메뉴 건너뛰기




Volumn 45, Issue 2, 2010, Pages 169-175

Efficient solution of a vibration equation involving fractional derivatives

Author keywords

Adomian decomposition; Fractional derivative; Fractional differential equation; Vibration

Indexed keywords

ADOMIAN DECOMPOSITION; ADOMIAN DECOMPOSITION METHOD; ANALYTICAL SOLUTIONS; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL ORDER; MECHANICAL OSCILLATORS; NON-TRIVIAL; NUMERICAL CALCULATION; NUMERICAL EXAMPLE; SERIES EXPANSION; TIME STEP; VIBRATION EQUATIONS; VIBRATION SYSTEMS;

EID: 73449121039     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2009.10.006     Document Type: Article
Times cited : (43)

References (38)
  • 2
    • 0020765202 scopus 로고
    • A theoretical basis for the application of fractional calculus to viscoelasticity
    • Bagley R.L., and Torvik P.J. A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 27 (1983) 201-210
    • (1983) J. Rheol. , vol.27 , pp. 201-210
    • Bagley, R.L.1    Torvik, P.J.2
  • 3
    • 0022660581 scopus 로고
    • On the fractional calculus model of viscoelastic behavior
    • Bagley R.L., and Torvik P.J. On the fractional calculus model of viscoelastic behavior. J. Rheol. 30 (1986) 133-155
    • (1986) J. Rheol. , vol.30 , pp. 133-155
    • Bagley, R.L.1    Torvik, P.J.2
  • 4
    • 33846010791 scopus 로고    scopus 로고
    • Modelling of constrained thin rubber layer with emphasis on damping
    • Alvelid M., and Enelund M. Modelling of constrained thin rubber layer with emphasis on damping. J. Sound Vib. 300 (2007) 662-675
    • (2007) J. Sound Vib. , vol.300 , pp. 662-675
    • Alvelid, M.1    Enelund, M.2
  • 5
    • 2442659366 scopus 로고    scopus 로고
    • Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements
    • Ramrakhyani D.S., Lesieutre G.A., and Smith E.C. Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements. Int. J. Solids Struct. 41 (2004) 3929-3948
    • (2004) Int. J. Solids Struct. , vol.41 , pp. 3929-3948
    • Ramrakhyani, D.S.1    Lesieutre, G.A.2    Smith, E.C.3
  • 6
    • 33750340240 scopus 로고    scopus 로고
    • Fractional calculus in biomechanics: a 3D viscoelastic model using regularized fractional derivative kernels with application to the human calcaneal fat pad
    • Freed A.D., and Diethelm K. Fractional calculus in biomechanics: a 3D viscoelastic model using regularized fractional derivative kernels with application to the human calcaneal fat pad. Biomech. Model. Mechanobiol. 5 (2006) 203-215
    • (2006) Biomech. Model. Mechanobiol. , vol.5 , pp. 203-215
    • Freed, A.D.1    Diethelm, K.2
  • 7
    • 15744376961 scopus 로고    scopus 로고
    • Fractional calculus description of non-linear viscoelastic behaviour of polymers
    • Heymans N. Fractional calculus description of non-linear viscoelastic behaviour of polymers. Nonlinear Dyn. 38 (2004) 221-231
    • (2004) Nonlinear Dyn. , vol.38 , pp. 221-231
    • Heymans, N.1
  • 9
    • 0036650160 scopus 로고    scopus 로고
    • Finite element formulation of viscoelastic constitutive equations using fractional time derivatives
    • Schmidt A., and Gaul L. Finite element formulation of viscoelastic constitutive equations using fractional time derivatives. Nonlinear Dyn. 29 (2002) 37-55
    • (2002) Nonlinear Dyn. , vol.29 , pp. 37-55
    • Schmidt, A.1    Gaul, L.2
  • 10
    • 34247475224 scopus 로고    scopus 로고
    • Homogenised finite element for transient dynamic analysis of unconstrained layer damping beams involving fractional derivative models
    • Cortés F., and Elejabarrieta M.J. Homogenised finite element for transient dynamic analysis of unconstrained layer damping beams involving fractional derivative models. Comput. Mech. 40 (2007) 313-324
    • (2007) Comput. Mech. , vol.40 , pp. 313-324
    • Cortés, F.1    Elejabarrieta, M.J.2
  • 11
    • 0032654412 scopus 로고    scopus 로고
    • Time domain modeling of damping using anelastic displacement fields and fractional calculus
    • Enelund M., and Lesieutre G.A. Time domain modeling of damping using anelastic displacement fields and fractional calculus. Int. J. Solids Struct. 36 (1999) 4447-4472
    • (1999) Int. J. Solids Struct. , vol.36 , pp. 4447-4472
    • Enelund, M.1    Lesieutre, G.A.2
  • 12
    • 33745712084 scopus 로고    scopus 로고
    • On the numerical evaluation of fractional derivatives in multi-degree-of-freedom systems
    • Schmidt A., and Gaul L. On the numerical evaluation of fractional derivatives in multi-degree-of-freedom systems. Signal Process. 86 (2006) 2592-2601
    • (2006) Signal Process. , vol.86 , pp. 2592-2601
    • Schmidt, A.1    Gaul, L.2
  • 13
    • 0003001893 scopus 로고    scopus 로고
    • An eigenvector expansion method for the solution of motion containing fractional derivatives
    • Suarez L.E., and Shokooh A. An eigenvector expansion method for the solution of motion containing fractional derivatives. J. Appl. Mech. 64 (1997) 629-635
    • (1997) J. Appl. Mech. , vol.64 , pp. 629-635
    • Suarez, L.E.1    Shokooh, A.2
  • 14
    • 0036554885 scopus 로고    scopus 로고
    • A numerical scheme for dynamic systems containing fractional derivatives
    • Yuan L., and Agrawal O.P. A numerical scheme for dynamic systems containing fractional derivatives. J. Vib. Acoust. 124 (2002) 321-324
    • (2002) J. Vib. Acoust. , vol.124 , pp. 321-324
    • Yuan, L.1    Agrawal, O.P.2
  • 15
    • 26444463136 scopus 로고    scopus 로고
    • On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems
    • Schmidt A., and Gaul L. On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems. Mech. Res. Commun. 33 (2006) 99-107
    • (2006) Mech. Res. Commun. , vol.33 , pp. 99-107
    • Schmidt, A.1    Gaul, L.2
  • 16
    • 55649120021 scopus 로고    scopus 로고
    • Methods for solving a semi-differential vibration equation
    • Pálfalvi A. Methods for solving a semi-differential vibration equation. Period. Polytech. Ser. Mech. Eng. 51 (2007) 1-5
    • (2007) Period. Polytech. Ser. Mech. Eng. , vol.51 , pp. 1-5
    • Pálfalvi, A.1
  • 17
    • 33751513961 scopus 로고    scopus 로고
    • Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method
    • Wang Q. Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method. Appl. Math. Comput. 182 (2006) 1048-1055
    • (2006) Appl. Math. Comput. , vol.182 , pp. 1048-1055
    • Wang, Q.1
  • 18
    • 10344238128 scopus 로고    scopus 로고
    • Adomian decomposition: a tool for solving a system of fractional differential equations
    • Daftardar-Gejji V., and Jafari H. Adomian decomposition: a tool for solving a system of fractional differential equations. J. Math. Anal. Appl. 301 (2005) 508-518
    • (2005) J. Math. Anal. Appl. , vol.301 , pp. 508-518
    • Daftardar-Gejji, V.1    Jafari, H.2
  • 19
    • 17444364074 scopus 로고    scopus 로고
    • Analytical solution of a dynamic system containing fractional derivative of order one-half by Adomian decomposition method
    • Saha Ray S., Poddar B.P., and Bera R.K. Analytical solution of a dynamic system containing fractional derivative of order one-half by Adomian decomposition method. J. Appl. Mech. 72 (2005) 290-295
    • (2005) J. Appl. Mech. , vol.72 , pp. 290-295
    • Saha Ray, S.1    Poddar, B.P.2    Bera, R.K.3
  • 20
    • 34248373867 scopus 로고    scopus 로고
    • Solving a multi-order fractional differential equation using Adomian decomposition
    • Daftardar-Gejji V., and Jafari H. Solving a multi-order fractional differential equation using Adomian decomposition. Appl. Math. Comput. 189 (2007) 541-548
    • (2007) Appl. Math. Comput. , vol.189 , pp. 541-548
    • Daftardar-Gejji, V.1    Jafari, H.2
  • 21
    • 46749134732 scopus 로고    scopus 로고
    • Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method
    • Daftardar-Gejji V., and Bhalekar S. Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method. Appl. Math. Comput. 202 (2008) 113-120
    • (2008) Appl. Math. Comput. , vol.202 , pp. 113-120
    • Daftardar-Gejji, V.1    Bhalekar, S.2
  • 22
    • 0037174280 scopus 로고    scopus 로고
    • Analytical approximate solutions for nonlinear fractional differential equations
    • Shawagfeh N.T. Analytical approximate solutions for nonlinear fractional differential equations. Appl. Math. Comput. 131 (2002) 517-529
    • (2002) Appl. Math. Comput. , vol.131 , pp. 517-529
    • Shawagfeh, N.T.1
  • 23
    • 33750901303 scopus 로고    scopus 로고
    • A numerical scheme for the solution of multi-order fractional differential equations
    • Momani S. A numerical scheme for the solution of multi-order fractional differential equations. Appl. Math. Comput. 182 (2006) 761-770
    • (2006) Appl. Math. Comput. , vol.182 , pp. 761-770
    • Momani, S.1
  • 24
    • 39849097024 scopus 로고    scopus 로고
    • Analytical solution of the linear fractional differential equation by Adomian decomposition method
    • Hu Y., Luo Y., and Lu Z. Analytical solution of the linear fractional differential equation by Adomian decomposition method. J. Comput. Appl. Math. 215 (2008) 220-229
    • (2008) J. Comput. Appl. Math. , vol.215 , pp. 220-229
    • Hu, Y.1    Luo, Y.2    Lu, Z.3
  • 25
    • 34250661428 scopus 로고    scopus 로고
    • Numerical approach to differential equations of fractional order
    • Momani S., and Odibat Z. Numerical approach to differential equations of fractional order. J. Comput. Appl. Math. 207 (2007) 96-110
    • (2007) J. Comput. Appl. Math. , vol.207 , pp. 96-110
    • Momani, S.1    Odibat, Z.2
  • 26
    • 33748425302 scopus 로고    scopus 로고
    • Numerical comparison of methods for solving linear differential equations of fractional order
    • Momani S., and Odibat Z. Numerical comparison of methods for solving linear differential equations of fractional order. Chaos Solitons Fractals 31 (2007) 1248-1255
    • (2007) Chaos Solitons Fractals , vol.31 , pp. 1248-1255
    • Momani, S.1    Odibat, Z.2
  • 27
    • 50949121966 scopus 로고    scopus 로고
    • An expansion formula for fractional derivatives and its application
    • Atanackovic T.M., and Stankovic B. An expansion formula for fractional derivatives and its application. Fractional Calc. Appl. Anal. 7 (2004) 365-378
    • (2004) Fractional Calc. Appl. Anal. , vol.7 , pp. 365-378
    • Atanackovic, T.M.1    Stankovic, B.2
  • 28
    • 50949125208 scopus 로고    scopus 로고
    • On a numerical scheme for solving differential equations of fractional order
    • Atanackovic T.M., and Stankovic B. On a numerical scheme for solving differential equations of fractional order. Mech. Res. Commun. 35 (2008) 429-438
    • (2008) Mech. Res. Commun. , vol.35 , pp. 429-438
    • Atanackovic, T.M.1    Stankovic, B.2
  • 29
    • 33745906525 scopus 로고    scopus 로고
    • Galerkin projections and finite elements for fractional order derivatives
    • Singh S.J., and Chatterjee A. Galerkin projections and finite elements for fractional order derivatives. Nonlinear Dyn. 45 (2006) 183-206
    • (2006) Nonlinear Dyn. , vol.45 , pp. 183-206
    • Singh, S.J.1    Chatterjee, A.2
  • 30
    • 33644896579 scopus 로고    scopus 로고
    • Revised Adomian decomposition method for solving a system of nonlinear equations
    • Jafari H., and Daftardar-Gejji V. Revised Adomian decomposition method for solving a system of nonlinear equations. Appl. Math. Comput. 175 (2006) 1-7
    • (2006) Appl. Math. Comput. , vol.175 , pp. 1-7
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 31
    • 33749518702 scopus 로고    scopus 로고
    • Revised Adomian decomposition method for solving systems of ordinary and fractional differential equations
    • Jafari H., and Daftardar-Gejji V. Revised Adomian decomposition method for solving systems of ordinary and fractional differential equations. Appl. Math. Comput. 181 (2006) 598-608
    • (2006) Appl. Math. Comput. , vol.181 , pp. 598-608
    • Jafari, H.1    Daftardar-Gejji, V.2
  • 32
    • 38049174418 scopus 로고    scopus 로고
    • Application of modified decomposition method for the analytical solution of space fractional diffusion equation
    • Saha Ray S., Chaudhuri K.S., and Bera R.K. Application of modified decomposition method for the analytical solution of space fractional diffusion equation. Appl. Math. Comput. 196 (2008) 294-302
    • (2008) Appl. Math. Comput. , vol.196 , pp. 294-302
    • Saha Ray, S.1    Chaudhuri, K.S.2    Bera, R.K.3
  • 33
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    • Heymans N., and Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheol. Acta 45 (2006) 765-771
    • (2006) Rheol. Acta , vol.45 , pp. 765-771
    • Heymans, N.1    Podlubny, I.2
  • 34
    • 4944232599 scopus 로고    scopus 로고
    • An algorithm for Adomian decomposition method
    • Chen W., and Lu Z. An algorithm for Adomian decomposition method. Appl. Math. Comput. 159 (2004) 221-235
    • (2004) Appl. Math. Comput. , vol.159 , pp. 221-235
    • Chen, W.1    Lu, Z.2
  • 35
    • 0001307255 scopus 로고    scopus 로고
    • Stability and creep of a fractional derivative order viscoelastic rod
    • Baclic B.S., and Atanackovic T.M. Stability and creep of a fractional derivative order viscoelastic rod. Bull. Acad. Serb. Sci. Arts CXXI (2000) 115-131
    • (2000) Bull. Acad. Serb. Sci. Arts , vol.CXXI , pp. 115-131
    • Baclic, B.S.1    Atanackovic, T.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.