Dynamic Stability of an Axially Accelerating Viscoelastic Beam With Two Fixed Supports

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.