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This paper investigates vibration analysis of a clamped-clamped beam attached to a nonlinear energy sink (with nonlinear stiffness and damping) under an external harmonic force. The bream is modeled using the Euler-Bernouli beam theory. Different locations for nonlinear energy sink are chosen and the effects of various parameters on behavior of the system are considered. Required conditions for occurring the Saddle-node bifurcations and the Hopf bifurcations in the system are studied. In vibration analysis, the frequency response diagram of the system is very important because it shows the best regions for attenuation of vibration and is a good criterion for designing nonlinear energy sinks; hence Complexification-Averaging method is used to find simply the amplitude of oscillation in terms of excitation load. For validation and comparison, numerical simulation (Runge-Kuta method) is used. The results demonstrate that by approaching the position of nonlinear energy sink to the beam supports, probability of occurrence of the Hopf and the saddle-node bifurcations decreases and increases, respectively, detached response curve will be formed in smaller range of external amplitude force. Moreover, by increasing external amplitude force, the steady state amplitude of the system increases smoothly.

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Passive vibration control of rotating nonlinear beams is crucial due to its potential to mitigate harmful vibrations in various engineering applications, including aerospace and industrial sectors. This study examines how different system parameters and inherent nonlinearities influence the vibrations of a nonlinear rotating beam subjected to periodic external forces. A nonlinear energy sink (NES) is attached to the beam's tip to attenuate vibrations. The system is modeled using the Euler-Bernoulli beam theory and von Kármán strain-displacement relations, with equations of motion derived via Hamilton’s principle. Complexification Averaging and Runge-Kutta methods are applied for analytical and numerical solutions, respectively. The findings reveal that increasing the stiffness reduces vibration amplitude, while a rise in the nonlinear coefficient induces hardening behavior. The system exhibits saddle-node and Hopf bifurcations under certain conditions, indicating complex dynamic transitions. These phenomena, driven by the beam's nonlinearity and the NES, effectively diminish the vibration amplitude, highlighting the system's complex dynamic responses and the NES's efficacy in vibration mitigation