Passive vibration isolation characteristics of negative extensibility metamaterials

Negative extensibility refers to the category of mechanical metamaterials that exhibit an unusual phenomenon where the system contracts upon tension. The dynamic analysis of such systems is crucial for exploring the vibration isolation characteristics, forming the prime focus of the present study. Inspired by Braess’s paradox, the mechanical model incorporates coupled tunable nonlinear spring stiffness properties (strain hardening and softening), which alternate when a certain displacement threshold is exceeded. This stiffness-switching mechanism facilitates wide-frequency passive vibration isolation using the phenomenon of counter-snapping instability. The vibration isolation characteristics resulting from the stiffness-switching mechanism are investigated using time- and frequency-domain plots. Furthermore, the relationship between the stiffness switching mechanism and various system parameters is visualized using a three-dimensional parametric space. The efficacy of the proposed system is evaluated by comparing it with the existing bi-stable systems, revealing superior performance in isolating high-amplitude vibrations. The proposed mechanism enhances the understanding of dynamic behaviors in critical structural elements for multi-stable mechanical metamaterials, providing insights and opportunities for innovative adaptive designs.