Title: On the wave propagation analysis and supratransmission prediction of a metastable modular metastructure for adaptive non-reciprocal energy transmission,
Abstract: In this research, we investigate the nonlinear energy transmission phenomenon
in a reconfigurable and adaptable metastable modular metastructure. Numerical
studies on a 1D metastable chain uncover that when the driving frequency is
within the stopband of the periodic structure, there exists a threshold input
amplitude, beyond which sudden increase in the energy transmission can be
observed. This onset of transmission is due to nonlinear instability and is
known as supratransmission. We show that due to spatial asymmetry of
strategically configured constituents, such transmission thresholds could shift
considerably when the structure is excited from different ends and therefore
enabling the non-reciprocal energy transmission. We discover that the critical
threshold amplitude can be predicted analytically using a localized
nonlinear-linear model combining harmonic balancing and transfer matrix
analyses. Additionally, influences of important parameters on the change of
threshold amplitude are investigated to provide insight on synthesizing systems
with desired non-reciprocal characteristics. These investigations elucidate the
rich and intricate dynamics achievable by nonlinearity, asymmetry, and
metastability, and provide new insights and opportunities to accomplish
adaptable non-reciprocal wave energy transmission.