Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator where the order is a real number satisfying 0 ≤ ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < < 1,...

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Bibliographic Details
Published in:Open Physics 2019-12, Vol.17 (1), p.850-856
Main Authors: Duan, Jun-Sheng, Xu, Yun-Yun
Format: Article
Language:English
Subjects:
02.30.Hq
46.35.+z
46.40.-f
83.60.Bc
fractional derivative
vibration
viscoelasticity
viscous inertia
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Summary:The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator where the order is a real number satisfying 0 ≤ ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < < 1, while it contributes to the viscous inertia if 1 < < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.
ISSN:2391-5471
2391-5471
DOI:10.1515/phys-2019-0088