Modelling of multilayered viscoelastic rotors – an operator based approach

Abstract

This paper presents a study of the dynamic behavior of a multilayered viscoelastic rotor-shaft system, where the material damping in different layers of the rotor shaft introduces rotary dissipative forces well known to cause instability of the rotor-shaft system. For the sake of modelling, material constitutive relationships of different layers are represented in the time domain with the help of Differential time operators and Anelastic Displacement Field (ADF) variables as this combination enables easy representation of general linear viscoelastic behaviour. Equations of motion of a rotor-shaft system are obtained in time domain after discretizing the shaft- continuum by using finite beam elements. The equations thus developed have been used to find the stability of a rotor-shaft system in terms of Stability Limit of spin-Speed (SLS) as well as the frequency response when the rotor-shaft-system is subject to dynamic forcing due to disc-unbalance. Effect of thickness and placement of viscoelastic layers is studied numerically for a 2-layered, 2-disc simply supported rotor-shaft system for an example.