Dynamics of bistable metamaterials under impulsive excitation

Recent studies highlight the potential of bistable acoustic metamaterials in energy harvesting, sound absorption, and damping. We explore the propagation of transition waves through a finite chain of oscillators with bistable substrate potential due to impulse loading. Depending on the initial velocity, transition waves propagate through the chain until a certain depth. The depth varies cyclically, with alternating ranges of initial velocities where the transition wave either propagates throughout the lattice or is not generated at all. These distinct ranges are intricately linked to the generation of kinks and antikinks due to the initial kinetic energy imparted to the lattice. We employ energy-based arguments to demonstrate a linear relationship between the initial kinetic energy values corresponding to each range and the index of the range. The slope and intercept of this linear trend are determined by a crucial design parameter – the onsite stiffness of the metamaterial. We also observe multiple sub-windows at the boundaries of the velocity ranges, resembling the 'n-bounce' resonance windows found during kink-antikink collisions. Unveiling how impulses generate transition waves in bistable acoustic metamaterials can help design materials that effectively absorb and dampen energy due to impact.