Nonlinear Modeling and Low-Frequency Isolation Characteristics of a Crab-Inspired Quasi-Zero-Stiffness Isolator with Compliant Compensation

Conventional linear isolators struggle to combine high static load-bearing capacity with effective low-frequency vibration isolation. To address this limitation, this study proposes an inclined rhombic crab-inspired quasi-zero-stiffness (I-QZS) isolator. A generalized static model is established based on the segmented linkage of crab walking legs. A physics-constrained NSGA-II algorithm is used to optimize the key geometric parameters while preventing bistable snap-through by imposing a positive-stiffness constraint over the full stroke. A stiffness-compensation strategy bridges the gap between the ideal rigid-body model and the actual 3D-printed compliant structure. The dynamic response is represented by a cubic polynomial restoring-force model, and the resulting equations are solved using the incremental harmonic balance method with SVD (singular value decomposition)-based null-space continuation. Large-amplitude excitation experiments show that the I-QZS shifts the resonance peak to 0.77 Hz, reducing the peak frequency by 64.19% and the peak transmissibility by 67.06% relative to a linear isolator, while substantially broadening the isolation bandwidth. Bifurcation analysis further identifies stability boundaries for engineering design. These results provide an integrated theoretical and experimental framework for ultra-low-frequency passive vibration isolation.