Dynamical Stability of Viscoelastic Column with Fractional Derivative Constitutive Relation |
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| Authors: | Gen-guo Li Zheng-you Zhu Chang-jun Cheng |
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| Institution: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;Departnent of Mathernatics, Shanghai University, Shanghai 201800, P R China
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;Department of mechanics, Shanghai University, Shanghai 200072, P R China |
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| Abstract: | 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. |
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| Keywords: | viscoelastic column fractional derivative constitutive relation averaging method weakly singular Volterra integro_differential equation dynamical stability |
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