Wave propagation in mass embedded and pre-stressed hexagonal lattices

Abstract

This paper investigates the elastic wave propagation, mode veering, and in-plane vibration of pre-stressed hexagonal lattice embedded in an elastic medium and composed of axially loaded Timoshenko beams with attached point masses. The frequency band structure of the lattice system is obtained by solving the corresponding eigenvalue problem based on the Bloch theorem and the finite element method. The parametric study is performed by investigating the effects of the pre-stress magnitude, stiffness of elastic medium, and attached point masses on the band structure of a lattice unit cell. For simulating the free vibration behavior of the proposed lattices with different topologies, the Hurty-Craig-Bampton method is introduced to reduce the number of degrees of freedom. Based on the reduced finite element model, the natural frequencies are determined for various boundary conditions. The additional interface reduction technique, called system-level reduction, has been observed to achieve accurate results compared to that of the full model. Numerical experiments demonstrated a significant influence of the additional masses, pre-stress, and stiffness of elastic medium on Bloch waves and eigenvalues of the proposed lattice systems. The effects of different parameters on the emergence of mode veering phenomenon and band gaps are investigated in detail.