Dynamical behavior of viscoelastic functionally graded tapered rotors partially filled with liquid

In this study, the dynamics and stability of a viscoelastic functionally graded tapered rotor partially filled with liquid are investigated. It is assumed that the radius of the rotor varies linearly, while the density and elastic modulus change exponentially along the longitudinal direction of the rotor. The Kelvin-Voigt model is utilized to describe the viscoelastic material. The governing equations of motion of the rotor system are established via Hamilton's principle. By using the Laplace transform and the Galerkin method, the characteristic equation of the system is obtained. Then, the complex frequencies of the system are computed in the first order on the basis of the characteristic equation. The critical divergence and flutter rotating speeds are acquired. The stability of the rotor system with viscoelastic effects is examined. Finally, the effects of the main parameters including the gradient parameter, taper ratio, hollowness ratio, mass ratio, cavity ratio, and the viscoelastic coefficient on the dynamical behavior of the system are discussed, respectively. The results show that the stability of the system is strongly dependent on these parameters. Also, the results indicate that the viscoelasticity of the material mainly affects the stability evolution of the rotor system.