الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 221 |  |  |
| | | from | 221 | | |
Abstract
In this thesis, three different models are investigated. The first one studies the motion of 2DOF dynamical model, consisting of a nonlinear spring pendulum moves in an elliptic trajectory with constant angular frequency under the influence of two harmonic forces in the longitudinal and transverse direction besides a harmonic external moment at the pivot point. The second model investigates the motion of another 3DOF dynamical model, consisting of a nonlinear damped spring pendulum connected with a linear damped absorber moves in an elliptic trajectory with constant angular frequency under the influence of an external force in the longitudinal direction of the spring besides an external moment at the pivot point. Finally, in the third model, we investigate the motion of the last model with, 3DOF in which it is consists of a nonlinear damped spring pendulum connected with a linear damped absorber moves in an elliptic trajectory with constant angular frequency in which the absorber is orthogonal to the spring’s direction under the influence of an external force in the longitudinal direction of the spring besides an external moment at the pivot point. For the above three models; the EOM are obtained using the Lagrange’s equations and solved asymptotically using the MSM up to the third approximations. The analytical solutions (AS) are compared with the numerical solutions (NS) for the first two models to show the consistence between them and to reveal the high accuracy of the used perturbation methods. The solvability conditions are obtained in view of the resonance cases and the steady-state oscillations, in which the stability of the studied dynamical models are investigated using the Criterion of Routh-Hurwitz (CRH). Time histories of the solutions and resonance curves are plotted to show the influence of several parameters on the solutions. Areas of stability and instability are also identified where it was found that the system is stable over a wide range of parameters. Therefore, the nonlinear stability is investigated to obtain the stability and instability regions.