Search results for " fractional calculus"
showing 10 items of 35 documents
Electrical analogous in viscoelasticity
2014
In this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical operators. Viscoelastic models have elastic and viscous components which are obtained by combining springs and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic models can be equivalently modeled as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. Moreover, a comparison with numerical expe…
Fractional visco-elastic systems under normal white noise
2011
In this paper an original method is presented to compute the stochastic response of singledegree- of-freedom structural systems with viscoelastic fractional damping. The key-idea stems from observing that, based on a few manipulations involving an appropriate change of variable and a discretization of the fractional derivative operator, the equation of motion can be reverted to a coupled linear system involving additional degrees of freedom, the number of which depends on the discretization adopted for the fractional derivative operator. The method applies for fractional damping of arbitrary order a (0 < α < 1). For most common input correlation functions, including a Gaussian white noise, …
Evaluation of the temperature effect on the fractional linear viscoelastic model for an epoxy resin
2016
The paper deals with the evolution of the parameters of a fractional model for different values of temperature. An experimental campaign has been performed on epoxy resin at different levels of temperature. It is shown that epoxy resin is very sensitive to the temperature.
A new representation of power spectral density and correlation function by means of fractional spectral moments
2009
In this paper, a new perspective for the representation of both the power spectral density and the correlation function by a unique class of function is introduced. We define the moments of order gamma (gamma being a complex number) of the one sided power spectral density and we call them Fractional Spectral Moments (FSM). These complex quantities remain finite also in the case in which the ordinary spectral moments diverge, and are able to represent the whole Power Spectral Density and the corresponding correlation function.
Prestress and experimental tests on fractional viscoelastic materials
2013
Creep and/or Relaxation tests on viscoelastic materials show a power-law trend. Based upon Boltzmann superposition principle the constitutive law with a power-law kernel is ruled by the Caputo’s fractional derivative. Fractional constitutive law posses a long memory and then the parameters obtained by best fitting procedures on experimental data are strongly influenced by the prestress on the specimen. As in fact during the relaxation test the imposed history of deformation is not instantaneously applied, since a unit step function may not be realized by the test machine. Aim of this paper, it is shown that, the experimental procedure, and in particular the initial ramp to reach the constan…
Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams
2022
A consistent nonlocal viscoelastic beam model is proposed in this paper. Specifically, a Timoshenko bending problem, where size- and time-dependent effects cannot be neglected, is investigated. In order to inspect scale phenomena, a stress-driven nonlocal formulation is used, whereas to simulate time-dependent effects, fractional linear viscoelasticity is considered. These two approaches are adopted to develop a new Timoshenko bending model. Analytical solutions and application samples of the proposed formulation are presented. Moreover, in order to show influences of viscoelastic and size effects on mechanical response, parametric analyses are provided. The contributed results can be usefu…
Fractional Calculus as a New Perspective in the Viscoelastic Behaviour of the Intervertebral Disc
2022
The spinal column is the load-bearing structure of the human being along with its components, which together build a strong, resistant, and stable structure, but there are a few different pathologies from which it can suffer, such as herniated discs. The intervertebral disc acts as a shock absorber and ensures the spine’s great capacity to support high loads and different states of stress, thanks to its viscoelastic properties. Some studies have attempted to describe the viscoelastic behaviour of the intervertebral disc using classical rheological models, such as the Kelvin-Voigt, or multi-parameter models. Even if these models partially describe the viscoelastic response of disc, all visco…
Timoshenko vs Euler-Bernoulli beam: fractional visco-elastic behaviour
2013
The Euler-Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of stress field or def lections of the elastic beam based on this theory. Conversely Timoshenko theory is not so much used by engineers. However in such cases Euler-Bernoulli theory that n eglects the effect of transversal shear deformation leads to unacceptable results. For inst ance when dealing with the visco-elastic behaviour the shear deformations play a fundamental role. Recent studies [1]-[2] on the response evaluation of visco-elastic Euler-Bernoulli beam under quasi-static and dynamic loads, have been stressed that for better capturing the visco-elastic behavio…