الفهرس 
Chapter 1: IntroductionOnly 14 pages are availabe for public view
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Abstract
The main aim of this thesis is a mathematical study for mechanical vibrations
of quarter car suspension system described by a nonlinear ordinary
differential equation. It is being suggested some forms of active conventional
control techniques with times delay to suppress its vibrations. They are
proportional derivative (PD), positive position feedback (PPF), nonlinear
saturation controllers (NSC), PD with PPF and PD with NSC. The
comparison between the controllers output are investigated to get the best
output of the controller by suppressing the vibration from the system. The
car is excited by the disturbances on the road surface. The active controlled
suspension system is investigated to comfort a ride improvement and provide
good leveling of stability at simultaneous resonance. The main idea is
attached the magneto-rheological or electrical-rheological damper in parallel
with the hydraulic damper (passive element). The passive components are
the backup for the failure of active controller .The controller is developed for
suppressing the vibration of the closed loop control system and
implementation by electronic system designed in the car. Then applying the
multiple scales perturbation method to solve these nonlinear differential
equations. The corresponding frequency-response equations are extracted and
plotted at the different system parameters. The obtained graphs are
confirmed numerically applying Rung-Kutta algorithm of fourth order. The
concluded results are summarized and a comparison of the obtained results
and the previously published results is held. Finally, a list of references are
cited