الفهرس 
Mathematical analysisOnly 14 pages are availabe for public view
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Abstract
Vibrations and dynamic chaos are undesired phenomenon in structures. They cause disturbance, discomfort, damage and destruction of the system or the structure. Money, time and effort are spent to get rid of both vibrations, noise and chaos or to minimize them. Also, resonance of oscillating systems may lead to their damage or destruction. For these reasons it is very important to study the behavior of the vibrating system under different resonance conditions.
The main object of this thesis is to study vibration behavior of the dynamical systems. Such systems represent many applications in the Held of physics, mechanics, electronics and engineering. One of the important systems expressed here is one degree of freedom system, which is governed by a second order non-linear differential equation. The nonlinearity of this system depends on the spring stiffness or the damping factors, or the excitation force.
In this work one degree of freedom system representing the vibration of a buckled beam under either external or both external and parametric excitation force have been considered. An extensively studies about the buckled beam have been demonstrated in chapter one.
In chapter two the non-linear differential equation that describe the vibration of buckled beam subjected to harmonic excitation force has been considered and solved analytically and numerically. The steady state response and its stability near the primary resonance case is investigated and studied. Effects of the different parameters on the system behavior and jump phenomenon on the frequency response curves are also investigated and studied. Some of the results of this chapter are published [44].