Quadramode materials: Their design method and wave property

Abstract Extremal materials with certain vanishing eigenvalues of their elastic matrix are able to manipulate elastic wave with their extremal static property, the devices designed with such materials can work in a broad frequency band, which is highly demanded in low frequency applications. A type of extremal materials with four zero eigenvalues called quadramode (QM) materials is the subject of this investigation. Wave properties of different QM materials, particularly their capacity on shaping iso-frequency curves, are firstly examined with homogeneous models. A three-dimensional QM material is then designed using a truss lattice model. The designed lattice is validated through comparison between the homogeneous and discrete models on their prediction on iso-frequency curves and polarizations. An out-of-plane shear (SH) wave polarizer is proposed with the designed QM material, it can effectively prevent the mode conversion at interface with fluids. This unique property is further explored for waterborne sound isolation, a prototype of this polarizer is also proposed and demonstrated through numerical simulation. This study paves the way for exploring the exotic wave properties of QM extremal materials, and opens a new route to control low frequency elastic wave.