弹性超材料波导的振动特性与界面波机理研究

Elastic metamaterial is a man-made functional composite constructed by sub-structural units arranged in lattice form. Owing to the eigen modes of monopole and multipole of these units, these composites can have various special dynamics that cannot be possessed by those materials of their components, extending extremely the space of material properties which cannot be achieved with existing natural materials. Research efforts of domestic and overseas scholars have been focused onto this new field in recent years and it has become an international frontier and hot-point which is developed rapidly..Existing research in elastic metamaterials focus mainly on the bulk wave behavior within 2D and 3D domains and lots of shinning achievements have been acquired. Researches on the dynamics of the elastic metamaterial waveguide are relatively limited, mainly embodying in two aspects, i.e., vibration properties within low and moderate frequency band together with their analyzing methods for finite waveguides made with elastic metamaterials; forming conditions together with propagating mechanisms of the elastic interface wave occurred near the interfaces within the infinite waveguides of elastic metamaterial. The understandings about above aspects are still not comprehensive and profound so far..Aiming at various basic elastic metamaterial waveguides, this project will conduct some works on above two aspects starting from the effective medium theory. Firstly, finite elastic metamaterial rod、shaft、beam、plate and corresponding composites will be studied comprehensively. The free and forced vibrational properties will be investigated and general vibration analyzing method and frame will be constructed for these special waveguides. Secondly, the interface wave behavior of infinite elastic metamaterial waveguides will be studied furtherly. Aiming at the elastic metamaterial layer、jointed half spaces and half space covered with elastic metamaterial layer, the Lamb type、Stonely type and Love type of interface wave will be investigated mainly on their existence and forming conditions.

弹性超材料（EMM）是一类由单胞以晶格点阵形式构成的复合介质。受单胞局域本征模式的影响，EMM可表现出组分材料所不具备的一系列独特的动力学性质，从而极大地拓展了自然介质难以达到的材料特性空间，近年来这一新兴领域已形成了一个迅猛发展的国际前沿热点。. 现有EMM研究主要集中于二维和三维无限域内的体波特性，而在EMM波导的中低频振动特性与分析方法，以及界面附近弹性波的传播机理等重要方面，人们的认识还远不够全面和深入。本项目针对典型EMM波导，从等效介质理论出发，开展两个方面的研究：1）全面考察有限EMM杆、轴、梁、板及其复合结构独特的模态特征及其振动规律，力图构建此类异质复合结构的一般振动分析方法；2）深入探索无限EMM波导内的界面波行为，针对EMM层、相联半空间和上覆EMM层的半空间，重点考察界面附近Lamb型、Stonely型和Love型等重要面波的形成机理与传播规律。

弹性超材料是一类由单胞以晶格点阵形式构成的复合介质，受单胞局域本征模式的影响，它们可表现出组分材料所不具备的一系列独特的动力学性质，从而极大地拓展了自然介质难以达到的材料特性空间，近年来这一新兴领域已形成了一个迅猛发展的国际前沿热点。已有弹性超材料研究主要集中于二维和三维无限域内的体波特性，而在弹性超材料波导的中低频振动特性与分析方法以及界面附近弹性波的传播机理等重要方面，目前的认识还不够全面和深入。本项目针对弹性超材料杆和梁等一维有限波导结构物及其复合结构，基于等效介质理论建立了一维等效介质分析模型，在此基础上将杆和梁以及夹芯杆梁的经典振动理论引入进来，给出了适合于中低频段振动特性研究的一般分析过程，研究了此类结构物的固有振动和受迫振动行为，揭示了等效介质参数的频率依赖性与负值性对模态特征和受迫振动特性的影响规律；针对二维弹性超材料板及其复合结构，构建了二维等效介质分析模型，将经典板壳和层合板振动理论拓展到此类具有频率依赖性和负值性介质参数的场景，给出了弯曲振动一般性分析方法和过程，得到了其异常的模态和受迫振动行为特征；针对弹性超材料层波导、由弹性超材料介质参与构成的相联半空间以及上覆弹性超材料层的半空间，从等效介质理论出发，建立了相应的等效介质分析模型，推导建立了各类波导中的波传播色散关系，深入分析了P-SV型和SH型波的界面传播行为和形成机理，揭示了等效介质的异常色散行为的影响规律。通过本项目的研究，不仅丰富和充实了弹性超材料领域的现有理论研究框架，同时也为弹性超材料理念的实际应用发展提供了有益的参考。