Nonlinear Delay Harmonic Oscillator Using Perturbation Analysis

Abstract

In this thesis, a mathematical study for mechanical vibrations of some dynamical systems in the presence of time-delay in some dynamical systems described by nonlinear ordinary differential equations. In chapter one, we stated a literature review, and some of work done in this field. In chapter two, we present comprehensive study for resonance cases of nonlinear dynamical system. Time-delayed position-velocity controller is proposed to suppress the considered system nonlinear vibrations. The acquired analytical results revealed that the loop-delay has a great influence on the controller efficiency. In chapter three, different time-delayed controllers are introduced to explore their efficiencies in suppressing the nonlinear oscillations of a parametrically excited system. In chapter four, a study for nonlinear integral resonant controller is presented that is used to suppress the vibration amplitude of a nonlinear dynamic model at parametrically excited system.