الفهرس 
Mathematical AnalysisOnly 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 a rotating compressor blade dynamical system that
are described by a pair of coupled nonlinear ordinary differential equations.
Different active control techniques, i.e. Positive Position Feedback (PPF),
Nonlinear Saturation Controller (NSC), Proportional-Derivative controller (PD)
and improved PPF, are being suggested to suppress such vibrations ideally
and in the presence of time delay (during sensing and actuating processes).
PPF, NSC and improved PPF are applied to control the primary
resonance case, while PD is applied to control primary, super-harmonic and
parametric resonance cases. The multiple time scales perturbation technique
is applied to solve those nonlinear differential equations approximately. Then,
the corresponding frequency-response equations are extracted and plotted
at different system parameters variations. The stability of the derived solutions
is investigated via Lyapunov first (indirect) method to show the best case for
the system to work in a stable steady state behavior.
The obtained graphs are confirmed numerically applying fourth order
Rung-Kutta algorithm to act as a simulation for the real system. The
concluded results are summarized and a comparison of the different control
methods is presented. Also, a comparison with the available previously
published work is included. Finally, a list of references is cited.