Design of periodic structures with application to phononic crystals and acoustic metamaterials

Abstract

The project intends to study classical periodic structures, phononic crystals and acoustic metamaterials by wave propagation techniques in order to create, mainly, band gaps (stop band) to control noise and vibration. The wave propagation methods present advantages to model periodic structures because they enable reduction in the calculation time, accuracy in all range frequency, modeling complex theory and complex geometries, and also allow easy assembly with other substructures. Phononic crystals and acoustic metamaterials are artificial periodic structures that have recently appeared, have interesting properties (band gaps, tunneling, wave acceleration, and local resonance, among others) and applications such as filtering, noise and vibration reduction, and also image processing - yet underexplored. Band gaps are frequency bands where wave propagation in the structure is not possible; they can be created by the difference of properties between the inclusions and the matrix host (phononic crystals) or through the inclusion of modified acoustic cells that are smaller than the wavelength (acoustic metamaterial). The case studies suggested (flexible rotating ring, nonlinear and/or multiscale modeling, vibration and noise absorber) allow the development of the numerical methods (SEM and WFE), physics concepts of acoustic metamaterials and phononic crystals, besides the conceiving of important design devices and with many applications. (AU)