الفهرس 
Title : Solution of Some Problems In - non - Linear Oscillation
ContantsOnly 14 pages are availabe for public view
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Abstract
The present thesis deals with some non-linear oscillation problems which have important applications in many engineering and industrial fields . Some physical systems with sub harmonic , super harmonic , sub -super harmonic oscillations, combination and simultaneous oscillations are considered .Such problems may be described by a non {u2013} linear ordinary differential equations with one or more degrees of freedom.The thesis consists of an introduction , four chapters , and a list of references.Chapter I is concerned with a sub - harmonic synchronization of even order for weakly nonlinear single degree of freedom system under a weakly non -linear parametric excitation. Approximate solution is obtained using synchronization method. Comparison and graphical studies are made to show the behavior of the periodic solutions and their stability. Chapter II is concerned with harmonic resonance of a weakly nonlinear system under a Bi {u2013} harmonic external excitation-. The multiple scale methods are used to get an approximation solution.The stability of the steady state case is illustrated.Chapter III, is devoted to the study of sub - harmonic oscillation of order one half and super harmonic of order two for a physical system considered in chapter I Analytical expressions for the amplitudes , phase, and a solution to the first order approximation are obtained.The stability behavior of the steady state is studied graphically.Chapter IV is devoted to the oscillation motion of a twin {u2013} tail of an aircraft. The twin -tail oscillates under viscous damping resistance , and it is subjected to a multi periodic forces with different frequencies . Also, this system is controlled by negative ( linear and quadratic ) velocity feedback. The method of multiple time scale perturbation is used to solve the non {u2013}linear differential equation to the first - order approximation. The stability of the system and different resonance cases are studied.A comparison study is made with the results available and published in the literature