Wave Propagation Porperties In The Phononic Crystals And The Structure Design Of The Acoustic Metasurfaces

Both the phononic crystal(PC)and the acoustic metasurface(AMS)are the primary subdisciplines of the the acoustic metamaterial(AMM).The AMM is the functional material that has extraordinary properties differing from those of the materials found in nature owing to the elaborately designed microstructures.The AMMs are often composed of one or more kinds of conventional materials.They exhibit the band gaps for elastic waves,negative mass density,and zero refractive index,etc.,thus showing the great potential in vibration isolation,noise reduction,super-resolution imaging,and acoustic stealth to name a few.The Bragg type PC is the first kind of AMM,which possesses the band gaps for elastic waves.The resonant PC shows the outstanding sound illusion performance at the subwavelength scale,and sets the trend for the AMMs in the following years.The diversity of the AMMs with different subwavelength dimensions has enriched the content of the related research field.The acoustic metasurface,which is derived from the subwavelength AMMs,has become the hot spot in recent years for the flexibility in modulating the sound field.The research on the AMMs is not only of great value in academics,but also of significance in engineering.The dissertation investigates the two-dimensional binary solid PCs for the polarization pass band to understand the complex mechanism of the elastic wave propagation in inhomogeneous solids.A purely longitudinal pass band(PLPB),which cannot support the transverse wave mode,is obtained and verified with the numerical calculations for the band structures,eigenstates and transmission spectra.The respective effects of the filling ratio,lattice constant,inclusion shape and material properties on the PLPB are evaluated through parametric studies.The width of the PLPB increases with the growing filling ratio;the PLPB moves downwards as the lattice constant increases;the PCs with square inclusions have a wider PLPB than those with circular inclusions for a given filling fraction,and the PLPBs differ from each other in each direction if the inclusion symmetry is broken;and the impedance mismatch for transverse waves in each component of the PC is required to obtain a PLPB.It is also found that there is no relation between the PLPB and the band gap and that the PLPB is independent of the Dirac cone.Our studies on the PLPB provide an alternative way for filtering certain types of elastic waves with the use of PCs.Numerical simulations are performed to investigate the anomalous reflection(AR)phenomena in the fluid-matrix PCs for the underlying mechanism and for their dependence on the incident wave.The AR angles are retrieved with the plane wave impinging from different angles and with varying frequencies,and with the finite structures corresponding to the PC that has wide band gaps.The broadband AR is observed in a wide range of oblique incident angle.It is found that the frequency is higher for a smaller incident angle to stir up the AR phenomena.The information of the normal specific acoustic impedance is retrieved at the interface to study its relation to the AR phenomena.It shows that the AR is governed by the unsymmetrical normal specific acoustic impedance in every single cell.Research effort is also made on the AMSs that are designed based on the generalized Snell's law,in which the labyrinthine metamaterials,Helmholtz resonators and their likes,grooved plates with gradient depths,and membranes supported by rigid frames are frequently used.However,these designs still suffer from being bulky.We propose a design strategy by introducing labyrinthine beams into a resonant cavity so that a unit with deep subwavelength dimensions both in the thickness and width could be obtained.Placing the labyrinthine beams perpendicular to the AMSs is the key to reducing the unit thickness.The unit is further reduced in view of the symmetrical geometry.By introducing the labyrinthine beams into the Helmholtz resonators,the AMS units acquire outstanding performance in shifting the reflection phase.This work provides a useful guide for the application of AMSs in the low frequency regime.The research findings reported in the dissertation are helpful for better understanding the PCs,and provide an effective method to construct ultrathin metasurfaces to manipulate the reflective wavefront at will.