Suppression of vibration transmission in coupled systems with an inerter-based nonlinear joint

This study proposes an inerter-based nonlinear passive joint device and investigates its performance in suppression of vibration transmission in coupled systems. The joint device comprises an axial inerter and a pair of lateral inerters creating geometric nonlinearity, with the nonlinear inertance force being a function of the relative displacement, velocity, and acceleration of the two terminals. Both analytical approximations based on the harmonic balance method and numerical integration are used to obtain the steady-state response amplitude. Force transmissibility and time-averaged energy flow variables are used as performance indices to evaluate the vibration transmission in the coupled system, with subsystems representing the dominant modes of interactive engineering structures. The effects of adding the proposed joint to the force-excited subsystem or to the coupling interface of subsystems on suppression performance are examined. It is found that the insertion of the inerter-based nonlinear joint can shift and bend response peaks to lower frequencies, substantially reducing the vibration of the subsystems at prescribed frequencies. By adding the joint device, the level of vibration force and energy transmission between the subsystems can be attenuated in the range of excitation frequencies of interest. It is shown that the inerter-based nonlinear joint can be used to introduce an anti-peak in the response curve and achieve substantially lower levels of force transmission and a reduced amount of energy transmission between subsystems. This work provides an in-depth understanding of the effects of inerter-based nonlinear devices on vibration attenuation and benefits enhanced designs of coupled systems for better dynamic performance.