الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The main objective of this thesis is a mathematical study for the nonlinear lateral
vibrations of rotating machinery. Rotating machinery vibrations are usually simulated using a
two-degree-of freedom nonlinear system known as Jeffcott-rotor system. Two basic models of
Jeffcott-rotor system have been investigated. The first is a horizontally supported nonlinear
Jeffcott-rotor system. The second is a vertically supported nonlinear Jeffcott-rotor system.
Influences of geometric nonlinearity, disc eccentricity, and rotor weight on the considered
systems vibrations were studied. Different control algorithms were proposed to suppress these
nonlinear vibrations. Moreover, bifurcation behaviors for both the horizontally and vertically
supported nonlinear Jeffcott rotor systems that have a transversely cracked shaft were
discussed for the purposes of crack diagnosis. All different mathematical models were analyzed
analytically applying multiple scales perturbation method. The acquired analytical results were
validated numerically utilizing the appropriate standard Matlab solvers. All obtained results
through this research were summarized and different comparisons were performed. Finally, a
list of references regarding this discipline was cited, where the thesis is outlined as follows:
Chapter 1 Presents the motivations for studding the rotating machinery vibrations and
the necessary background to understand the causes of vibrations and main sources of
nonlinearity in such machines. In addition, some related research papers concerning nonlinear
vibrations analysis and control of rotating machinery, thesis objectives, and thesis organization
are included.
Chapter 2 introduces a comprehensive study to lateral vibrations analysis and control
of a horizontally supported nonlinear Jeffcott-rotor system. The mathematical model
simulating the considered system vibrations was derived. Multiple scales perturbation method
and the standard Matlab solver ODE45 and DDE23 are employed to investigate the system
dynamical behaviors. Five different control techniques are suggested to suppress the system
vibrations.
Chapter 3 is devoted to modeling, simulating, and control lateral vibrations of a
vertically supported nonlinear Jeffcott-rotor system. Three different control algorithms are
purposed to suppress the nonlinear system vibrations. Multiple scales perturbation method and
standard Matlab solvers ODE45 and DDE23 are utilized to analyze the considered system
vibrations before and after control.
Chapter 4 is dedicated to analyze the dynamical interactions for both the vertically and
horizontally supported nonlinear Jeffcott rotor system when their shafts having transverse
cracks. Equations of motion of the cracked systems are studied analytically using multiple
scales perturbation method, and numerically by means of bifurcation diagrams, frequency
spectrum, whirling orbits, and time histories. It is found that the obtained results can be
utilized for the purpose of cracks diagnosis.
Chapter 5 introduces the most important results obtained in chapter 2, 3, and 4, and
comparisons between the different control algorithms. Moreover, recommendations for future
work are also included. Following to chapter 5, a list of references is included.