An inerter-based X-structure vibration isolator

The X-structure has been used for vibration isolation due to its nonlinear characteristic. Here, the use of an inerter-based X-structure vibration isolator is proposed to improve the dynamic performance of the traditional X-structure vibration isolator by exploiting the mass amplification characteristic of the inerter while satisfying the lightweight design requirement. Based on the arrangement of the inerter and X-structure, transverse-mounted, series-connected and parallel-connected inerter-based X-structure vibration isolators are designed. The relevant dynamic equations for these isolators are established using the Lagrange principle, their dynamic responses are obtained using the harmonic balance method and pseudoarc-length method, and their isolation performances are evaluated by three performance indices and compared with those of the X-structure and traditional linear vibration isolators. The results show that the transverse-mounted inerter-based X-structure vibration isolator has nonlinear inertial, nonlinear conservative forcing and nonlinear stiffness characteristics and that the series-connected and parallel-connected inerter-based X-structure vibration isolators have linear inertial and nonlinear stiffness characteristics. The transverse-mounted and parallel-connected inerter-based X-structure vibration isolators have a smaller relative dynamic displacement peak, absolute dynamic displacement peak, absolute displacement transmissibility peak and resonance frequency and wider isolation frequency band than the X-structure isolator, and only the high-frequency absolute displacement transmissibility is larger for the transverse-mounted and parallel-connected inerter-based X-structure vibration isolators. A series-connected inerter-based X-structure vibration isolator can isolate a relatively low-frequency vibration because of the antiresonance frequency and thus can improve the high-frequency absolute displacement transmissibility, while the relative dynamic displacement peak, absolute dynamic displacement peak and absolute displacement transmissibility peak are larger for the series-connected inerter-based X-structure vibration isolator than for the X-structure isolator. The parallel-connected inerter-based X-structure vibration isolator exhibits the best isolation performance and the transverse-mounted inerter-based X-structure vibration isolator exhibits the best shock performance among the four X-structure and linear vibration isolators studied. In addition, the experimental prototype of the inerter-based X-structure vibration isolator is built to test its performance, the theoretical and experimental results are compared to verify the validity of the theoretical modelling. This paper verifies the benefit of introducing the inerter in the X-structure and offers a better choice for effective vibration isolation in practical engineering.