On the stability of viscoelastic tapered rotors with internal flow

In this paper, the stability of viscoelastic tapered rotors with internal flow is investigated. The constitutive equation of the viscoelastic material is described on the basis of the Kelvin-Voigt model. Using Hamilton's principle, the governing equation of motion for the rotor system is formulated. The Galerkin discretization technique is then employed to discrete the partial differential equations. Thus, the complex frequencies in the first two modes of the simply supported rotor system are calculated, which are utilized to discriminate the stability of the system. Then, the stability evolution process of the system is analyzed. Also, the divergence flow velocity and spinning speed are computed numerically. Finally, a comprehensive parametric discussion is carried out to evaluate the effect of parameters such as hollowness ratio, mass ratio, taper ratio, and viscosity coefficient on the stability and critical spinning speed of the fluid-structure interaction system. The results show that for a viscoelastic tapered rotor with the internal flow, the rotor experiences a stability evolution of "stable-first mode divergence-stable-first mode flutter-first mode divergence-first mode flutter." The dynamic behavior of the rotor system depends strongly on the mass ratio, hollowness ratio, taper ratio, flow velocity, and viscoelasticity of the material.