Nonlinear shock isolation using the bottleneck phenomenon near a saddle–node ghost

Recent shock-protection technologies have leveraged elastic instability in nonlinear bistable mechanisms. These innovations include a bistable shock isolator (BSI), which uses a zero-frequency singularity to delay and mitigate force transmission. However, a well-escape accompanying the singularity of the BSI has a critical drawback as the well-escape alters the initial conditions, which precludes repetitive applications of the singularity for subsequent shock loading. To address this issue, we propose a transitional shock isolator (TSI; from asymmetric bistability to asymmetric monostability) designed to possess a saddle–node ghost (TSI-snG) remnant after the saddle–node bifurcation. A symmetry-breaking parameter is introduced into the shock isolator model and designed such that the initial conditions for every shock loading are maintained at one fixed point, and the other two fixed points are mutually annihilated. After the annihilation, the TSI-snG ensures that the payload — oscillating mass exposed to shock loading — reliably returns to the original position after every shock loading, which indicates that the limitation of the BSI is resolved. For engineering practicality, we also consider the inevitable fabrication errors by using an imperfection parameter, which is a perturbation of the symmetry-breaking parameter. We demonstrate that TSI-snG with imperfections exhibits a bottleneck near the ghost and exploits the bottleneck to delay and nullify the force-transmission pathway. Therefore, the TSI-snG produces similar benefits from the BSI (delay and mitigation of force transmission), while resolving the drawback of the BSI (well-escape). Parametric studies reveal the dynamics of the TSI model, and experimental verifications corroborate the benefits of the TSI-snG.