Study of Modal Behaviour of Viscoelastic Rotors Using
Finite Element Method

Abstract

The Property which combines elasticity and viscosity is called as viscoelasticity. Such
materials store energy as well as dissipate it to the thermal domain when subjected to
dynamic loading. The storage and loss of energy depends upon the frequency of excitation.
Modeling of elastic materials is easier, compared to the Modeling of viscoelastic materials.
This work attempts to study the influence of internal material damping on the modal
behaviour of a rotor shaft system. Rotary forces are generated due to the internal material
damping of rotor shaft system and are proportional to the spin speed and acts tangential to
the rotor orbit. These forces influence the dynamic behaviour of a rotor and tend to
destabilize the rotor shaft system as spin speed increases. Hence, the modal behaviour of rotor
shaft is studied by finite element method, to get better ideas about the dynamic behaviour of
the rotor shaft system.
The dynamic characteristics of rotor systems are closely related with the rotor spin
speed; hence the directivity of modes becomes very important in rotor dynamics. In the
approach used in this work, a natural mode of the rotor is represented as the sum of two sub
modes which are rotating to the forward and backward directions. This work explains the use
of directional information when the equation of motion of a rotor is formulated in complex
form. This methodology has an advantage of incorporating the directionality. Work
establishes the fact that directional frequency response functions (dFRF) relate the forward
and backward components of the complex displacement and excitation functions. The dFRFs
are obtained as the solution to the forced vibration solution to the equation of motion.
The finite element analysis is used for modeling the system. The rotor shaft system with
simply supported ends having three discs has been considered for the study. In this work the Study of modal behaviour of viscoelastic rotors using finite element method
NIT Rourkela Page III

effects of internal viscous damping have been incorporated into the finite element model. In
the analysis, the equations of motion are obtained to a good degree of accuracy by
discretizing the rotor-shaft continuum using 2-noded finite Rayleigh beam elements. These
equations are used for eigenanalysis. A finite element code is written in MATLAB to find out
the eigenvalues, eigenvectors and modal damping factor. Stability limit of spin speed and
effect of modal damping factor on the spin speed have been studied. This work establishes the
fact that directional frequency response functions (dFRF) relate the forward and backward
components of the complex displacement and excitation functions. The dFRFs are obtained as
the solution to the forced vibration solution to the equation of motion. The Campbell diagram
and the dFRF plots are obtained by using the Matlab.