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- W3000563606 abstract "Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow class=MJX-TeXAtom-ORD> </m:mrow> <m:mrow class=MJX-TeXAtom-ORD> <m:mo>−</m:mo> <m:mi mathvariant=normal>∞</m:mi> </m:mrow> </m:msub> <m:msubsup> <m:mi>D</m:mi> <m:mi>t</m:mi> <m:mi>β</m:mi> </m:msubsup> <m:mo>,</m:mo> </m:math> ${}_{-infty} D_t^beta,$ where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 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." @default.
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- W3000563606 date "2019-01-01" @default.
- W3000563606 modified "2023-09-27" @default.
- W3000563606 title "Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia" @default.
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- W3000563606 doi "https://doi.org/10.1515/phys-2019-0088" @default.
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