Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation

LI Gen-guo; ZHU Zheng-you; CHENG Chang-jun

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(3): 250-258

LI Gen-guo, ZHU Zheng-you, CHENG Chang-jun. Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation[J]. Applied Mathematics and Mechanics, 2001, 22(3): 250-258.

Citation:

LI Gen-guo, ZHU Zheng-you, CHENG Chang-jun. Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation[J]. Applied Mathematics and Mechanics, 2001, 22(3): 250-258.

Citation:

LI Gen-guo, ZHU Zheng-you, CHENG Chang-jun. Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation[J]. Applied Mathematics and Mechanics, 2001, 22(3): 250-258.

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Dynamical Stability of Viscoelastic Column With Fractional Derivative Constitutive Relation

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;
2.
Department of Mathematics, Shanghai University, Shanghai 201800, P R China;
3.
Department of mechanics, Shanghai University, Shanghai 200072, P R China

Received Date: 2000-01-25
Rev Recd Date: 2000-12-19
Publish Date: 2001-03-15

Abstract

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-di-f ferential 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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References(10)

References

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