Dynamical stability of viscoelastic column with fractional derivative constitutive relation
- 41 Downloads
The dynamic stability of simple supported viscoelastic column, subjected to a periodic axial force, is investigated. The viscoelastic material was assumed to obey the fractional derivative constitutive relation. The governing equation of motion was derived as a weakly singular Volterra integro-partial-differential equation, and it was simplified into a weakly singular Volterra integro-ordinary-differential equation by the Galerkin method. In terms of the averaging method, the dynamical stability was analyzed. A new numerical method is proposed to avoid storing all history data. Numerical examples are presented and the numerical results agree with the analytical ones.
Key wordsviscoelastic column fractional derivative constitutive relation averaging method weakly singular Volterra integro-differential equation dynamical stability
CLC numbersO165.6 O345
Unable to display preview. Download preview PDF.
- HUANG Wen-hu, WANG Xing-qing, ZHANG Jing-hui, et al. Some advances in the vibration control of aerospace flexible structures [J].Advances in Mechanics, 1997,27(1):5–18. (in Chinese)Google Scholar
- Enelund M, Mahler L, Runesson K, et al. Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws [J].Int J Solids Strut, 1999,36(7):1417–1442.Google Scholar
- Samko S G, Kilbas A A, Marricher O Z.Fractional Integrals and Derivatives: Theory and Application [M], New York: Gordon and Breach Science Publishers, 1993.Google Scholar
- LIU Yan-zhu, CHEN Wen-liang, CHEN Li-qun.Mechanics of Vibrations [M]. Beijing: Advanced Educational Press, 1988. (in Chinese)Google Scholar