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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한기계학회 Journal of Mechanical Science and Technology Journal of Mechanical Science and Technology Vol.20 No.5
- 발행연도
- 2006.5
- 수록면
- 658 - 667 (10page)
이용수
초록· 키워드
오류제보하기
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＜α＜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.
목차
Abstract
1. Introduction
2. Fractional Dynamic Model and General Solution
3. Expression for the Fractional Green‘s Function
4. Application Analysis of Vibration under Different Forcing Conditions
5. Conclusions
Acknowledgments
References
Appendix
참고문헌 (21)
참고문헌 신청
Agrawal, O. P., 2001, "Stochastic Analysis of Dynamic System Containing Fractional Derivatives," Journal of Sound and Vibration, Vol.247, No.5, pp.927~938.
Bagley, R. L. and Torvik, P. J., 1983, "Fractional Calculus-a Different Approach to the Analysis of Viscoelastic ally Damped Structures," AIAA Journal, Vol.21, pp.741~748.
Elshehawey, E. F., Elbarbary, E. M. E., Afifl, N. A. S. and EI-Shahed, M., 2001, "On the Solution of Theendolymph Equation Using Fractional Calculus," Applied Mathematics and Computation, Vol.124, pp.337~341.
Enelund, M. and Josefson, B. L., 1997, "Time-domain Finite Element Analysis of Viscoelastic Structures with Fractional Derivative Constitutive Relations," American Institute of Aeronautics and Astronautics Journal, Vol.35, pp.1630~1637.
Enelund, M., Ahler, L. M., Runesson, K. and Jonsefson, B. L., 1999, "Formulation and Integration of the Standard Linear Viscoelastic Solid with Fractional Order Rate Laws," International Journal of Solid and Structures, Vol.36, pp.2417~2442.
Bagley, R. L. and Torvik, P. J., 1983, "Fractional Calculus-a Different Approach to the Analysis of Viscoelastic ally Damped Structures," AIAA Journal, Vol.21, pp.741~748.
Elshehawey, E. F., Elbarbary, E. M. E., Afifl, N. A. S. and EI-Shahed, M., 2001, "On the Solution of Theendolymph Equation Using Fractional Calculus," Applied Mathematics and Computation, Vol.124, pp.337~341.
Enelund, M. and Josefson, B. L., 1997, "Time-domain Finite Element Analysis of Viscoelastic Structures with Fractional Derivative Constitutive Relations," American Institute of Aeronautics and Astronautics Journal, Vol.35, pp.1630~1637.
Enelund, M., Ahler, L. M., Runesson, K. and Jonsefson, B. L., 1999, "Formulation and Integration of the Standard Linear Viscoelastic Solid with Fractional Order Rate Laws," International Journal of Solid and Structures, Vol.36, pp.2417~2442.
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