Reduction of transmissibility and increase in efficacy of vibration isolation using negative stiffness device with enhanced damping

Effect of passive vibration isolation heavily depends on force–displacement characteristic of the isolation system. In view of this dependence, this paper investigates the influence of negative stiffness device (NSD) on the effect of vibration isolation system. Detailed evaluation of transmissibility is performed. The critical parameters are identified. It is found that with NSD, significant vibration reduction for both absolute and relative displacement transmissibility is obtained. A modified Lindstedt–Poincaré method (modified L–P method) is used to obtain analytical periodic solutions for the approximated piecewise linear dynamic system. The analytical limit cycles by the modified L–P solution agree satisfactorily with the ones by numerical simulation. The most important finding of this study is that larger damping in a system with NSD helps in reducing transmissibility, thus increasing the efficacy of the isolation system; this is in contrast to other conventional isolation systems, wherein increased structural damping decreases the efficacy of vibration control in the frequency range of interest. It is worth noting that this finding of NSD enhancing the structural damping is consistent with earliest studies by senior author and collaborators.