Dynamics of axially moving viscoelastic liquid-filled rotors under nonlinear stress-temperature case

This study focuses on the vibration and stability of axially moving viscoelastic liquid-filled rotors under the nonlinear stress-temperature case. Based on the Euler–Bernoulli beam theory and the Kelvin–Voigt model, the governing equations of motion of the rotor system involving the double gyroscopic coupling effect are established via the Hamilton principle. The Galerkin truncation technique is adopted to solve the complex characteristic frequencies of the rotor system. The influences of axial motion, thermal load, and material viscoelasticity on the system's frequency characteristics, complex modal motion, and time-domain response are investigated. The present model is degenerated into an axially moving beam, and the dynamical behavior is compared with literature data to verify the rationality of the proposed model and calculation method. The results show that thermal load and axial velocity exert significant impacts on the natural frequency and instability threshold of the rotor system. After considering the viscoelasticity of the material, the system exhibits complex dynamic behaviors. For the axially moving liquid-filled rotor system, the mode motion consists of traveling wave motion and whirling motion, and the complex eigenvectors of the rotor system can only describe the mode motion in the stable region. In addition, the time history of the system is governed by key factors such as thermal load, mass ratio, cavity ratio, and material viscoelasticity.