Mechanical Vibration Control via Tailored Symmetry Group-Driven Phononic Crystals with 4-Fold Rotational Symmetry
Phononic crystals (PnCs) are periodic materials with a specific geometry that creates a periodic impedance contrast, allowing them to attenuate elastic waves across various frequencies. The phononic band structure of single-phase PnCs is determined by their geometry, mechanical properties, and symmetry. Higher symmetries increase the probability of achieving a complete omnidirectional bandgap (BG), where waves are exponentially attenuated for all directions and polarizations due to Bragg scattering or local resonance mechanisms. The current challenges are enhancing wave attenuation, broadening BGs, and lowering their frequencies.
We investigate the BG formation mechanisms in 2D single-phase PnCs with 4-fold rotational symmetry, namely the symmorphic p4 and p4mm, and the nonsymmorphic p4gm plane groups. Based on these groups, we introduce simple designs that can be readily 3D printed. We calculate the band structures using the Bloch-Floquet approach and determine the BG mechanisms by examining the vibration patterns and the imaginary Bloch wave vectors. Through a comprehensive parametric study, we elucidate the BG mechanisms in PnCs with enhanced attenuation and extremely wide BGs, revealing that they result from the strong coupling of the Bragg scattering and local resonance mechanisms.
To validate the BG width and attenuation, we 3D-printed finite PnCs and measured ultrasonic transmission loss (TL) on a custom-built experimental setup, which employs both P- and S-wave transducers at different frequencies. The experiments also matched the 3D TL simulations. The findings confirmed the presence of strongly coupled BGs with superior performance for both P- and S-waves, while also highlighting TL differences for the distinct polarizations and mechanisms.
The work is towards M.Sc. degree under the supervision of Asst. Prof. Pavel I. Galich, Aerospace Engineering faculty, Technion – Israel Institute of Technology.
