Dispersion relationship of phononic generalized beams

• DOI: 10.48550/arxiv.2410.04549
• Publication Date: 2024-10-06
• Authors: Mario Lázaro; Richard Wiltshaw; Richard V. Craster; Vicente Romero‐Ga...
• Keywords: FOS: Physical sciences; Physics - Applied Physics; Applied Physics (physics.app-ph)

In this work, we present a comprehensive method for determining the dispersion relation in one-dimensional waveguides, applicable to wide range of structures, regardless their specific characteristics. This general framework employs unified mathematical model, referred as *generalized beams*, where varying types waveguides and scatterers are incorporated by adjusting certain parameters. The generalized beam consists host waveguide, which is homogeneous elastic structure with physical properties represented matrix form. model also accounts an arbitrary set within unit cell, including resonators (discrete continuous), small material inclusions, or variations cross-sectional area. Based on assumptions, develop matrix-based algorithm utilizing plane wave expansion derive solution. Additionally, propose iterative procedure that provides analytical expressions first- second-order terms, particularly useful context weak scattering. convergence conditions rigorously defined. approach's effectiveness demonstrated through several numerical examples, highlighting its versatility different waveguide configurations scattering scenarios.