Effect of finite mass on phononic band structure of face centered pentamodal lattice

Abstract

Owing to the unique and fascinating property of very high resistance to compressibility in comparison to relatively very small resistance to shear deformation, pentamode lattice has become a coveted form of the metamaterial. Ideally, the connection points in the pentamode lattice are infinitely small which renders it impractical to realize physically. In the present paper, a new pentamode lattice is proposed having a finite spherical mass at the connection point. Effect of added mass at the connection points on the phononic band structure of the proposed pentamode lattice is investigated. Numerical modeling of the proposed lattice is done using COMSOL Multiphysics and dispersion relation of the proposed model is obtained using appropriate boundary conditions. From the dispersion diagram of the proposed pentamode lattice, relative band gap is identified. Effect of various parameters such as Young’s Modulus, density, Poisson’s ratio and geometry of the lattice unit cell on the dispersion relation is studied. It is observed that the relative bandwidth is not affected by the material variation; however, the geometric properties have slight influence on it.