| CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
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Mechanical Analogies of Fractional Elements |
| HU Kai-Xin, ZHU Ke-Qin |
| Department of Engineering Mechanics, Tsinghua University, Beijing 100084 |
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| Cite this article: |
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HU Kai-Xin, ZHU Ke-Qin 2009 Chin. Phys. Lett. 26 108301 |
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Abstract A Ffactional element model describes a special kind of viscoelastic material. Its stress is proportional to the fractional-order derivative of strain. Physically the mechanical analogies of fractional elements can be represented by spring-dashpot fractal networks. We introduce a constitutive operator in the constitutive equations of viscoelastic materials. To derive constitutive operators for spring-dashpot fractal networks, we use Heaviside operational calculus, which provides explicit answers not otherwise obtainable simply. Then the series-parallel formulas for the constitutive operator are derived. Using these formulas, a constitutive equation of fractional element with 1/2-order derivative is obtained. Finally we find the way to derive the constitutive equations with other fractional-order derivatives and their mechanical analogies.
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| Keywords:
83.60.Bc
46.35.+z
02.30.Vv
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Received: 05 May 2009
Published: 27 September 2009
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| PACS: |
83.60.Bc
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(Linear viscoelasticity)
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46.35.+z
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(Viscoelasticity, plasticity, viscoplasticity)
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02.30.Vv
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(Operational calculus)
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