Theory And Application Of Acoustic Thin Plate Metamaterials

Acoustic metamaterials (MMs) are artificial composite materials with special effectivematerial parameters, such as negative effective mass density and modulus. They have beenattracting an increasing interest due to their unique physical property and their potentialapplications to low frequency noise isolation, supper-resolution acoustic imaging, andacoustic cloaking. The thesis focuses on thin plate metamaterial, by idealizing the resonantunit cell as a mass-spring model, the analytical solution under oblique sound wave are derived.Then we use the proposed thin plate metamaterial to design acoustic cloak and to alleviatesound radiation. The main contributions are summarized as follows:1. The analytic solutions are derived for a thin-plate attached periodically withresonators under plane acoustic wave incident at an arbitrary angle, it is found that thisstructure can be homogenized by an effective medium with anisotropic mass density.Approximate analytic expressions of the effective mass density are derived under thecondition of normally incident wave, and it is shown that the effective mass density followseither Lorentz or Drude medium models, depending on nature of resonator. In obliqueincidence, the effective mass density is found to be dependent on the lateral wave number ofthe incident waves, such spatial dispersion effect is induced by the interplay between theincident acoustic wave and the flexural wave in the thin plate. With the parameter study, theresonant effect will be significantly enhanced with increase of the spring stiffness or the mass.The effective mass density is influenced mainly by the plate thickness h and the resonant unitperiod L.2. The analytic solution is derived for a multilayer thin-plates each attached withresonator for plane acoustic wave incident at an arbitrary angle. Effective dynamic propertiesare studied using the transfer matrix method, and again this structure can be homogenizedas an effective medium with anisotropic mass density. In the oblique incidence, the firstresonance is not much influenced by the incident angle. With the increasing of resonantfrequency, the effect of spatial dispersion is gradually enhanced. For a fixed incident angle,the steady transmission characteristic and the effective material parameters are independenton the number of thin plates. When each thin plate layer is simply supported, the multilayerkeeps the same effective property as the corresponding single layer below the cut-offfrequency for both normal and oblique incidences. Therefore the multilayer MMs willexhibits the same spatial dispersion as that of the single layer. Finally, this particular spatial dispersion effect is utilized for designing directive wave radiation, and the radiation anglecan be controlled by the operating frequency without the change of structural parameters ofthe metamaterial.3. Based on the proposed thin plate MMs, a prototype of acoustic cloak is proposed. Theanalytic solution on a plane acoustic wave incident on a rigid cylinder coated with three-layermetafluids each with anisotropic mass density is first derived. The required materialparameters of each shell for the cloaking are obtained through an optimization procedure byminimizing the external scatterings. These material parameters can be readily realized bymetamaterials with the unit cell consisting of fixed thin plate. The proposed structured cloakis composed of nine layers of thin plates and totally900plate units are used. At the targetingfrequency, the scattering is one order lower with the thin plate cloak compared with the barecylinder. The thin plate cloak is further improved by setting the fluid adjacent to the outerplate to be the same as the background medium, which is more easy to implement in practice.4. Interaction between an enclosed structure made of thin plate MMs and sound sourceis systematically examined, which includes two main parts:(1) Based on the analyticalsolution of one dimensional enclose structure, the sound reduction (SR) is studied withtraditional material and MMs of negative density. The cavity resonance and the resonancedue to the layered structure both exist for the traditional material even increasing the materialthickness. For the MMs, there is only cavity resonance in the negative density band of theMMs, and the resonance will be rapidly weakened with increasing of the material thickness.(2) Based on a circularly-shaped metamaterial model, we studied the sound reductioncharacteristic of the metamaterial enclosure with an internal source. Sound radiationproperties by either centered or eccentric sources are analyzed based on numericalsimulations for the structured metamaterial enclosure under monopole, dipole or quadrupoleexcitations. The SRs of the structured and the homogeneous enclosure agree well each other.The parametric analyses are based on the barrier thickness, the cavity size, and the sourcetype. In the centered source case, the dip frequency increases if the higher order of themultipole source is considered, while in the eccentric source case, it remains almostunchanged against the variation of the source type and eccentricity. Increasing the barrierthickness is found to be most effective in obtaining efficient sound reduction over the entirenegative-mass band.