Novel S-type inertial nonlinearities and their effects on dynamic vibration responses

This paper reveals significant inertial nonlinearities using a unique X-mechanism, validated through experiments. The system features a local rotating unit connected to a specially designed X-mechanism via a four-bar linkage, leading to the discovery of novel symmetric and asymmetric S-shaped inertial nonlinearities. These have not been reported before and allow the resonant frequency to be tuned as low as 1 Hz. An innovative modification of the classic harmonic balance method is proposed to obtain the nonlinear dynamic response of the system, enabling analytical solutions without polynomial fitting. Key findings include (a) New S-type inertial nonlinearities can lower the resonance frequency/peak with a higher decay rate while suppressing potential saddle-node bifurcation; (b) Symmetric S-shaped nonlinearity achieves the highest decay rate, maintains good high-frequency performance, and adapts well to varying excitations; (c) Nonlinear inertia equivalence is revealed which means that the rotation unit's nonlinear inertia is equivalent to a linear motion oscillator, a novel discovery; (d) Adjustability of the X-mechanism allows for large relative motion and independent tuning of high-frequency vibration isolation and resonance peaks; (e) Special nonlinear dynamics are also unveiled, including nonlinear energy transfer and band-stop properties, effectively achieved with the proposed X-mechanism. The study advances the understanding of nonlinear inertia, inspiring new technical innovations in vibration control, energy harvesting, motion control of robots, and the design of novel robotic systems. © 2025 Elsevier Ltd.