Effective Medium Theory For Elastic Metamaterial Thin Plates

Over the past decades,the propagation of elastic waves in artificial periodic structures such as phononic crystals or metamaterials has received a lot of attention for their unprecedented physical properties and potential applications in many various fields.In elastic metamaterials,many exotic parameters have been investigated,such as negative mass density,negative bulk modulus,negative shear modulus,extreme anisotropy,hybrid properties,etc.These renewed properties give rise to novel phenomena and applications such as low-frequency blocking,negative refraction,cloaking,perfect absorption and topological effects,etc.In this work,we study the effective media theories of different elastic metamaterials.We propose a new method to control the effective bending stiffness of elastic metamaterial thin plates:via out-of-plane rotational resonances.The dissertation is organized as follows:In the chapter one,we briefly introduce the background and research progress of elastic metamaterials.In the chapter two,we summarize the effective media theories of different elastic metamaterials.In the chapter three,we systematically investigate the resonant behaviors of an elastic metamaterial thin plate.Specifically,we prove that the effective bending stiffness of the metamaterial thin plate is closely related to the out-of-plane rotational resonances of the metamaterial.By engineering the out-of-plane rotational resonances,we can control the resonant behavior in the effective bending stiffness,independently with the effective mass density,which renders the resonant frequencies of the thin plate predictable and configurable.Realization of double negativity in bending stiffness and mass density has been shown to produce a negative band with negative group velocity.Our work demonstrates a novel design principle in controlling flexural waves in elastic thin plates,which could lead to important applications in acoustics and mechanical engineering.