Nonlinear Dynamics of Bistable Lattices with Defects

Heterogeneity in a lattice system has gained continued attention from researchers due to its ability to support interesting localized dynamics and engineering applications. Most studies on the influence of the defects have been done in a one-dimensional monoatomic chain with both linear and nonlinear interactions. However, analysis of defect dynamics in a lattice under on-site potential is still a rare finding. Recently, extreme wave propagation has been demonstrated theoretically and experimentally on a bi-stable lattice with magnetic inter-site force, featuring quartic on-site potential. In this work, the nonlinear dynamics of introducing engineered defects in the form of mass impurities and inter-site forcing disparities on lattices of bi-stable elements are studied. We investigate the effect of the defect presence on the local wave propagation speed and identify the critical conditions that governs the stable propagation of transition waves. With the control of damping, we further observe a special satellite region, where stable transition of wave with intermediate jumps between the stable states of the local unit cell occurs.