Multidirectional hybrid pendulum-magnetic quasi-zero-stiffness isolator: modeling, analysis and experimental validation

Multidirectional quasi-zero-stiffness vibration isolation remains challenging owing to the low dynamic stiffness, static stability, coupled rigid-body motion, and the weak linearity of conventional negative-stiffness mechanisms. To address these limitations, this paper proposes a hybrid pendulum-magnetic quasi-zero-stiffness (HPM-QZS) isolator combining a four-point flexible suspension with a centralized magnetic negative-stiffness (MNS) module. It employs separated positive–negative stiffness combinations in the horizontal and vertical directions, respectively. Horizontally, the pretensioned suspension provides positive pendulum stiffness, while the elevated payload mass center introduces an inverted-pendulum effect that reduces the effective horizontal stiffness through translation-rotation coupling. Vertically, the suspension springs act in parallel with the MNS module, whose force is transmitted to the moving frame through a compliant rod. A closed-form linearized six-degree-of-freedom model is derived from suspension-point kinematics and incremental force and moment relations. The model provides an analytical basis for stability, modal, and transmissibility analyses and guides suspension-parameter selection. In order to improve stiffness linearity within the working stroke, an unequal-size three-stator-two-mover MNS is further developed. In addition, static calibration and passive modal tests are conducted to confirm the accuracy of the analytical model. Finally, supplementary absolute-velocity feedback is introduced to suppress residual low-frequency resonance, and passive/active-assisted transmissibility tests demonstrate effective attenuation in all three translational directions. The experimental results demonstrate that the HPM-QZS isolator combines separate horizontal and vertical stiffness-regulation mechanisms, exhibits excellent stiffness linearity in the vertical direction, and offers superior vibration isolation performance, indicating its potential for low-frequency vibration isolation in fields such as precision manufacturing and metrology.