Elastic wave propagation and vibration characteristics of diamond-shaped metastructures

Abstract

In this work, the elastic wave propagation behavior of the proposed diamond-shaped metastructure is investigated analytically based on the 8 degrees of freedom mass-spring discretized structure and numerically by finite element method (FEM), and an experiment was carried out with the 3D printed specimen. Analytically, the dispersion relation of the metastructure is derived based on Bloch’s theorem, and the transmittance of the metastructure with finite periods is investigated. Also, the extreme cases of the lattice structure parameters, such as the stiffness and mass, are investigated to examine different configuration effects. When the inner spring’s stiffness tends to infinity or infinitesimal, which is the rigid connection or string connection, it opens a lower boundary of 6.26 Hz with infinitesimal stiffness. Then cases with some specific masses tending to infinity or infinitesimal, representing fixed or missing mass, are discussed, which opens a lower boundary of 19.9 Hz with the largest mass. Also, tuning the FEM model parameters opens lower bandgaps, where a similar trend can be observed from the theoretical and simulation studies. Finally, the frequency response of the finite element solution is validated by conducting a vibration experiment on the 3D printed specimen, and a good agreement can be observed. The proposed metastructure can be utilized in the design of vibration isolators.