Journal of Mechanical Science and Technology

  • 제20권5호
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  • Pages.658-667
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  • 2006
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  • 1738-494X(pISSN)
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  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

A New Approach for the Analysis Solution of Dynamic Systems Containing Fractional Derivative

  • Hong Dong-Pyo (Department of Precision Mechanical Engineering, Choubuk National University) ;
  • Kim Young-Moon (Department of Architecture and Urban Engineering, Chonbuk National University) ;
  • Wang Ji Zeng (Department of Mechanics, Lanzhou University)
  • 발행 : 2006.05.01
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초록

Fractional derivative models, which are used to describe the viscoelastic behavior of material, have received considerable attention. Thus it is necessary to put forward the analysis solutions of dynamic systems containing a fractional derivative. Although previously reported such kind of fractional calculus-based constitutive models, it only handles the particularity of rational number in part, has great limitation by reason of only handling with particular rational number field. Simultaneously, the former study has great unreliability by reason of using the complementary error function which can't ensure uniform real number. In this paper, a new approach is proposed for an analytical scheme for dynamic system of a spring-mass-damper system of single-degree of freedom under general forcing conditions, whose damping is described by a fractional derivative of the order $0<{\alpha}<1$ which can be both irrational number and rational number. The new approach combines the fractional Green's function and Laplace transform of fractional derivative. Analytical examples of dynamic system under general forcing conditions obtained by means of this approach verify the feasibility very well with much higher reliability and universality.

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참고문헌

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