Fractional derivative rheological models were recognised to be very effective in describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems the resulting equations of motion, after a fractional state-space expansion, can still be studied in terms of modal analysis. But the growth in matrix dimensions brought about by this expansion is in general so fast as to make the calculations too cumbersome. In this paper a discretization method for continuous structures is presented, based on the Rayleigh-Ritz method, aimed at reducing the computational effort. The solution of the equation of motion is approximated by a linear combination of shapefunctions selected among the analytical eigenfunctions of standard known structures. The resulting condensed eigen-problem is then expanded in a low dimension fractional statespace. The Fractional Standard Linear Solid is the adopted rheological model, but the same methodology could be applied to problems involving different fractional derivative linear models. Examples regarding two different continuous structures are proposed and discussed in detail.

Discrete spectral modelling of continuous structures with fractional derivative viscoelastic behaviour / Catania, Giuseppe; Sorrentino, Silvio. - 1:PART A(2008), pp. 375-384. (Intervento presentato al convegno 21st Biennial Conference on Mechanical Vibration and Noise, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 tenutosi a Las Vegas (Nevada, USA) nel 4-7 september 2007) [10.1115/DETC2007-34671].

### Discrete spectral modelling of continuous structures with fractional derivative viscoelastic behaviour

#### Abstract

Fractional derivative rheological models were recognised to be very effective in describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems the resulting equations of motion, after a fractional state-space expansion, can still be studied in terms of modal analysis. But the growth in matrix dimensions brought about by this expansion is in general so fast as to make the calculations too cumbersome. In this paper a discretization method for continuous structures is presented, based on the Rayleigh-Ritz method, aimed at reducing the computational effort. The solution of the equation of motion is approximated by a linear combination of shapefunctions selected among the analytical eigenfunctions of standard known structures. The resulting condensed eigen-problem is then expanded in a low dimension fractional statespace. The Fractional Standard Linear Solid is the adopted rheological model, but the same methodology could be applied to problems involving different fractional derivative linear models. Examples regarding two different continuous structures are proposed and discussed in detail.
##### Scheda breve Scheda completa Scheda completa (DC)
2008
21st Biennial Conference on Mechanical Vibration and Noise, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
4-7 september 2007
1
375
384
Catania, Giuseppe; Sorrentino, Silvio
Discrete spectral modelling of continuous structures with fractional derivative viscoelastic behaviour / Catania, Giuseppe; Sorrentino, Silvio. - 1:PART A(2008), pp. 375-384. (Intervento presentato al convegno 21st Biennial Conference on Mechanical Vibration and Noise, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 tenutosi a Las Vegas (Nevada, USA) nel 4-7 september 2007) [10.1115/DETC2007-34671].
File in questo prodotto:
File
ASME-2007.pdf

Accesso riservato

Descrizione: Articolo principale
Tipologia: Versione dell'autore revisionata e accettata per la pubblicazione
Dimensione 405.92 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1146979`