Search results for "fractional calculu"
showing 10 items of 145 documents
Structural vibration control through Tuned Liquid Column Dampers: theoretical and experimental analysis
Fractional models for capturing both relaxation and creep phase
2010
Stochastic dynamic analysis of structures with fractional viscoelastic constitutive laws
The main purpose of this thesis is to provide a new way to correctly perform stochastic analysis of structures with viscoelastic constitutive law. The reason for this kind of problem relates the fact that structures with viscoelastic materials are built in many areas of mechanical, civil and aerospace engineering. To perform this kind of stochastic analysis there are two fundamental problems. That is, the mechanical description of the viscoelastic phenomenon, and the correct representation of the external loads. Both of these problems are addressed and solved by the proposed modeling that involves some advanced mathematical tools. The reason to describe materials as viscoelastic is given by…
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …
Free energy and states of fractional-order hereditariness
2014
AbstractComplex materials, often encountered in recent engineering and material sciences applications, show no complete separations between solid and fluid phases. This aspect is reflected in the continuous relaxation time spectra recorded in cyclic load tests. As a consequence the material free energy cannot be defined in a unique manner yielding a significative lack of knowledge of the maximum recoverable work that can extracted from the material. The non-uniqueness of the free energy function is removed in the paper for power-laws relaxation/creep function by using a recently proposed mechanical analogue to fractional-order hereditariness.
Fractional viscoelastic characterization of laminated glass beams under time-varying loading
2021
Abstract Laminated glass is a composite made of elastic glass layers sandwiching thin viscoelastic polymeric interlayers. There are several types of polymers, traditionally modelled as linear viscoelastic materials using a Prony’s series of units in the Maxwell-Wiechert arrangement. We show that one single element with fractional viscoelastic properties (two constitutive parameters that depend on environmental temperature), is sufficient to provide an accurate description of the polymer response under arbitrary time-varying actions. This is a great advantage over the classical viscoelastic characterization, which requires at least 10–15 terms in the Prony’s series, each one characterized by…
An explicit mechanical interpretation of Eringen non-local elasticity by means of fractional calculus
2009
If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen non-local elastic model. Aim of the present paper is to provide a mechanical interpretation to this non-local fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; static, kinematic and constitutive equations as well as the proper boundary conditions are derived and discussed.