6533b838fe1ef96bd12a3f10
RESEARCH PRODUCT
Fractional differential equations and related exact mechanical models
Mario Di PaolaMassimiliano ZingalesFrancesco Paolo Pinnolasubject
Mechanical systems Power-law description Fractional hereditary materials Discretized models Modal transformation.Differential equationFractional hereditary materialDiscretized modelMathematical analysisRelaxation (iterative method)Extension (predicate logic)Mechanical systems Power-law description Fractional hereditary materials Discretized modelsModal transformationDashpotMechanical systemMechanical systemComputational MathematicsComputational Theory and MathematicsCreepModeling and SimulationPower-law descriptionModal transformationLinear combinationRepresentation (mathematics)Settore ICAR/08 - Scienza Delle CostruzioniMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 |