Studies on the Motion of Continuous Viscoelastic Rotors
Norwood, Robert Lee
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https://hdl.handle.net/2142/68513
Description
Title
Studies on the Motion of Continuous Viscoelastic Rotors
Author(s)
Norwood, Robert Lee
Issue Date
1980
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
This analytical investigation of continuous viscoelastic rotor motion is based upon undeformed rotor geometry being that of a right circular cylindrical shaft. The derivation of the motion equations for this Euler beam rotating shaft utilizes the work-energy approach. It is assumed that constant torque is applied at the shaft ends which are fixed in long ideal bearings. The derived field equations are three coupled, higher order, linear, partial differential equations. The coupling is effected through the shaft unbalance forcing terms. In this study, both coupled and uncoupled motion is considered.
The uncoupled steady-state motion analysis includes single mode expansion with internal and external damping. The solution of the motion equations is written with general initial conditions of position and velocity. The results show that the backward whirl mode is positively damped for all rotational speeds; that the forward mode is stable for a range of speeds; and that with no external damping, speeds beyond the first critical are unstable.
The uncoupled non steady-state motion analysis concerns an initially bent shaft returning to a straight configuration under deceleration with external damping. The results describe the decay of modal motion as it depends on the damping factor, damped natural frequency and angular position.
The coupled steady-state motion analysis investigates the effect of various mass unbalance position vectors on the torsion coordinate. The results show that with particular unbalance configurations where the unbalance is non-planar or external damping, the shaft undergoes torsion different than that due solely to end applied torques. Additionally, it is shown that shaft deflection increases with shaft length when rotating at natural frequency.
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