Dynamic stability of an axially accelerating viscoelastic beam

{ "0" : "Department of Mechanics, Shanghai University, Shanghai 200436, China" , "1" : "Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China" , "3" : "Axially accelerating beam" , "4" : "Viscoelasticity" , "5" : "Method of averaging"}
European Journal of Mechanics - A/Solids (Impact Factor: 1.9). 07/2004; DOI: 10.1016/j.euromechsol.2004.01.002

ABSTRACT This work investigates dynamic stability in transverse parametric vibration of an axially accelerating viscoelastic tensioned beam. The material of the beam is described by the Kelvin model. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a infinite set of ordinary-differential equations under the fixed–fixed boundary conditions. The method of averaging is employ to analyze the dynamic stability of the 2-term truncated system. The stability conditions are presented and confirmed by numerical simulations in the case of subharmonic and combination resonance. Numerical examples demonstrate the effects of the dynamic viscosity, the mean axial speed and the tension on the stability conditions.

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    ABSTRACT: The dynamic stability of an axially accelerating viscoelastic beam with two fixed supports is investigated. The Kelvin model is used for the constitutive law of the beam. A small simple harmonic is allowed to fluctuate about the constant mean speed applied to the beam, and the governing equation is truncated using the Galerkin method based on the eigenfunctions of the stationary beam. The averaged equations are derived for the cases of subharmonic and combination resonance. Finally, numerical examples are presented to demonstrate the effects of the viscosity coefficient, the mean axial speed and the beam bending stiffness on the stability boundaries.
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