الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Spring pendulum is a physical system where a piece of mass is connected to a springso that the resulting motion contains elements of both asimple pendulum and a one-dimensional spring-mass system. The system exhibits chaotic behavior and is sensitive to initial conditions. The motion of an elastic pendulum is governed by a system consists of a set of ordinary differential equations. Thissystem is much more complex than the other which governs a simple pendulum motion, as the properties of the spring add an extra dimension of freedom to the system. The importance of these kinds of pendulum models is owing to its applications in a wide range of fields such as swaying buildings, ships motion, transportation devices and rotor dynamics. In this thesis, three important models are investigated. The first one investigates a general model of a double pendulum with three degrees of freedom (DOF), in which its supported point moves in an elliptical trajectory with constant angular velocity. This point is considered one end of a massless rod with constant length, while the second end is connected with a damped harmonically excited spring pendulum. The governing system of equations of motion (EOM) is derived utilizing Lagrange’s equations in terms of three generalized coordinates, and it is solved using the multiple scales technique (MST) up to the second approximation. The modulation equations are obtained by providing the solvability conditions corresponding to the resonance cases for stable solutions. The time histories and resonance curves are outlined. In comparison with the numerical solutions (NS) of the EOM; the obtained results show a strong consistency, which implies the high accuracy of the utilized perturbation technique.