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We present a numerical study for the suppression of self-excited vibrations represented by a Rayleigh oscillator using an impact viscous damper. A systematic approach based on a univariate search optimization method is used to determine the best design parameters for suppressing self-excited vibrations. The suggested system is found to be effective in suppressing this type of vibration. Optimum parameters for complete quenching of such vibrations are obtained. We investigate quasi-static as well as dynamic variations of the bifurcation parameter for both supercritical and subcritical Hopf bifurcation.

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