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Volumn 11, Issue , 2009, Pages 389-423

Fractional mechanical model for the dynamics of non-local continuum

Author keywords

Fractional calculus; Modes of vibration and dynamics of non local bar; Non local elasticity; Power law attenuation function

Indexed keywords

ABSOLUTE DISTANCE; COHESIVE FORCE; FRACTIONAL CALCULUS; FRACTIONAL DIFFERENTIAL EQUATIONS; INVERSE POWER LAW; LIMITING CASE; LINEAR SPRING; LONG RANGE INTERACTIONS; MATERIAL PARTICLES; MATHEMATICAL FORMULATION; MECHANICAL MODEL; MODES OF VIBRATION AND DYNAMICS OF NON-LOCAL BAR; NON-LOCAL INTERACTIONS; NONLOCAL; POWER LAW ATTENUATION FUNCTION; STATIC CONSTRAINTS;

EID: 75849133762     PISSN: 18761100     EISSN: 18761119     Source Type: Book Series    
DOI: 10.1007/978-0-387-76483-2_33     Document Type: Article
Times cited : (34)

References (37)
  • 2
    • 0037343002 scopus 로고    scopus 로고
    • Update on a class of gradient theories
    • Aifantis EC (2003) Update on a class of gradient theories. Mechanics of Materials 35:259-280
    • (2003) Mechanics of Materials , vol.35 , pp. 259-280
    • Aifantis, E.C.1
  • 3
    • 0036964107 scopus 로고    scopus 로고
    • A model for the uniaxial isothermal deformation of viscoelastic body
    • Atanackovic TM (2002) A model for the uniaxial isothermal deformation of viscoelastic body. Acta Mechanica 159:77-86
    • (2002) Acta Mechanica , vol.159 , pp. 77-86
    • Atanackovic, T.M.1
  • 5
    • 0036841605 scopus 로고    scopus 로고
    • Non-local integral formulations of plasticity and damage
    • Bažant ZP, Jirásek M (2002) Non-local integral formulations of plasticity and damage. Journal of Engineering Mechanics 128:1129-1239
    • (2002) Journal of Engineering Mechanics , vol.128 , pp. 1129-1239
    • Bažant, Z.P.1    Jirásek, M.2
  • 8
    • 0035834542 scopus 로고    scopus 로고
    • Static-kinematic duality and the principle of virtual work in the mechanics of fractal media
    • DOI 10.1016/S0045-7825(01)00241-9, PII S0045782501002419, Micromechanics of Brittle Materials and Stochastic Analysis of Mechanical Systems
    • Carpinteri A, Chiaia B, Cornetti P (2001) Static-kinematic duality and the principle of virtual work in the mechanics of fractal media. Computer Methods in Applied Mechanics and Engineering 191:3-19 (Pubitemid 33105419)
    • (2001) Computer Methods in Applied Mechanics and Engineering , vol.191 , Issue.1-2 , pp. 3-19
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 9
    • 1842471297 scopus 로고    scopus 로고
    • A mesoscopic theory of damage and fracture in heterogeneous materials
    • DOI 10.1016/j.tafmec.2003.11.004, PII S0167844203000892
    • Carpinteri A, Chiaia B, Cornetti P (2004) A mesoscopic theory of damage and fracture in heterogeneous materials. Theoretical and Applied Fracture Mechanics 41:43-50 (Pubitemid 38439141)
    • (2004) Theoretical and Applied Fracture Mechanics , vol.41 , Issue.1-3 , pp. 43-50
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 10
    • 0042121430 scopus 로고    scopus 로고
    • On the mechanics of quasi-brittle materials with a fractal microstructure
    • DOI 10.1016/S0013-7944(02)00220-5
    • Carpinteri A, Chiaia B, Cornetti P (2003) On the mechanics of quasi-brittle materials with a fractal microstructure. Engineering Fracture Mechanics 70:2321-2349 (Pubitemid 36941621)
    • (2003) Engineering Fracture Mechanics , vol.70 , Issue.16 , pp. 2321-2349
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 12
    • 79957491159 scopus 로고    scopus 로고
    • On the use of fractional calculus for the probabilistic characterization of random variables
    • (Submitted)
    • Cottone G, Di Paola M (2007) On the use of fractional calculus for the probabilistic characterization of random variables. Probabilistic Engineering Mechanics (Submitted)
    • (2007) Probabilistic Engineering Mechanics
    • Cottone, G.1    Di Paola, M.2
  • 13
    • 40549105738 scopus 로고    scopus 로고
    • Path integral solution handled by fractional calculus
    • doi: 10.1088/1742-6596/96/1/012007
    • Cottone G, Di Paola M, Pirrotta A (2008) Path integral solution handled by fractional calculus. Journal of Physics: Conference Series, 96: 012007. doi: 10.1088/1742-6596/96/1/012007
    • (2008) Journal of Physics: Conference Series , vol.96 , pp. 012007
    • Cottone, G.1    Di Paola, M.2    Pirrotta, A.3
  • 14
    • 51249121333 scopus 로고    scopus 로고
    • Long-range cohesive interactions of non- local continuum faced by fractional calculus
    • (to appear)
    • Di Paola M, Zingales M (2008) Long-range cohesive interactions of non- local continuum faced by fractional calculus. International Journal of Solids and Structures (to appear)
    • (2008) International Journal of Solids and Structures
    • Di Paola, M.1    Zingales, M.2
  • 16
    • 0037217762 scopus 로고    scopus 로고
    • Closed form solution for a nonlocal elastic bar in tension
    • DOI 10.1016/S0020-7683(02)00547-4, PII S0020768302005474
    • Fuschi P, Pisano AA (2003) Closed form solution for a non-local elastic bar in tension. International Journal of Solids and Structures 40:13-23 (Pubitemid 36036345)
    • (2003) International Journal of Solids and Structures , vol.40 , Issue.1 , pp. 13-23
    • Angela Pisano, A.1    Fuschi, P.2
  • 18
    • 0036248726 scopus 로고    scopus 로고
    • Stationary solutions of the fractional kinetic equation with a symmetric power-law potential
    • DOI 10.1023/A:1015118206234
    • Gonchar V, Tanatarov L, Chechkin A (2002), Stationary solutions of the fractional kinetic equation with a symmetric power-law potential. Theoretical and Mathematical Physics 131(1):582-594 (Pubitemid 37131942)
    • (2002) Theoretical and Mathematical Physics , vol.131 , Issue.1 , pp. 582-594
    • Gonchar, V.Yu.1    Tanatarov, L.V.2    Chechkin, A.V.3
  • 21
    • 49949143801 scopus 로고
    • Elasticity theory of materials with long-range cohesive forces
    • Kroner E (1967) Elasticity theory of materials with long-range cohesive forces. International Journal of Solids and Structures 3:731-742
    • (1967) International Journal of Solids and Structures , vol.3 , pp. 731-742
    • Kroner, E.1
  • 22
    • 0002564873 scopus 로고
    • Some considerations of the relations between solid state physics and generalized continuum mechanics
    • Kroner (ed) Springer Verlag, Berlin Heidelberg New York
    • Krumhanls JA (1967) Some considerations of the relations between solid state physics and generalized continuum mechanics. In: Kroner (ed) Mechanics of Generalized Continua. Proc. IUTAM symposium. Springer Verlag, Berlin Heidelberg New York
    • (1967) Mechanics of Generalized Continua. Proc. IUTAM Symposium
    • Krumhanls, J.A.1
  • 23
    • 33745839870 scopus 로고    scopus 로고
    • Non-local continuum mechanics and fractional calculus
    • Lazopoulos KA (2006) Non-local continuum mechanics and fractional calculus. Mechanics Research Communication 33:751-757
    • (2006) Mechanics Research Communication , vol.33 , pp. 751-757
    • Lazopoulos, K.A.1
  • 24
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • Metzler R, Klafter J (2000) The random walk's guide to anomalous diffusion: a fractional dynamics approach. Physics Reports 339:1-77
    • (2000) Physics Reports , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 25
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics
    • DOI 10.1088/0305-4470/37/31/R01, PII S0305447004713190
    • Metzler R, Klafter J (2004) The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. Journal of Physics A 37:R161-R208 (Pubitemid 39063557)
    • (2004) Journal of Physics A: Mathematical and General , vol.37 , Issue.31
    • Metzler, R.1    Klafter, J.2
  • 28
    • 2942532686 scopus 로고    scopus 로고
    • Damping characteristic of a fractional oscillator
    • Narahari ABN, Hanneken JW, Clarke T (2004) Damping characteristic of a fractional oscillator. Physica A 339:311-319
    • (2004) Physica A , vol.339 , pp. 311-319
    • Narahari, A.B.N.1    Hanneken, J.W.2    Clarke, T.3
  • 32
    • 0032155927 scopus 로고    scopus 로고
    • A thermodynamics-based formulation of gradient-dependent plasticity
    • Polizzotto C, Borino G (1998) A thermodynamics-based formulation of gradient- dependent plasticity. European Journal of Mechanics A/Solids 17:741-761 (Pubitemid 128402329)
    • (1998) European Journal of Mechanics, A/Solids , vol.17 , Issue.5 , pp. 741-761
    • Polizzotto, C.1    Borino, G.2
  • 33
    • 0035860410 scopus 로고    scopus 로고
    • Nonlocal elasticity and related variational principles
    • DOI 10.1016/S0020-7683(01)00039-7, PII S0020768301000397
    • Polizzotto C (2001) Non-local elasticity and related variational principles. International Journal of Solids and Structures 38:7359-7380 (Pubitemid 32889985)
    • (2001) International Journal of Solids and Structures , vol.38 , Issue.42-43 , pp. 7359-7380
    • Polizzotto, C.1
  • 34
    • 0242490335 scopus 로고    scopus 로고
    • Gradient elasticity and nonstandard boundary conditions
    • DOI 10.1016/j.ijsolstr.2003.06.001
    • Polizzotto C (2003) Gradient elasticity and non standard boundary conditions. International Journal of Solids and Structures 40:7399-7423 (Pubitemid 37418353)
    • (2003) International Journal of Solids and Structures , vol.40 , Issue.26 , pp. 7399-7423
    • Polizzotto, C.1
  • 36
    • 33748604058 scopus 로고    scopus 로고
    • On the convergence of difference schemes for differential equations with a fractional derivative (in Russian)
    • Shkanukov MK (1996) On the convergence of difference schemes for differential equations with a fractional derivative (in Russian). Dokl. Akad. Nauk. 348:746-748
    • (1996) Dokl. Akad. Nauk. , vol.348 , pp. 746-748
    • Shkanukov, M.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.