Theoretical and experimental analysis of symmetric and asymmetric magnet-based bistable vibration isolators

The bistable vibration isolator (BVI) has attracted the interest in the field of nonlinear vibration isolation. The tunable symmetric and asymmetric BVIs can be generated through nonlinear magnetic repulsion forces and linear structures. However, the intricate structures of magnet-based BVI systems currently available are responsible for their limited versatility and flexibility, ultimately leading to a deficiency in general theory regarding vibration isolation. Notably, the deficiency includes inadequate understanding of the impact of structural asymmetry on isolation performance, highlighting the need for further research. This paper proposes a magnet-based BVI and the axial nonlinear magnetic force analysis model utilizing the filament method. By utilizing the harmonic balance method, analytical formulas for the displacement transmissibility of both symmetric and asymmetric magnet-based BVIs (SBVIs and ABVIs) are derived. The influence of different parameters on the bistable shape, the snap-though behavior and the vibration isolation performance has been revealed. An experimental platform is established for verification and analysis. Theoretical and experimental analysis show that there is a contradiction between the isolation bandwidth and allowable excitation amplitude, and compared to the symmetric bistable structures, the asymmetric bistable shape involves more structural parameters. Nonetheless, the ABVI exhibits better adjustability and adaptivity for different excitation amplitudes, which leads to the unique advantages for vibration isolation. Additionally, the ABVI exhibits superior flexibility, enabling the dynamic performance of the system to be tailored to compensate for potential linear stiffness mismatches through installation modifications.