Analytical H∞ Optimization for a Novel Lever-Type Voigt Model-Based Dynamic Vibration Absorber with Ungrounded Negative Stiffness

Purpose A novel lever-type Voigt model-based dynamic vibration absorber with ungrounded negative stiffness (NS-LVDVA) is proposed in this paper in order to reduce the maximum resonant displacement of the primary structure, which can be implemented without inter-layer installation problem. Methods The NS-LVDVA is mounted on an undamped primary structure under force excitation, and the equations of motion are first derived; after establishing the resulting main steady-state displacement response, the optimal frequency ratio, the approximate optimal damping ratio, and the optimal ungrounded negative stiffness ratio are derived analytically based on the fixed point theory (FPT) in order to minimize the maximum resonant displacement of the primary structure; then the high accuracy and efficiency of the FPT is demonstrated by comparing the numerical and analytical optimized response of the primary structure. Results and conclusion The results analysis shows that the smaller the lever ratio, the better the vibration reduction performance of the proposed DVA; thus by comparing with other typical DVAs under harmonic and random excitation, it is found that the model in this paper can greatly reduce the resonant displacement and broaden the frequency bandwidth of the suppressed vibrations, also shows a good random vibration reduction effect. From the above results, the proposed DVA model is relevant for engineering practice.