On the wave propagation analysis and supratransmission prediction of a metastable modular metastructure for non-reciprocal energy transmission

Abstract

In this research, we investigate in-depth the nonlinear energy transmission phenomenon in a metastable modular metastructure and develop efficient tools for the design of such systems. Previous studies on a one-dimensional (1D) reconfigurable metastable modular 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 caused by nonlinear instability and is known as supratransmission. 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. This one-way propagation characteristic can be adaptable via reconfiguring the metastable modular system. In this new study, we build upon these findings and advance the state of the art by (a) exploring the different mechanisms that are able to activate the onset of supratransmission and their implications on wave energy transmission potential, and (b) developing an effective design tool - a localized nonlinear-linear model combined with harmonic balancing and transfer matrix analyses to analytically and efficiently predict the critical threshold amplitude of the metastable modular chain. These investigations provide important new understandings of the rich and intricate dynamics achievable by nonlinearity, asymmetry, and metastability, and create opportunities to accomplish adaptable non-reciprocal wave energy transmission.