Bandgap Formation Mechanisms in Phononic Crystals with Square Bravais Lattice

The engineered periodic structures, known as phononic crystals, exploit variations in geometric design to achieve distinct impedance contrasts, thereby controlling wave propagation characteristics. These materials can effectively attenuate acoustic waves across a broad range of frequencies. The band structure of these metamaterials, which dictates the range of frequencies over which wave propagation is prohibited, is heavily influenced by the geometry, mechanical properties, and the symmetry group of the phononic crystal. The presence of higher symmetries often correlates with the emergence of complete omnidirectional bandgaps (BGs) — frequency ranges where waves of all polarizations attenuate exponentially due to mechanisms such as Bragg scattering, local resonances, or their combination.

In this work, we calculate the band structures of p4, p4mm and p4gm phononic crystals for real and imaginary Bloch wavevectors to understand the mechanisms behind the BG formation. We evaluate the BG’s attenuation properties by analyzing the real eigenvalues of the imaginary Bloch wavevectors, which provide measurable evidence of the waves’ exponential decay. Furthermore, we conduct experimental and numerical measurements of transmission loss for both P- and S-waves via finite crystals, confirming the superior attenuation facilitated by the coupling of the Bragg and resonance BG mechanisms. This research validates the correlation between the measured transmission loss and the theoretically predicted evanescent modes within the BGs.

Speaker: Prof. Pavel I. Galich

Biography: Pavel I. Galich, PhD, is an Assistant Professor at the Technion – Israel Institute of Technology, where he leads the Wave Mechanics and Metamaterials Laboratory within the Faculty of Aerospace Engineering. He earned his PhD from the Technion, AE and his MSc and BSc in Applied Mathematics and Physics from the Moscow Institute of Physics and Technology, both with honors. His research interests focus on acoustic metamaterials, wave propagation in non-linear materials, and advanced composites for aerospace applications. Pavel has published extensively in high-impact journals and has presented his work at numerous international conferences.