Stability of axially accelerating viscoelastic beams: asymptotic perturbation analysis and differential quadrature validation

An asymptotic perturbation method is proposed to investigate stability of an axially accelerating viscoelastic beam. The material time derivative is used in the viscoelastic constitutive relation. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The stability condition can be determined via the asymptotic perturbation method. The differential quadrature scheme is developed to solve numerically the equation of axially accelerating viscoelastic beams with simple supports. The stability boundaries are numerically located in the summation parametric resonance and the principal parametric resonance. Numerical examples show the effects of the beam viscoelasticity and the mean axial speed. The numerical calculations validate the analytical results in the principal parametric resonance.