الفهرس 
1 IntroductionOnly 14 pages are availabe for public view
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Abstract
The main objective of this thesis is a mathematical study for mechanical vibrations of some dynamical systems described by nonlinear
ordinary differential equations. We studied two basic systems. The first is
a single-degree-of-freedom system simulating the nonlinear vibrations of
a cantilever beam. The second one is a two-degree-of-freedom system
simulating the rotor active magnetic bearing vibrations. We suggested some forms of active conventional control techniques to suppress such vibrations. Then, we applied the multiple scales perturbation method to solve those nonlinear equations. The corresponding frequency-response equations were extracted and presented graphically at the different
system parameters. The obtained curves were confirmed numerically
applying Rung-Kutta algorithm. The deduced results were summarized
and a comparison of the different control methods was presented. Finally,
important list of references was cited.
This thesis consists of four chapters as follows:
The first chapter is concerned with introducing the background
necessary to understand the mechanical vibration problem, some of the
important researches that deal with the nonlinear vibrations of the
cantilever beam and the rotor active magnetic bearing system, the thesis
objectives, and the thesis organization.
A mathematical study for the two considered systems (cantilever
beam, and rotor active magnetic bearing) subjected to the different control methods was presented in chapter two. The autonomous amplitude-phase modulating equations were extracted applying the
multiple scale perturbation method. Then, the corresponding frequencyresponse equations were deduced.
The third Chapter is devoted to solving the frequency-response
equations given at chapter two numerically, and presents them at
graphical forms. Also the discussion of each control case was presented.
In chapter four, the most important results were concluded and
recommendations for the open research directions were given.