In this study, an energy harvesting strategy that utilizes the input-independent, invariant transition waves in periodic lattices of bistable elements is explored. We observe that oscillatory tails are induced in a discrete array as transition waves propagate along the lattice. The generated tail at each unit cell vibrates predominantly at a single frequency, which indicates that the tail energy can be efficiently harvested through resonant transduction mechanisms. We introduce inertially and elastically equivalent lattice models to study the discreteness effect of the bistable lattice on the characteristic behaviors of the oscillatory tails and observe that the energy harvesting potential from transition waves can be significantly increased with growing discreteness.
In this study, the dynamics of a lattice of bistable elements connected by linear springs are investigated with emphasis on the spatial dependence of the response profiles created by the nonlinear transition wave. We address the difficulty in creating a permanent-form transition wave in real-world settings even though such a solution theoretically exists and explain how to utilize the speed difference in wave propagation to minimize this undesirable behavior through numerical investigations. We further introduce dissipative elements along with asymmetric on-site potentials to the baseline lattice and show that almost perfect response invariance can be achieved, where the response is not only spatially independent but also input-independent.
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.
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