Finite Element Modelling of Viscoelastic Rotors: An Operator Based Approach

Abstract

Damping exists in every material in varying degrees. So materials in general are viscoelastic in nature.Modelling of viscoelastic materials is always difficult since such materials store energy as well as dissipate it to the thermal domain. This paper presents a theoretical study of the dynamics of a viscoelastic rotorshaft system, where the internal material damping in the rotor shaft introduces a rotary force well known to cause instability of the rotor-shaft system. For this the material constitutive relationship has been represented by a differential time operator. Use of operators enables to consider general linear viscoelastic behaviours, represented in the time domain, for which, in general, instantaneous stress and its derivatives are proportional to instantaneous strain and also its derivatives. The operator may be suitably chosen according to the material model. An efficient modelling technique for viscoelastic material augmenting thermodynamic field (ATF) has been found in literature. The constitutive relationships for ATF approach is represented in differential time operator to obtain the equations of motion of a rotorshaft system after discretizing the system using finite element method. The equations thus developed may easily be used to find the stability limit speed of a rotor-shaft system as well as the time response when the rotor-shaft-system is subjected to any kind of dynamic forcing function.