الفهرس 
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Abstract
Mechanical systems frequently experience friction-induced vibration, which has drawn a lot of attention and been the subject of numerous studies. However, due to the enormity of this issue’s complexity, it has not yet been fully solved. In this thesis, the friction-induced vibration is theoretically studied on discrete and continuous mechanical models that aim is to enhance the understanding about the causes, the dynamic behaviors, and the suppression of the friction-induced vibration in mechanical systems. Moreover, the behavior of 4DOF dynamical system has been examined and analyzed. The following notes express about the important obtained results in this thesis. 1. A 2DOF mechanical simulation model is used in Chapter (1) to examine the stability and the SS behaviors of the PHIS. 2. The influence of various system characteristics, such as the speed of excitation, equal stiffness along the x -axis, damping of the system, and the coefficient of friction, have been investigated. 3. The SMD mechanical model is used to investigate the dynamic properties of hydraulic plastic injection mechanisms. According to theoretical results. 4. The system’s stability is investigated using Lyapunov stability theory. 5. Both of critical instability speed and critical SS speed have been calculated to be 0.4703m / s and 0.1688m / s , respectively. 6. If the excitation speed is greater than 0.4703m / s , the system has a stable behavior, while the system will be unstable when excitation velocity falls below 0.4703m / s . 7. The innervation and decay rate of the system have an important impact on the stability and behavior of SS plastic hydraulic injection. As the rate of excitation and decay of the system increases, the system reaches the asymptotic steady-state after the unstable state and shortens the adhesion phase until it vanishes completely. 8. There is good agreement between the practical results and the numerical solutions of the governing system. General conclusion 132 9. The impact of various values of the stiffness for the nonlinear spring and the damping on the system’s behavior has a good influence on the model’s motion . 10. The motion of two nonlinear spring masses subjected to a smooth friction-velocity curve has been investigated in Chapter (2). 11. For varied excitation speeds, the dynamical system under study is asymptotically stable, and the SS phase is important throughout the cycle. 12. It is noted that the mobility and stability of the system are influenced by the connection between two masses, in which the obtained outcomes have been improved with the consideration of the stiffness of nonlinear springs. 13. Critical instability velocity is calculated using the Hurwitz model to be 0 3.9855 / b v = m s , and the system critical SS speed is determined to be 2.4722m/s . The system becomes stable if the excitation speed exceeds 0 3.9855 / b v = m s . 14. The effects of different stiffness values, whether linear or nonlinear, have been examined, where the nonlinear one having an excellent influence over the linear. 15. The behavior of the system is significantly influenced by the adjustment of damping and friction coefficients, in addition to the various masses of the blocks. 16. A 4DOF dynamical system of a connected spring with a double rigid body as pendulum model was studied in Chapter (3) . 17. The EOM of this system have been derived using Lagrange’s equations in light of the system’s generalized coordinates and solved analytically using the MSA. 18. The solvability conditions have been achieved in view of the elimination of the arising secular terms. 19. All resonance cases have been classified and the modulation equations have been obtained according to the study of three resonance cases simultaneously. 20. The modified amplitudes and the corresponding phases have been recognized for the steady-state solutions. 21. All possible fixed points are examined and represented graphically as stable and unstable zones. General conclusion 133 22. Computer codes are used to represent the attained 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. 23. The time histories of the achieved solutions, the resonances curves in terms of the modified amplitudes and phases, and the regions of stability are outlined for the different parameters of the considered system 24. There is a good agreement between AS using MSA and NS using the fourth-order Runge-Kutta method, which reveals the accuracy of the used perturbation approach.