Anhysteretic high-static–low-dynamic stiffness vibration isolators with tunable inertial nonlinearity

This study proposes an anhysteretic high-static–low-dynamic stiffness (HSLDS) vibration isolator with tunable nonlinear inerters. The aim is to overcome the drawbacks of conventional HSLDS vibration isolators. The conventional systems experience an abrupt, undesirable change in frequency response due to stiffness-hardening nonlinearity, leading to hysteresis. This hysteresis issue worsens under a strong excitation force, consequently narrowing the frequency bandwidth for vibration isolation. To address this limitation, several recent investigations have examined the beneficial effects of geometrically nonlinear inertance. Nonetheless, these studies have mainly concentrated on the quasi-zero-stiffness (QZS) scenario, yielding findings that mitigate, rather than eliminating, hysteresis. This study redirects focus to an HSLDS vibration isolator that goes beyond QZS systems, exploring the exact condition for hysteresis elimination through the integration of tunable nonlinear inerters that counterbalance stiffness-hardening effects. Bifurcation analyses uncover how dynamic hysteresis cancellation depends on various system parameters, including inertance, stiffness, length, and damping ratios. This study delineates three distinct parametric regions based on inertance and length ratios: those conducive to hysteresis elimination, suppression, and magnification. The findings of these rigorous conditions for passive hysteresis control are valid across the full parametric spectrum of the HSLDS vibration isolator. Theoretical analysis further validates the advantages of the proposed system, emphasizing its HSLDS characteristics, reduced maximum force transmissibility, and widened frequency bandwidth for isolation. Insights from this research establish a foundational framework for future advancements in designing nonlinear inerter-based anhysteretic vibration isolators.