2002•Unpublished venueRequires access

QUASI-STATIC AND DYNAMICAL ANALYSIS FOR VISCOELASTICTIMOSHENKO BEAM WITH FRACTIONAL DERIVATIVECONSTITUTIVE RELATION

Zheng Zhu

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 parameters 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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Key concepts: Viscoelasticity, Timoshenko beam theory, Beam (structure), Rotary inertia, Deflection (physics), Classical mechanics, Vibration, Constitutive equation