Mutalikdesai, Pavan Ramesh (2013) *Study of Modal Behaviour of Viscoelastic Rotors Using Finite Element Method.* MTech thesis.

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## 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

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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.

Item Type: | Thesis (MTech) |
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Uncontrolled Keywords: | Internal Material Damping, Modal analysis, Modal Damping Factor, Stability Limit of Spin Speed, directional Frequency Response Function (dFRF). |

Subjects: | Engineering and Technology > Mechanical Engineering > Machine Design |

Divisions: | Engineering and Technology > Department of Mechanical Engineering |

ID Code: | 5158 |

Deposited By: | Hemanta Biswal |

Deposited On: | 10 Dec 2013 11:46 |

Last Modified: | 20 Dec 2013 15:37 |

Supervisor(s): | Roy, H |

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