Properties And Operations Of Waves In Folded Structures

Phononic crystals as a new kind of periodic materials exhibit lots of interesting properties which is beyond those known in nature.This thesis arms to discuss wave properties in the folded structure---a kind of phononic crystals,and proposes some device models to operate the propagation of elastic waves.It has been found that a perturbation for the folded structure may lead to a shift of resonance peak,a step change in transmission,a tunable chirality,etc.To explore the influence of perturbation to elastic wave properties in the folded structure,this thesis discusses the following three issues:Firstly,based on the theory of thin plate with an axial force,the wave equations are developed.The transfer matrix method is applied to solve the equations and yields the band structures which agree well with those obtained by the Finite Element Method(FEM).The results show that the coupling effects between multiple wave modes are strong enough to open the direct(i.e.the single mode band gap)and indirect band gap.The numerical transmission spectra and the band structures obtained by the Faster Fourier Transformation(FFT)verify the appearance of the direct and the indirect band gaps once more.Secondary,a two-dimensional(2D)Miura-Ori folded structure is built to explore wave properties,including band structure,polarization and anisotropy.The results show that this folded structure has some single mode band gaps and obvious anisotropy.The statistics of group velocity clearly displays a bias toward some particular directions,implying the function of a directional refraction.The sensitivity analysis of the structure parameters confirms the region of operations for the width of the directional band gap,the anisotropy and the distribution of the group velocity.The influence of the surface truncation of the structure on the wave propagation is analyzed.An easy method to suppress the resonance phenomenon due to the surface truncation is suggested.Finally,two devices for tuning the wave properties are designed based on the 2D Miura-Ori folded structure:1)a directional transmission device.With the gradient design waves can be gradually corrected from the oblique direction into the normal one,or gradually scattered from the normal incidence into an oblique emission.2)a nonreciprocal transmission device.By using the different directional band gaps of two cells,a kind of stable and nonreciprocal transmission device is design.Within a limit of perturbation,waves can pass through this device stably and efficiently in only one direction.Once the perturbation is beyond the limit the function of nonreciprocal transmission will disappear.With the sensitivity of perturbation,this device provides a tunable method to switch the function of nonreciprocal transmission.