Analysis and design of a novel arrayed magnetic spring with high negative stiffness for low-frequency vibration isolation

Paralleling magnetic negative stiffness mechanism (NSM) with positive stiffness serves as an effective way to resolve the inherent contradiction between high load capacity and ultra-low frequency vibration isolation ability. Nevertheless, the stiffness nonlinearity and oversize of common magnetic NSMs restrict their further applications. In this paper, a novel compact arrayed-magnetic-spring with negative stiffness (AMS-NS) is proposed. The AMS-NS, which consists of cuboidal magnets arranged as a rectangular array, possesses high negative stiffness density and ameliorative nonlinearity. An analytical model of the AMS-NS is established based on the magnetic charge model and validated by static experiments. Parametric studies are conducted to provide guidelines for the optimal design of the AMS-NS. In addition, the nonlinear displacement transmissibility of an isolator with the AMS-NS and positive stiffness in parallel (APSP) is derived utilizing the harmonic balance method, and effect of stiffness characteristic of the AMS-NS on the isolation performance are furtherly investigated. Finally, dynamic experiments were conducted on a prototype with APSP, the results demonstrated that the proposed AMS-NS has high negative stiffness density and can effectively reduce the resonance frequency to broaden the vibration isolation band; and the analytical results showed good agreements with the experimental results.