In this research, the nonreciprocal wave transmission features in one-dimensional and two-dimensional metastable modular metastructures are studied. Unlike previous work, in which the nonreciprocal transmission in metastable metastructures is realized by utilizing the supratransmission phenomenon when the excitation frequency is inside the linearized bandgap, a new approach is explored to achieve nonreciprocal wave transmission exploiting metastability and asymmetric dual-threshold snap-through. It is found that because of the asymmetry of potential energy wells of the equilibria, there will be two excitation amplitude thresholds for a metastable component when it is initially at the high-potential-energy equilibrium with excitation frequency within the passband. When the excitation amplitude increases and exceeds the first threshold, the metastable component will snap to the low-potential-energy equilibrium and maintain intrawell motion around this stable point, which will cause a significant decrease of the wave transmission. And when the excitation amplitude exceeds the second threshold, the metastable component will start to perform interwell motion, and now the wave transmission will increase suddenly. By using this “dual-threshold” phenomenon, nonreciprocal wave transmission in a one-dimensional structure is realized by connecting a metastable chain with a linear periodic part. Because of the wave attenuation effect of the linear part of the system, the excitation amplitude thresholds on different sides of the one-dimensional structure will be discrepant. Therefore, nonreciprocal wave transmission can be developed when the excitation amplitude is within certain ranges. It is interesting to note that the direction of nonreciprocal wave transmission can be changed by setting the excitation amplitude to different values. By changing the configuration of the metastable chain, the operation frequency and excitation amplitude ranges of the nonreciprocal transmission can be tuned. For a two-dimensional metastable metastructure, nonreciprocal wave transmission can be realized by adjusting the parameters of some metastable modules in the metastructure in the manner that the potential energy and energy thresholds of the adjusted modules and the unadjusted modules are different, but the passbands of the adjusted modules and the unadjusted modules will overlap in some frequency regions. Numerical studies provide clear insight of the proposed nonreciprocal wave transmission approach.

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