Dynamics of rotationally symmetric elastic quasicrystals: numerical and experimental investigations

Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterials structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry buy are unrestricted in rotational symmetries, which lead to largely unexplored mechanical and dynamic properties. In this talk, we investigate a family of continuous elastic quasicrystals with different rotational symmetry orders that are directly enforced through a design procedure in reciprocal space. Numerical results illustrate that higher order symmetries, such as 8, 10 and 14-fold, allow for nearly isotropic wave motion when compared to periodic counterparts, such as 4- and 6-fold symmetric crystals. Spectral contents are investigated by enforcing rotational symmetry constraints in a wedge-type unit cell, which allows for the estimation of band gaps that are also confirmed in frequency response computations. Finally, a series of experiments are conducted on 3D-printed quasicrystal plates to validate the behavior, wave propagation, and band gaps, predicted by the simulations.