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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.

Keywords: Euler-Bernouli Beam, Nonlinear Energy Sink, Hopf Bifurcation, Saddle-node Bifurcations Detached Resonance curve

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