On a broadband vibration isolator with tunable stiffness: from quasi-zero-stiffness to zero-stiffness behavior

Abstract A novel vibration isolation system designed for superior performance in low-frequency environments is proposed in this work. The isolator is based on a unique hexagonal arrangement of linear springs, allowing for an adjustable geometric configuration via the initial inclination angle. Based on the principle of Lagrangian mechanics, the equation of motion governing the structural dynamics is rigorously derived. The system is modeled as a strongly nonlinear single-degree-of-freedom dynamical system, loaded with a normalized payload and subject to harmonic base excitation. To analyze the steady-state response, the harmonic balance method is employed, providing accurate predictions of the payload’s vibration amplitude and displacement transmissibility as functions of both the base excitation amplitude and frequency. The analysis reveals a direct relationship between the isolator’s geometric and stiffness parameters and its load-bearing capacity, leading to the identification of three distinct operational regimes. Depending on the unloaded initial inclination angle, the equivalent stiffness ratio, and the payload design configuration, the system can exhibit one of three vibration isolation modes: (i) the quasi-zero stiffness (QZS) isolation mode, (ii) the zero linear stiffness with controllable nonlinear stiffness, and (iii) the full-band perfect zero stiffness. The vibration isolation performance of the proposed structure is thoroughly discussed for all three oscillation modes in terms of frequency response curves, displacement transmissibility, and time-domain responses. The key novel finding is that this structure can operate as a full-band, high-performance vibration isolator when the initial inclination angle is designed to be a right angle, enabling full isolation of the maximum possible payload. Moreover, the analytical results and numerical simulations demonstrate that the isolator’s displacement transmissibility T with the unit dB tends to −∞ as the air-damping coefficient approaches zero, enabling ideal vibration isolation across the entire excitation frequency range. These analytical insights are validated through comprehensive numerical simulations, which show excellent agreement with the theoretical predictions.