2024/10/06 by Mario Lázaro, Richard Wiltshaw, Lázaro, Mario +5
Engineering · #Acoustic Wave Phenomena Research #Applied Physics (physics.app-ph) #FOS: Physical sciences
paper · pdf · doi:10.48550/arxiv.2410.04549
openalex publication_date 2024/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a comprehensive method for determining both exact and approximate dispersion relations for one-dimensional resonant phononic crystals, applicable to a wide range of structures, regardless of their specific characteristics. This general framework employs a unified mathematical model, referred to as generalized one-dimensional (1D) phononic crystal, in which different types of waves and scatterers/resonators can be considered by adjusting certain parameters. The generalized 1D phononic crystal consists of both a host one-dimensional homogeneous elastic material with physical properties represented in matrix form and an arbitrary set of scatterers within the unit cell, including resonators (discrete and continuous), small material inclusions, or variations in cross-sectional area. Based on general assumptions, and imposing the periodicity and Bloch solutions we develop a matrix-based algorithm utilizing the plane wave expansion method to derive the solution. Additionally, we propose an iterative procedure that provides analytical expressions for the first- and second-order terms, particularly useful in the context of weak scattering. The convergence conditions of the method are rigorously defined. The efficiency of the approach is demonstrated through several numerical examples, highlighting its versatility in different waveguide configurations and scattering scenarios.