Dynamic stability of a beam-model viscoelastic pipe for conveying pulsative fluid

The dynamic stability in transverse vibration of a viscoelastic pipe for conveying pulsative fluid is investigated for the simply-supported case. The material property of the beam-model pipe is described by the Kelvin-type viscoelastic constitutive relation. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. The method of multiple scales is applied directly to the governing partial differential equation without discretization when the viscoelastic damping and the periodical excitation are considered small. The stability conditions are presented in the case of subharmonic and combination resonance. Numerical results show the effect of viscosity and mass ratio on instability regions.