Polynomial-based stiffness design of inerter systems for vibration control

This is the authors' abstract. We don't add key points for this paper.

To systematically evaluate the impact of various types of nonlinear stiffness on control-system performance, this paper focuses on stiffness design for nonlinear stiffness inerter systems (NSIS). Balancing generalization with feasibility, the proposed design is formulated within a polynomial basis-function space. First, the physical feasibility of implementing various polynomial stiffnesses via the track method is experimentally validated. Subsequently, polynomial-based stiffness is classified into monostable and multistable stiffness configurations according to their distinct dynamical behaviors. For monostable cases, the influence of the highest polynomial order on the number of slow invariant manifold (SIM) bifurcations is analyzed. For multistable cases, the effects of the number, width, and depth of potential wells on control performance are examined. The results show that higher-order monostable NSIS provide a broader effective control range, although at the cost of increased design complexity. In contrast, multistable NSIS with fewer potential wells exhibit greater robustness. Moreover, shallower and wider potential wells improve control performance but require higher excitation levels. These findings provide a systematic design perspective for harnessing nonlinear restoring effects in inerter-based vibration control systems.