In the present paper, a dynamic vibration absorber with negative stiffness is developed. This study aims to optimize absorber components by using the two-fixed point approach and H ∞ maximization criterion. Optimum values of the grounded stiffness and tuned mass damper components are derived to minimize resonance amplitude of an un-damped system under harmonic excitation. The two-fixed point theory is employed to minimize the tuning frequency, damping ratio and negative stiffness parameter. Optimum parameters of the absorber are then formulated and used to quantify the influence of each factor on the primary system response. Finally, the mitigation of resonance oscillation amplitude of the primary structure is compared with those of the traditional one. Thus it is shown that the pre-tensioned stiffness provides well attenuation at the resonant vibration range. Adding, this device can be also broadening the efficient frequency range of vibration

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