Quasi-Static Analysis of Beam Described by Fractional Derivative Kelvin Viscoelastic Model under Lateral Load

Qing Zhao Yao; Lin Chao Liu; Qi Fang Yan

doi:10.4028/www.scientific.net/AMR.189-193.3391

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 189-193Quasi-Static Analysis of Beam Described by...

Quasi-Static Analysis of Beam Described by Fractional Derivative Kelvin Viscoelastic Model under Lateral Load

Abstract:

The beam is assumed to obey a three-dimensional viscoelastic fractional derivative constitutive relations, the mathematical model and governing equations of the quasi-static and dynamical behavior of a viscoelastic Euler-Bernoulli beam are established, the quasi-static mechanical behavior of Euler-Bernoulli beam described by fractional derivative model is investigated, and the analytical solution is obtained by considering the properties of the Laplace transform of Mittag-Leffler function and the properties of fractional derivative. The result indicate that the quasi-static mechanical behavior of Euler-Bernoulli beam described by fractional derivative viscoelastic model can reduced to the cases of classic viscoelastic and elastic, the order of fractional derivative has great effect on the quasi-static mechanical behavior of Euler-Bernoulli beam.

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Periodical:

Advanced Materials Research (Volumes 189-193)

Pages:

3391-3394

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.189-193.3391

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Online since:

February 2011

Authors:

Qing Zhao Yao, Lin Chao Liu, Qi Fang Yan

Keywords:

Constitutive Relation, Fractional Derivative, Mittag-Leffler Function, Quasi-Static, Viscoelasticity

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