Applied Mathematics & Information Sciences

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This paper investigates the vibration control of a harmonically excited Duffing oscillator via a simple pendulum. The amplitude-phase modulating equations governing the system dynamics are extracted utilizing perturbation methods. Bifurcation analyses are conducted and the Lyapunov direct method is applied to study the system stability. The uncontrolled system exhibits a variety of nonlinear phenomena such as jump phenomenon, saddle-node, and transcritical bifurcations. The analysis showed that the oscillator vibrational energy could be transferred to the pendulum parametrically when the pendulum natural frequency is equal to one-half the oscillator natural frequency. Numerical validation for the obtained analytical results was performed, which is in excellent agreement with the analytical ones. By the end of this work, a comparison with published work is included.

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