Harnessing quasiperiodic pattern to widen the low-frequency band gap of quasi-zero-stiffness metamaterials

While the quasi-zero-stiffness (QZS) property has been widely incorporated into locally resonant (LR) metamaterials to facilitate the opening of low-frequency band gaps, the resulting gap widths typically remain narrow. In response to this limitation, here we introduce a new type of QZS LR metamaterial. In our design, the compression of resonators is systematically modulated by a quasiperiodic pattern, leading to the emergence of the well-known Hofstadter butterfly spectrum with a fractal network of frequency gaps. These fractal gaps, elucidated by the integrated density of states (IDS), exhibit topologically nontrivial characteristics and are traversed by edge-localized modes. Leveraging the advantageous fractal effect, we optimize the modulation parameters of the quasiperiodic pattern. The optimized quasiperiodic configuration demonstrates the ability to open a low-frequency and wide band gap—a significant increase (465%) in width compared to a periodic configuration with a compression of 5 mm. This work is anticipated to serve as a valuable guide for designing broad low-frequency band gaps, thus offering potential applications in vibration reduction and wave attenuation purposes.