  We present a novel approach to achieve adaptable band structures and
non-reciprocal wave propagation by exploring and exploiting the concept of
metastable modular metastructures. Through studying the dynamics of wave
propagation in a chain composed of finite metastable modules, we provide
experimental and analysis results on non-reciprocal wave propagation and unveil
the underlying mechanisms in accomplishing such unidirectional energy
transmission. Utilizing the property adaptation feature afforded via
transitioning amongst metastable states, we uncovered an unprecedented bandgap
reconfiguration characteristic, which enables the adaptivity of wave
propagation within the metastructure. Overall, this investigation elucidates
the rich dynamics attainable by periodicity, nonlinearity, asymmetry, and
metastability, and creates a new class of adaptive structural and material
systems capable of realizing tunable bandgaps and non-reciprocal wave
transmissions.
