2011/11/14 by Liao Liu, Mahmoud I. Hussein · 340 citations
Engineering · Health Professions · Neuroscience · #Acoustic Wave Phenomena Research #Band gap #Band-pass filter #Beam (structure) #Bloch wave #Boundary value problem #Bragg's law #Computational physics #Condensed matter physics #Diffraction #Flexural strength #Hearing Loss and Rehabilitation #Materials science #Noise Effects and Management #Optics #Periodic boundary conditions #Physics #Quantum mechanics #Scattering #Stopband #Timoshenko beam theory #Transfer-matrix method (optics) #Wave propagation
paper · doi:10.1115/1.4004592
published in Journal of Applied Mechanics 79(1) (ASM International)
openalex publication_date 2011/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26
Band gaps appear in the frequency spectra of periodic materials and structures. In this work we examine flexural wave propagation in beams and investigate the effects of the various types and properties of periodicity on the frequency band structure, especially the location and width of band gaps. We consider periodicities involving the repeated spatial variation of material, geometry, boundary and/or suspended mass along the span of a beam. In our formulation, we implement Bloch’s theorem for elastic wave propagation and utilize Timoshenko beam theory for the kinematical description of the underlying flexural motion. For the calculation of the frequency band structure we use the transfer matrix method, derived here in generalized form to enable separate or combined consideration of the different types of periodicity. Our results provide band-gap maps as a function of the type and properties of periodicity, and as a prime focus we identify and mathematically characterize the condition for the transition between Bragg scattering and local resonance, each being a unique wave propagation mechanism, and show the effects of this transition on the lowest band gap. The analysis presented can be extended to multi-dimensional phononic crystals and acoustic metamaterials.