Broadband unidirectional vibration transmissibility governed by an eigenfrequency-transmissibility correlation

Unidirectional transmission is attracting increasing attention for applications in wave manipulation and sensing. Although asymmetric wave scattering in acousto-elastic systems is well-studied, asymmetric dynamic responses of finite structures remain less exploited and poorly understood, in terms of underlying mechanisms and design strategy. This work proposes a universal principle, referred to as eigenfrequency-transmissibility correlation, to elucidate how the unidirectional vibration transmissibility (UVT) would occur and behave in asymmetric finite structures. We analytically demonstrate such correlation through a simplified model to show that transmissibility extrema occur at the anti-resonance frequencies with vanishing response at excitation point, which strictly correspond to the eigenfrequencies of the adjoint subsystem or complementary subsystem with the excitation point fixed. Guided by this principle, a periodic beam with inherent asymmetry and broadband bandgap is designed, in which both theoretical and experimental results demonstrate a bilateral transmissibility difference exceeding 20 dB across a 4500 Hz bandwidth, testifying a broadband high-efficiency UVT. These findings provide a fundamental understanding on asymmetric dynamics and a generalized design framework for high-performance unidirectional wave devices.