Dynamic responses and vibration reduction performance of a magnetic nonlinear energy sink with designable stability

Multistable systems generate multiple stable equilibrium points and energy barriers through multilevel potential well configurations, enabling directional vibration energy transfer and efficient dissipation via inter-well oscillations and barrier-crossing motions, and have become an important research direction in vibration control. To this end, this paper proposes a magnetic nonlinear energy sink with designable stability for vibration mitigation. The device exploits the coupling between the cantilever-beam elasticity and dipole-dipole magnetic interactions to enable designable regulation of the multistable potential energy. Based on magnetic dipole theory and the Euler-Bernoulli beam model, an analytical nonlinear mechanical model of the NES is established, and equilibrium bifurcation analysis is performed to reveal the effects of geometric parameters on the number of stable equilibria and the evolution of the multistable potential energy structure. A nonlinear dynamic system model of the linear oscillator coupled with the NES is developed, and numerical simulations are conducted to analyze the dynamic responses under different stability configurations, revealing the regulatory effects of multiple parameters on inter-well transition thresholds, attractor evolution, and energy dissipation. The harmonic balance method is also employed for cross-validation of the steady-state predictions. On this basis, a vibration reduction efficiency index is defined to quantitatively evaluate the device performance. The results demonstrate that the designable regulation of stability characteristics can significantly reshape the system’s dynamic response, enabling efficient vibration suppression over a wide excitation range, with a reduction efficiency of up to 86%. The present findings provide new insights into the regulation and utilization of multistable characteristics and their application in broadband vibration control.