Quasi-Static and Dynamical Analysis for Viscoelastic Timoshenko Beam With Fractional Derivative Constitutive Relation

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

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(1): 1-10

ZHU Zheng-you, LI Gen-guo, CHENG Chang-jun. Quasi-Static and Dynamical Analysis for Viscoelastic Timoshenko Beam With Fractional Derivative Constitutive Relation[J]. Applied Mathematics and Mechanics, 2002, 23(1): 1-10.

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Quasi-Static and Dynamical Analysis for Viscoelastic Timoshenko Beam With Fractional Derivative Constitutive Relation

1.
Shanghai Institute of Applied Mathematics and Mechancis, Shanghai University, Shanghai 200072, P R China;
2.
Department of Mathematics, Shanghai University, Shanghai 200072, P R China;
3.
Shanghai Supercomputer Center, Shanghai 201203, P R China;
4.
Department of Mechanics, Shanghai University, Shanghai 200072, P R China

Received Date: 2000-10-27
Rev Recd Date: 2001-08-23
Publish Date: 2002-01-15

Abstract

Abstract

The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived.The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation.The quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained.The influence of material paraeters on the deflection is investigated.The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions.And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.

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References(11)

References

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