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Journal of Vibration and Control
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A Condensation Technique for Finite Element Dynamic Analysis Using Fractional Derivative Viscoelastic Models

Giuseppe Catania

DIEM, Dipartimento di Meccanica, Università di Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy

Silvio Sorrentino

DIEM, Dipartimento di Meccanica, Università di Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy, silvio.sorrentino{at}mail.ing.unibo.it

Alessandro Fasana

DIMEC, Dipartimento di Meccanica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

Fractional derivative rheological models are known to be very useful for 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. The increase in matrix dimensions produced by this expansion, however, is often so fast as to make the calculations too cumbersome for finite element applications. This article presents a condensation technique based on the computation of two reduced-size eigenproblems. The rheological model adopted is the fractional Zener (fractional standard linear solid) model, but the same methodology can be applied to problems using different fractional derivative linear models.

Key Words: Fractional calculus • viscoelasticity • modal analysis • finite element analysis

Journal of Vibration and Control, Vol. 14, No. 9-10, 1573-1586 (2008)
DOI: 10.1177/1077546307087429
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