Quasi-zero stiffness (QZS) vibration isolators exhibit excellent performance in low-frequency vibration isolation but require the negative stiffness to be consistent or close to the positive stiffness, which may lead to an excessively large volume or weight of the negative stiffness mechanism. In this paper, a lightweight QZS (L-QZS) vibration isolator using the lever amplification mechanism is developed, theoretically investigated, and experimentally verified. The negative stiffness can be amplified by one order of magnitude through the amplification effect of the lever structure, enabling a lower negative stiffness to compensate for the positive stiffness. Meanwhile, the lever increases the inertia effect of the negative stiffness structure, leading to an increase in the system’s effective mass and further reducing the resonance frequency. Results indicate that with a small negative stiffness, the isolation bandwidth of L-QZS isolators is significantly enlarged. The transmissibility at high frequencies of the L-QZS isolator tends to a certain value, which is mainly determined by the lever ratio and the tip mass of the lever. Furthermore, the negative stiffness can be controlled by adjusting the lever ratio, providing a viable method for matching various positive stiffnesses in engineering applications.
This paper presents a comprehensive method for designing a robust active vibration control system to suppress low-frequency vibrations in smart structures. A novel finite element method based on the first-order shear deformation theory is used to calculate the dynamic response of a smart beam. Through a comprehensive system identification process, the uncertain model of the smart beam is extracted considering both the magnitude and phase. The model fits the experimental data successfully. In addition, a generalized low-frequency vibration control performance function is designed for the piezoelectric smart beam. Using a linear fractional transformation, the system is converted into a standard μ-synthesis control framework, and the controller K is synthesized using structural singular values μ. The effectiveness of the proposed method is experimentally validated using a setup with a piezoelectric smart beam. The experimental results suggest that the proposed control method exhibits robust stability and robust performance, effectively enhancing the performance of smart structure control in various scenarios. The proposed control framework utilizes structured singular value analysis to provide optimal robust stability margins and superior robust control performance, effectively addressing system uncertainties and non-linearities.