The Design Of The Phononic Crystal Based On Band Gap And Wave Control

Phononic crystal is a kind of periodic complicated artificial structure composed of two or more kinds of media.Due to the modulation of phononic crystal,band gap can be generated when the elastic wave propagates in the structure.The formation of band gaps is attributed to the Bragg scattering or the Local Resonance.Due to the effective control on elastic wave,phononic crystal have broad application prospects in vibration and noise reduction,acoustical devices,micro/nano technology and stealth technology.So it is necessary to obtain the wider band gap or the band gap in the frequency range considered by design and optimization of phononic crystal.At the same time,the elastic waves with certain specific frequency can propagate along specific direction inside the phononic crystal to achieve the directional propagation of the sound source.Therefore,the wave beam propagation control can be achieved by special phononic crystal structure design.In this paper,the phononic crystals are designed and optimizated based on the band gap characteristics by using the finite element software Comsol and Matlab programming language.The corresponding band gap mechanism equivalent models are proposed.At the same time,beam splitter is designed to control the wave beam based on the self-collimation effect of phononic crystals.Firstly,two kinds of phononic crystals which include periodic holes are new designed.Compared with the traditional phononic crystals with one pillar or two pillars,the new designed hybrid structures have wider and lower band gap and better vibration isolation characteristics.At the same time,the introduction of the holes reduces the structure weight and the production cost.The influences of the structure paramaters and shape on the band gap are stuied.The theoretical formulas of the upper and lower edges are proposed to explain the mechanism of band gap variation.Secondly,the effects of symmetry and filling rate on two-component phononic crystal thin plate are discussed.The influences of the order of magnitude of elastic modulus are studied emphatically.The formation condition and change rule of the flat band are discussed for the three-component phononic crystal.The bigger radius of the coating layer makes the pillar radius range wider for the appearance of the flat band.Three kind of equivalent models for transverse,longitudinal and torsional modes are newly updated for explanation of physical mechanism accounts according to the eigenmode and strain energy density distribution.The errors between the theoretical and numerical results are much smaller.Thirdly,the two-component phononic crystal thin plate,the in-plane and out-of-plane modes of the three-component phononic crystal are optimized based on the plane wave expansion(PWE)and the genetic optimization algorithm.The unit cell is devided first and filled with material then.The structure function is calculated according to the Fourier displacement property.Results indicate that filling rates,symmetry,dispersion and material parameters are key factors for design of topological configurations.The relations between the key factors and different topologies are studied in detail.Compared with the standard genetic algorithm,the improved algorithm based on CBR has better convergence and faster search speed,which improves the performance of the standard genetic algorithm to some extent.Finally,the propagation properties of self-collimation-based acoustic waves are investigated by finite element method in the designed PC structure.The line-defects can make the acoustic beams split into two beams:one beam is the transmitted beam which propagates in the original direction and another beam is the reflected beam which is perpendicular to the incident acoustic beam.The beam splitter PC structure can be controlled by adjusting the radii of the rods and the coating layer in the line defects.Three wave beams get to the boundary when the radii of the rod and coating layer meet certain conditions.The effects of the acoustic speed of the coating layer on acoustic wave splitting are discussed.The output acoustic wave can be altered by controlling the phase of the two sound sources.