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EnglishFractional hereditary materials are characterized for the presence, in the stress-strain relations, of fractional-order operators with order beta a[0,1]. In Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) exact mechanical models of such materials have been extensively discussed obtaining two intervals for beta: (i) Elasto-Viscous (EV) materials for 0a parts per thousand currency sign beta a parts per thousand currency sign1/2; (ii) Visco-Elastic (VE) materials for 1/2a parts per thousand currency sign beta a parts per thousand currency sign1. These two ranges correspond to different continuous mechanical models. In this paper a discretization scheme based upon the continuous models proposed in Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) useful to obtain a mechanical description of fractional derivative is presented. It is shown that the discretized models are ruled by a set of coupled first order differential equations involving symmetric and positive definite matrices. Modal analysis shows that fractional order operators have a mechanical counterpart that is ruled by a set of Kelvin-Voigt units and each of them provides a proper contribution to the overall response. The robustness of the proposed discretization scheme is assessed in the paper for different classes of external loads and for different values of beta a[0, 1].
DI PAOLA, M., Pinnola, F., & Zingales, M. (2013). A discrete mechanical model of fractional hereditary materials. MECCANICA, 48(7), 1573-1586.
| Data di pubblicazione: | 2013 |
| Titolo: | A discrete mechanical model of fractional hereditary materials |
| Autori: | |
| Citazione: | DI PAOLA, M., Pinnola, F., & Zingales, M. (2013). A discrete mechanical model of fractional hereditary materials. MECCANICA, 48(7), 1573-1586. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s11012-012-9685-4 |
| Abstract: | Fractional hereditary materials are characterized for the presence, in the stress-strain relations, of fractional-order operators with order beta a[0,1]. In Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) exact mechanical models of such materials have been extensively discussed obtaining two intervals for beta: (i) Elasto-Viscous (EV) materials for 0a parts per thousand currency sign beta a parts per thousand currency sign1/2; (ii) Visco-Elastic (VE) materials for 1/2a parts per thousand currency sign beta a parts per thousand currency sign1. These two ranges correspond to different continuous mechanical models. In this paper a discretization scheme based upon the continuous models proposed in Di Paola and Zingales (J. Rheol. 56(5):983-1004, 2012) useful to obtain a mechanical description of fractional derivative is presented. It is shown that the discretized models are ruled by a set of coupled first order differential equations involving symmetric and positive definite matrices. Modal analysis shows that fractional order operators have a mechanical counterpart that is ruled by a set of Kelvin-Voigt units and each of them provides a proper contribution to the overall response. The robustness of the proposed discretization scheme is assessed in the paper for different classes of external loads and for different values of beta a[0, 1]. |
| URL: | http://link.springer.com/article/10.1007%2Fs11012-012-9685-4 |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/10447/83756
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