A distichous-opposite metamaterial beam and its asymmetric transmission

Abstract

In this study, we present a novel metamaterial beam with asymmetric wave transmission properties under reciprocal conditions, termed the distichous-opposite metamaterial beam (DOMB), realized through a distichous-opposite arrangement of resonators. Based on the DOMB's mechanical characteristics in each propagation direction, the transfer matrices for forward and backward wave propagation are derived, and corresponding computational models are developed. An experimental test rig is designed and fabricated to investigate the DOMB's bidirectional vibration characteristics. Experimental measurements and transfer matrix method calculations consistently demonstrate that elastic waves exhibit strongly asymmetric transmission in the DOMB. Within specific frequency ranges, forward-propagating waves are significantly suppressed and blocked, while reverse-propagating waves transmit unimpeded, confirming the asymmetric wave transmission characteristics of the metamaterial beam. Analysis of the asymmetric transmission mechanism reveals that the resonators' bending moments act in opposite directions during forward and backward wave propagation, inducing distinct flexural wave responses in the main beam. As a result, a localized vibration mode emerges under backward propagation, but is absent in forward propagation, leading to the observed asymmetric wave transmission in the DOMB. Structural parametric studies reveal that the asymmetric transmission in the metamaterial beams maintains a consistent asymmetric transmission peak frequency under a designated resonator natural frequency, regardless of coupling beam stiffness. The DOMBs produce pronounced asymmetric bands with surrounding broadband gaps under varying unit cell counts, demonstrating stable directional wave control.