Nonlinear vibration and dynamic performance analysis of the inerter-based multi-directional vibration isolator

Motivated by the demand of improving the multi-directional vibration dynamic performance, an inerter-based multi-directional (IMD) vibration isolator is proposed in this paper, which is composed of the inerter, damper and spring structures in multiple directions. The dynamic equation of the IMD vibration isolator is established using the Lagrange theory, its dynamic response under base harmonic excitation is obtained using the harmonic balance method and pseudo-arc-length method, and the stability of the dynamic response is considered. The dynamic performance of the IMD vibration isolator under harmonic and shock excitations is studied and compared with those of the conventional multi-directional (MD) vibration isolator consist of the damper and spring structure, and the effect of structural parameters on its dynamic performance is investigated in detail. The results show that the IMD vibration isolator has nonlinear inertial, damping and stiffness characteristics, and it further reduces the dynamic displacement and absolute displacement transmissibility peaks, widens the isolation frequency band than the MD vibration isolator and also has better shock performance in the middle severity parameter range. In order to obtain better isolation and shock performance, the vertical and horizontal inertance-to-mass ratios are chosen as larger values, and the stiffness ratio and the horizontal spring compression ratio are chosen as smaller values. Therefore, the design of the proposed IMD vibration isolator exhibits the advantages of applying the inerter and provides excellent isolation and shock performance in multiple directions.