Parameter optimisation and performance analysis of tuned mass negative stiffness inerter dampers for vibration isolation systems

A novel vibration isolator, the tuned mass negative stiffness inerter damper (TMNID), is constructed by adding a negative stiffness element to a tuned mass damper inerter to further enhance the vibration isolation performance of existing vibration isolators. The transmissibility of a single-degree-of-freedom system (SDOF) with a TMNID and the parameter range of negative stiffness are derived. Based on the H_∞ and H₂ norms, the analytical solutions of the optimal parameters of the TMNID are derived. The parameter variation rule and sensitivity of the TMNID are analysed. Enhancing the inertance-mass ratio, mass ratio or decreasing the negative stiffness ratio can raise the optimal parameters, and decreasing the negative stiffness ratio can improve the isolation performance of the TMNID system. The maximum transmissibility of the TMNID system is most sensitive to the stiffness ratio, while the performance measure is highly dependent on the negative stiffness ratio and inertance-mass ratio. Finally, the isolation control effect of TMNID for base excitations is evaluated using a SDOF and an isolated building as examples. For the same inertance-mass ratio, the isolation control effect of TMNID is better than that of TID, TVMD and TMDI, and its effect enhances as inertance-mass ratio increases or the negative stiffness ratio decreases, which is attributed to negative stiffness effect increasing the energy dissipation of TMNID and reducing the natural frequency of the controlled system.