Purpose <p>Inerter-based components can effectively adjust the frequency characteristics of a system without significantly increasing its physical mass, which makes them widely used in engineering vibration control. However, structural systems often exhibit nonlinear behaviors, and the impact of such nonlinearities on the resonance and anti-resonance characteristics of inerter systems has not been comprehensively studied. This research aims to explore how nonlinear stiffness influences the dynamic response of inerter-based systems, especially in the context of resonance and anti-resonance.</p> Methods <p>A single-degree-of-freedom inerter system with nonlinear stiffness is modeled. The linear version of the system is first analyzed to determine its baseline resonance and anti-resonance characteristics. Based on this, the multi-scale perturbation method is applied to investigate how nonlinear stiffness affects the dynamic behavior of the system under harmonic excitation. Numerical simulations are also performed to verify the analytical results and to explore the deformation of resonance profiles under varying excitation frequencies.</p> Results <p>The analysis reveals that due to the frequency-dependent nature of external excitation, the presence of hardening stiffness can fundamentally alter the system’s resonance profile, leading to a shift and distortion in the resonant response. Furthermore, the anti-resonance performance is significantly degraded in the presence of nonlinearities. These results are validated through numerical simulations, which confirm the theoretical predictions.</p> Conclusions <p>This study demonstrates that nonlinear stiffness has a substantial effect on both resonance and anti-resonance characteristics of inerter systems. The findings provide theoretical insights into the dynamic behavior of such systems and offer guidance for their design and optimization in vibration control applications.</p>