Asymptotic stability analysis with numerical confirmation of an axially accelerating beam constituted by the standard linear solid model

Stability of an axially accelerating viscoelastic beam constituted by the standard linear solid model is investigated. The material time derivative is used in the viscoelastic constitutive relation. The instability condition is determined for combination and principal parametric resonances via the asymptotic analysis. The differential quadrature scheme is developed to solve numerically the partial differential equation governing transverse motion of axially accelerating viscoelastic beams. The stability boundaries are numerically located in the excitation amplitude and the excitation frequency plane. Numerical simulation demonstrates the effects of the stiffness, the viscosity and constant mean speed of beam. The numerical calculations validate the analytical results in the principal parametric resonance.