Wave propagation in multistable magneto-elastic lattices

One dimensional (1D) and two dimensional (2D) magneto-elastic lattices are investigated as examples of multistable, periodic structures with adaptive wave propagation properties. Lumped-parameter lattices with embedded permanent magnets are modeled as point magnetic dipole moments, while elastic interactions are described as axial and torsional springs. The equilibrium configurations for the lattices are identified through minimization of the lattice potential energy. Bloch wave analysis is then conducted for small perturbations about stable equilibria to predict corresponding wave propagation properties. Finally, nonlinear dynamic simulations validate the findings of the linearized unit cell analysis, and illustrate the changes in dynamic behavior caused by topological transitions. Case studies for 1D systems show how pass bands and bandgaps are defined by lattice reconfigurations and by changes in lattice magnetization. In 2D systems, hexagonal lattices transition from regular honeycombs to re-entrant ones, which leads to significant changes in wave speeds, and directionality of wave motion and transition fronts.