Enhancing the near-linear working region of quasi-zero stiffness vibration isolators using a tri-rectangular-magnet configuration

Magnetic quasi-zero stiffness (QZS) vibration isolators often suffer from a narrow near-linear working region around static equilibrium, which limits their usable working stroke in practice. To address this issue, a QZS vibration isolator with a tri-rectangular-magnet configuration is proposed. Based on the equivalent surface magnetic charge theory, a three-dimensional analytical model is established to characterize the nonlinear magnetic force and negative stiffness of the tri-rectangular-magnet negative stiffness mechanism. The effects of the outer-magnet dimensions on the negative stiffness characteristics are analyzed to identify the design variables. A constraint-guided optimization framework is then established to maximize the near-linear working region under stiffness-matching, nonlinearity, and dimensional constraints, and the Whale Optimization Algorithm is used to solve the resulting problem. Under a predefined stiffness nonlinearity limit of 5%, the model-predicted near-linear working region increases from 4.00 mm to 7.26 mm after optimization. Static tests show good agreement with the analytical predictions, while small-excitation frequency-sweep experiments indicate that the resonance frequency decreases from 5.51 Hz to 1.86 Hz. These results demonstrate that the proposed configuration and design framework can effectively enlarge the near-linear working region around static equilibrium and improve low-frequency vibration-isolation performance under the tested small-excitation condition.