Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

Area of Science:

• Physics
• Materials Science
• Acoustics

Background:

• Phononic crystals exhibit unique wave propagation properties.
• Granular lattices present complex behaviors due to particle interactions.

Purpose of the Study:

• To investigate linear and nonlinear mechanisms of conical wave propagation.
• To analyze wave packet diffraction and wave front characteristics in granular lattices.

Main Methods:

• Analysis of dispersion relations in linear phononic crystals.
• Heuristic and asymptotic analysis for wave packet propagation.
• Examination of granular lattices under static compression.

Main Results:

• Conical diffraction is identified in phononic crystals under strong precompression.
• Non-oscillatory wave fronts emerge in weakly compressed lattices.
• The interplay of discreteness, nonlinearity, and geometry governs wave propagation.

Conclusions:

• Both linear and nonlinear regimes support conical wave propagation.
• The lattice geometry and precompression significantly influence wave behavior.
• Understanding these mechanisms is crucial for designing advanced phononic materials.