TY - CONF
T1 - Fractional differential equations and related exact mechanical models
AU - Pinnola, Francesco Paolo
AU - Zingales, Massimiliano
AU - Di Paola, Mario
PY - 2012
Y1 - 2012
N2 - Creep and relaxation tests, performed on various materials like polymers, rubbers and so on are well-fitted by power-laws with exponent β ∈ [0, 1] (Nutting (1921), Di Paola et al. (2011)). The consequence of this observation is that the stress-strain relation of hereditary materials is ruled by fractional operators (Scott Blair (1947), Slonimsky (1961)). A large amount of researches have been performed in the second part of the last century with the aim to connect constitutive fractional relations with some mechanical models by means of fractance trees and ladders (see Podlubny (1999)). Recently, Di Paola and Zingales (2012) proposed a mechanical model that corresponds to fractional stress-strain relation with any real exponent and they have proposed a description of above model (Di Paola et al. (2012)). In this study the authors aim to extend the study to cases with and to fractional Kelvin-Voigt model of hereditariness.
AB - Creep and relaxation tests, performed on various materials like polymers, rubbers and so on are well-fitted by power-laws with exponent β ∈ [0, 1] (Nutting (1921), Di Paola et al. (2011)). The consequence of this observation is that the stress-strain relation of hereditary materials is ruled by fractional operators (Scott Blair (1947), Slonimsky (1961)). A large amount of researches have been performed in the second part of the last century with the aim to connect constitutive fractional relations with some mechanical models by means of fractance trees and ladders (see Podlubny (1999)). Recently, Di Paola and Zingales (2012) proposed a mechanical model that corresponds to fractional stress-strain relation with any real exponent and they have proposed a description of above model (Di Paola et al. (2012)). In this study the authors aim to extend the study to cases with and to fractional Kelvin-Voigt model of hereditariness.
KW - Discretized models
KW - Fractional hereditary materials
KW - Mechanical systems
KW - Modal transformation.
KW - Power-law description
KW - Discretized models
KW - Fractional hereditary materials
KW - Mechanical systems
KW - Modal transformation.
KW - Power-law description
UR - http://hdl.handle.net/10447/74526
M3 - Other
SP - 1
EP - 10
ER -