Rossikhin, Y.1    Shitikova, M.V.2
  • 127
    • 85025188286 scopus 로고    scopus 로고
    • Impact of two independent fractional parameters upon the damping properties of hereditarily elastic single-mass systems, submitted for publication in
    • Rossikhin YuA, Shitikova MV, and Kolesnikov MA (1996b), Impact of two independent fractional parameters upon the damping properties of hereditarily elastic single-mass systems, submitted for publication in J Vib Control.
    • (1996) J Vib Control
    • Rossikhin, Y.1    Shitikova, M.V.2    Kolesnikov, M.A.3
  • 128
    • 6144255784 scopus 로고
    • Features of special operators used in the creep theory (Russian)
    • Rozovsky MI (1959), Features of special operators used in the creep theory (Russian), PrikI Mat Mekh 23(5), 978-980.
    • (1959) Priki Mat Mekh , vol.23 , Issue.5 , pp. 978-980
    • Rozovsky, M.I.1
  • 129
  • 130
    • 3242828914 scopus 로고
    • One feature of the order of a special operator and its application to the dynamic problem solution (Russian)
    • YuN Rabotnov and NI Malinin (eds), Novosibirsk
    • Rozovsky MI (1963), One feature of the order of a special operator and its application to the dynamic problem solution (Russian), Creep and Endurance Limit, YuN Rabotnov and NI Malinin (eds), Novosibirsk, 128-133.
    • (1963) Creep and Endurance Limit , pp. 128-133
    • Rozovsky, M.I.1
  • 132
    • 6144290178 scopus 로고
    • Vibrations of the oscillator having hereditary creep (Russian)
    • Rozovsky MI and Sinaisky ES (1966), Vibrations of the oscillator having hereditary creep (Russian), PrikI Mat Mekh 30(3), 584-589.
    • (1966) Priki Mat Mekh , vol.30 , Issue.3 , pp. 584-589
    • Rozovsky, M.I.1    Sinaisky, E.S.2
  • 136
    • 84889532822 scopus 로고
    • Application of a viscoelastic boundary element formulation in time domain
    • 3-7 July 1995, Hamburg
    • Schanz M (1995), Application of a viscoelastic boundary element formulation in time domain, Abs of 3d Int Congress on Industrial and Applied Mathematics, 3-7 July 1995, Hamburg, 429.
    • (1995) Abs of 3D Int Congress on Industrial and Applied Mathematics , pp. 429
    • Schanz, M.1
  • 137
    • 0001559473 scopus 로고
    • Approximate methods in transform inversion for viscoelastic stress analysis
    • Schapery RA (1962), Approximate methods in transform inversion for viscoelastic stress analysis, Proc of 4th US Nat Congress of Appi Mech 2, 1075-1085.
    • (1962) Proc of 4Th US Nat Congress of Appi Mech , vol.2 , pp. 1075-1085
    • Schapery, R.A.1
  • 138
    • 0001553919 scopus 로고
    • Fractional diffusion and wave equation
    • Schneider WR and Wyss W (1989), Fractional diffusion and wave equation, J Math Phys 30(1), 134-144.
    • (1989) J Math Phys , vol.30 , Issue.1 , pp. 134-144
    • Schneider, W.R.1    Wyss, W.2
  • 140
    • 0010127267 scopus 로고
    • Application of the theory of quasiproperties to the treatment of anomalous stress-strain relations
    • Scott Blair GW and Caffyn JE (1949), Application of the theory of quasiproperties to the treatment of anomalous stress-strain relations, Philos Mag 40, 80-94.
    • (1949) Philos Mag , vol.40 , pp. 80-94
    • Scott Blair, G.W.1    Caffyn, J.E.2
  • 141
    • 6144238041 scopus 로고
    • Classification of the rheological properties of industrial materials in the light of power-law relations between stress, strain and time
    • Scott Blair GW and Coppen FMV (1942), Classification of the rheological properties of industrial materials in the light of power-law relations between stress, strain and time, J Sci Instr 19, 88-93.
    • (1942) J Sci Instr , vol.19 , pp. 88-93
    • Scott Blair, G.W.1    Coppen, F.2
  • 142
    • 0006981852 scopus 로고
    • Rheological law underlying the Nutting equation
    • Scott Blair GW and Reiner M (1950), Rheological law underlying the Nutting equation, Appi Sci Res ÀI, 225-234.
    • (1950) Appi Sci Res ÀI , pp. 225-234
    • Scott Blair, G.W.1    Reiner, M.2
  • 143
    • 22244470069 scopus 로고
    • Limitations of the Newtonian scale in relation to non-equilibrium rheological states and a theory of quasi-properties
    • A
    • Scott Blair GW, Veinolou BC, and Caffyn JE (1947), Limitations of the Newtonian scale in relation to non-equilibrium rheological states and a theory of quasi-properties, Proc Royal Soc 189 A, 69-87.
    • (1947) Proc Royal Soc , vol.189 , pp. 69-87
    • Scott Blair, G.W.1    Veinolou, B.C.2    Caffyn, J.E.3
  • 145
    • 85025183238 scopus 로고
    • Laws of deformation of real materials (Russian)
    • Slonimski GL (1939), Laws of deformation of real materials (Russian), Zh Tekhn Fiziki 9(20).
    • (1939) Zh Tekhn Fiziki , vol.9 , Issue.20
    • Slonimski, G.L.1
  • 146
    • 0010093317 scopus 로고
    • Law of deformation of elastic polymer bodies (Russian)
    • Slonimski GL (1961), Law of deformation of elastic polymer bodies (Russian), Dokl Akad Nauk SSSR 140(2).
    • (1961) Dokl Akad Nauk SSSR , vol.140 , Issue.2
    • Slonimski, G.L.1
  • 147
    • 0000818209 scopus 로고
    • Laws of mechanical relaxation processes in polymers
    • Slonimski GL (1967), Laws of mechanical relaxation processes in polymers, J Polymer Sci C16, 1667-1672.
    • (1967) J Polymer Sci , vol.C16 , pp. 1667-1672
    • Slonimski, G.L.1
  • 148
    • 0000052592 scopus 로고
    • Rheological models containing fractional derivatives
    • Smit W and de Vries H (1970), Rheological models containing fractional derivatives, Rheol Acta 9, 525-534.
    • (1970) Rheol Acta , vol.9 , pp. 525-534
    • Smit, W.1    De Vries, H.2
  • 149
    • 0018505722 scopus 로고
    • Application of fractional calculus for the formulation of viscoelastic models
    • Stiassnie M (1979), Application of fractional calculus for the formulation of viscoelastic models, Appi Math Model 3, 300-302.
    • (1979) Appi Math Model , vol.3 , pp. 300-302
    • Stiassnie, M.1
  • 150
    • 3242823784 scopus 로고
    • Response of systems with damping materials modeled using fractional calculus
    • Godoy LA, Idelsohn SR, Laura PA, and Mook DT (eds), Santa Fe: AAM and AMCA
    • Suarez LE and Shokooh A (1995a), Response of systems with damping materials modeled using fractional calculus, Applied Mechanics in the Americas 2, Godoy LA, Idelsohn SR, Laura PA, and Mook DT (eds), Santa Fe: AAM and AMCA, 147-152.
    • (1995) Applied Mechanics in the Americas , vol.2 , pp. 147-152
    • Suarez, L.E.1    Shokooh, A.2
  • 151
    • 24244455970 scopus 로고
    • Response of systems with damping materials modeled using fractional calculus
    • Part 2
    • Suarez LE and Shokooh A (1995b), Response of systems with damping materials modeled using fractional calculus, Appi Mech Rev 48(11), Part 2, 118-126.
    • (1995) Appi Mech Rev , vol.48 , Issue.11 , pp. 118-126
    • Suarez, L.E.1    Shokooh, A.2
  • 152
    • 0000099566 scopus 로고
    • Generalized Burgers’ equations and fractional calculus
    • Jeffrey A (ed), Longman Sci and Tech
    • Sugimoto N (1989), Generalized Burgers’ equations and fractional calculus, Nonlinear Waves Motion, Jeffrey A (ed), Longman Sci and Tech, 162-179.
    • (1989) Nonlinear Waves Motion , pp. 162-179
    • Sugimoto, N.1
  • 153
    • 0026135818 scopus 로고
    • Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves
    • Sugimoto N (1991), Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves, J Fluid Mech 225(4), 631 -653.
    • (1991) J Fluid Mech , vol.225 , Issue.4
    • Sugimoto, N.1
  • 154
    • 0022130907 scopus 로고
    • Generalized Burgers’ equation for nonlinear viscoelastic waves
    • Sugimoto N and Kakutani T (1985), Generalized Burgers’ equation for nonlinear viscoelastic waves, Wave Motion 7, 447-458.
    • (1985) Wave Motion , vol.7 , pp. 447-458
    • Sugimoto, N.1    Kakutani, T.2
  • 157
    • 0021626769 scopus 로고
    • Oscillatory structured shock waves in a nonlinear elastic rod with weak viscoelastic rod
    • Sugimoto N, Yamane Y, and Kakutani K (1984b), Oscillatory structured shock waves in a nonlinear elastic rod with weak viscoelastic rod, Trans ASME J Appi Mech 51,766.
    • (1984) Trans ASME J Appi Mech , vol.51 , pp. 766
    • Sugimoto, N.1    Yamane, Y.2    Kakutani, K.3
  • 158
    • 84889549572 scopus 로고
    • Longitudinal impact of a semi-infinite circular viscoelastic rod
    • Testa RB (1966), Longitudinal impact of a semi-infinite circular viscoelastic rod, Trans ASME J Appi Mech 33(3), 687-689.
    • (1966) Trans ASME J Appi Mech , vol.33 , Issue.3 , pp. 687-689
    • Testa, R.B.1
  • 160
    • 0021439912 scopus 로고
    • Appearance of the fractional derivative in the behavior of real material
    • Torvik PJ and Bagley RL (1984), Appearance of the fractional derivative in the behavior of real material, Trans ASME J Appi Mech 51, 294-298.
    • (1984) Trans ASME J Appi Mech , vol.51 , pp. 294-298
    • Torvik, P.J.1    Bagley, R.L.2
  • 161
    • 0022077904 scopus 로고
    • Different view of viscous damping
    • Torvik PJ and Bagley RL (1985), Different view of viscous damping. Shock Vib Bull 55(3), 81 -84.
    • (1985) Shock Vib Bull , vol.55 , Issue.3
    • Torvik, P.J.1    Bagley, R.L.2
  • 162
    • 0028176403 scopus 로고
    • Temperature effect of viscoelastic dampers during earthquakes
    • Tsai CS (1994), Temperature effect of viscoelastic dampers during earthquakes, J Struct Eng 120(2), 394-409.
    • (1994) J Struct Eng , vol.120 , Issue.2 , pp. 394-409
    • Tsai, C.S.1
  • 164
    • 6144267593 scopus 로고
    • Propagation and attenuation of waves in linear viscoelastic solids
    • Valanis KC (1965), Propagation and attenuation of waves in linear viscoelastic solids, J Math Phys 44,227-239.
    • (1965) J Math Phys , vol.44 , pp. 227-239
    • Valanis, K.C.1
  • 165
    • 0000535044 scopus 로고
    • Sulle Equazioni Integro-Differenziali della Theoria dell’Elasticità (Italian)
    • Volterra V (1909), Sulle Equazioni Integro-Differenziali della Theoria dell’Elasticità (Italian), Atti Reale Acad naz Lincei Rend Cl sci fls, mat e natur 18, 295-300.
    • (1909) Atti Reale Acad Naz Lincei Rend Cl Sci Fls, Mat E Natur , vol.18 , pp. 295-300
    • Volterra, V.1
  • 167
  • 168
    • 6144284045 scopus 로고
    • Thermal stresses in concrete solid masses with due account for creep in concrete (Russian)
    • Wolfson SZ (1960), Thermal stresses in concrete solid masses with due account for creep in concrete (Russian), Izv Akad Nauk SSSR Mekh Mashinostroenie (1), 162-165.
    • (1960) Izv Akad Nauk SSSR Mekh Mashinostroenie , Issue.1 , pp. 162-165
    • Wolfson, S.Z.1
  • 169
    • 0009481303 scopus 로고
    • Fractional diffusion equation
    • Wyss W (1986), Fractional diffusion equation, JMath Phys 27, 2782.
    • (1986) Jmath Phys , pp. 27
    • Wyss, W.1
  • 170
    • 6144238161 scopus 로고
    • About an ay -function singularity parameter impact on damped vibrations of hereditary elastic systems (Russian)
    • Zelenev VM, Meshkov SI, and Rossikhin YuA (1970), About an ay -function singularity parameter impact on damped vibrations of hereditary elastic systems (Russian), Izv Akad Nauk SSSR. Mekh Tverdogo Tela (3), 115-117.
    • (1970) Izv Akad Nauk SSSR. Mekh Tverdogo Tela , Issue.3 , pp. 115-117
    • Zelenev, V.M.1    Meshkov, S.I.2    Rossikhin, Y.3
  • 171
    • 84889536578 scopus 로고
    • Relaxation and retardation spectra connected with damped vibrations of hereditarily elastic systems (Russian)
    • Moldova Acad of Sci, Kishinev
    • Zelenev VM, Meshkov SI, and Rossikhin YuA (1971), Relaxation and retardation spectra connected with damped vibrations of hereditarily elastic systems (Russian), Applied Mathematics and Programming 6, Moldova Acad of Sci, Kishinev, 107-112.
    • (1971) Applied Mathematics and Programming , vol.6 , pp. 107-112
    • Zelenev, V.M.1    Meshkov, S.I.2    Rossikhin, Y.3
  • 172
    • 3242866873 scopus 로고
    • Damped vibrations of hereditary elastic systems with weakly singular kernels
    • Zelenev VM, Meshkov SI, and Rossikhin YuA (1972), Damped vibrations of hereditary elastic systems with weakly singular kernels, J Appl Mech Techn Phys (Engl transl) 11(2), 290-293.
    • (1972) J Appl Mech Techn Phys (Engl Transl) , vol.11 , Issue.2 , pp. 290-293
    • Zelenev, V.M.1    Meshkov, S.I.2    Rossikhin, Y.3
  • 173
    • 84889513790 scopus 로고
    • Fractional derivatives and numerical solution of one class of convolutional equations (Russian)
    • Zheludev VA (1982), Fractional derivatives and numerical solution of one class of convolutional equations (Russian), Differentsialnye Uravnenija 18(11), 1950-1960.
    • (1982) Differentsialnye Uravnenija , vol.18 , Issue.11 , pp. 1950-1960
    • Zheludev, V.A.1


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