Dynamics of polymer and polymer composite rotors – An operator based finite element approach

Abstract

This paper presents a differential time operator based approach to obtain equations of motion of a generally viscoelastic rotor–shaft after discretizing the shaft continuum with finite beam elements. The equations of motion are utilized to study dynamic behaviour of a generic viscoelastic composite rotor–shaft comprising of viscoelastic reinforcing fibres in a viscoelastic matrix. Anelastic Displacement Field model (ADF), a time-domain material model, is used to represent the viscoelastic constitutive relationships. The model parameters are extracted by a Genetic Algorithm based optimisation procedure from frequency-dependent values of storage and loss modulii. For an example the composite rotor is assumed to be made by reinforcing unidirectional long graphite fibres in a PVC (Poly-Vinyl-Chloride) matrix. The equations of motion are used for numerical simulation as well as comparison of stability limit of spin speed and unbalance response amplitude at the disc of two rotor–shaft systems, one made of pure PVC and the other made by reinforcing graphite fibres in the PVC matrix. It is concluded that reinforcement of long fibre, enhances the stability limit of spin speed as well as the first natural frequency in comparison with those of rotor–shaft made of pure PVC.