الفهرس 
On some perturbation techniquesOnly 14 pages are availabe for public view
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Abstract
1. The motion of 3DOF dynamical model consists of a connected rigid body with a harmonically excited spring pendulum moves in an elliptic path is investigated in (Chapter 2). 2. The governing system of motion is obtained using Lagrange’s equations. 3. The MS method is used to obtain the approximate solutions up to the third approximation and the solvability conditions for the steady state solutions are established. 4. The primary external resonance has been investigated according the modulation equations. 5. The comparison between the time history diagrams of the obtained approximate solutions and the numerical ones shows that there is a well agreement between them and gives an indication about the good accuracy of the used MS method. 6. The graphical representations of the Poincaré maps for the attained solutions are presented to reveal the well effect of the different parameter on the motion. 7. The mentioned study in (Chapter 2) is considered as a more general case than the previous studies in the works [20] (when the supported point is fixed and in the absence of rigid body), [21] (in the absence of a rigid body) and [56] (for a fixed supported point). 8. The motion of a simple pendulum connected with nonlinear absorber in an elliptic path is studied in (Chapter 3). It is considered that the movement of absorber is constrained to be in a longitudinal direction. 9. The approximate solutions of the equations of motion are obtained utilizing the MS technique up to the third approximation. 10. The internal and external resonances are investigated through the modulation equations. 11. The amplitude and the phase variables are renowned to study the steady state solutions and to recognize their stability conditions. 12. The equilibrium points are obtained and represented graphically to obtain the possible steady state solutions near resonances in framework of the stability conditions of these solutions. 13. Computer codes are used to represent the obtained solutions graphically in order to interpret the behavior of the dynamical system under the influence of the applied forces and the different parameters on the motion of the considered dynamical model at any time. 14. The obtained solutions generalized the previous works as its limiting cases such as in [9,11] (in the absence of absorber), [10] (when the absorber has a longitudinal direction) and [15] (when the supported point moves in a circular path and in the absence of absorber).