Uni-directional wave propagation in time-modulated inerter-based lattice

Abstract

In this work, we investigate the uni-directional wave propagation in elastic locally resonant mechanical metamaterials with inerter elements, where mass and stiffness properties are simultaneously modulated as periodic functions of time. Time-modulated properties of inerter elements are adopted in order to highlight the effect of time-dependent inertia amplification on mass properties. By considering the Bloch theorem and Fourier expansion, the system of Hill equations is reduced to the eigenvalue problem that gives dispersion relations with asymmetric frequency band structures.