The X-shaped structure with nonlinear positive stiffness compensation for low-frequency vibration isolation

X-shaped structure with quasi-zero stiffness (QZS) properties are suitable for low-frequency vibration isolation because of its simple structure. The effective working range of classic X-shaped structure (CXS) is narrow for the existence of negative stiffness region, and using positive stiffness compensation to overcome this deficiency is a common way. This paper proposes a novel nonlinear positive stiffness compensation method (NPSC) to improve the load capacity and QZS range of CXS. Different from the previous studies that utilize linear or hardening stiffness compensation, the NPSC exhibits the characteristics of softening stiffness first and then hardening stiffness and is provided by torsion springs simply. The static properties of X-shaped structure with NPSC are investigated. The result indicates the NPSC possesses dual significant advantages. Firstly, the X-shaped structure with NPSC can achieve larger load capacity and wider QZS range than that with linear or hardening stiffness compensation in optimal parameter region. Secondly, the X-shaped structure with NPSC can conveniently overlap the equilibrium position with QZS point to obtain ultra-low frequency vibration isolation effect compared to that with linear stiffness compensation. The motion equation of the proposed system is derived, and the dynamic response is solved through harmonic balance method (HBM). The influence of different parameters on displacement transmissibility is investigated and the result is verified by numerical simulation. The transmissibility comparison between the proposed model and the CXS with linear compensation shows that the proposed model possesses better vibration isolation performance. Besides, the static compression test and dynamic sweep frequency experiment are implemented, and the experiment results verify the validity of proposed model. The proposed NPSC is an important inspiration for the stiffness compensation research of X-shaped structures.