Investigation of a nonlinear energy sink based on magnetic inerter

Nonlinear characteristics have demonstrated significant advantages in mitigating vibrations across various engineering applications, particularly in effectively suppressing vibrations over a wide frequency range. This paper introduces a novel nonlinear energy sink with a magnetic inerter (MINES). The MINES features a magnetic lead screw that incorporates a pair of helical permanent magnets. When the inner part undergoes linear motion, it is transformed into the rotation of the outer part at a predetermined conversion ratio. Subsequently, the MINES is incorporated into a system with a single degree of freedom, and the corresponding differential equations of motion are derived. The approximate analytical method and the numerical method are used to validate each other. This process clarifies the effectiveness of the MINES in reducing vibrations when subjected to harmonic excitation. The influence of the parameters of the MINES is analyzed. The findings demonstrate that the MINES offers significant benefits in terms of vibration suppression efficiency when the depths of the three barriers are equal. Furthermore, with the increase in excitation amplitude, the MINES enters the nonlinear range, leading to a reduction in system damping. This can effectively prevent the phenomenon of traditional damping stiffening under conditions of high amplitude excitation. Finally, the vibration reduction capability of this nonlinear energy sink was experimentally demonstrated, enhancing its applicability in vibration mitigation.