Asymmetric viscoelastic metamaterials for broad bandgap design and unidirectional zero reflection

We propose an asymmetric viscoelastic metamaterial constructed from a unit with two distinct resonators selected to isolate elastic waves in a large coupled locally resonant bandgap (LRBG) and simultaneously realize designed unidirectional zero reflection (UZR). A generalized Maxwell model, as opposed to a Kelvin–Voigt model or standard linear solid model, is adopted to more accurately describe actual linearly viscoelastic mechanical response in both the epoxy and rubber components over the frequency range of application. The analysis of the band structure of this asymmetric viscoelastic matamaterial shows that there is a quasi-bandgap formed between the two LRGBs when they are close, allowing a broadening of the bandwidth of wave isolation. Interface response theory and finite element methods are used to show that the quasi-bandgap forms in the frequency domain for both discrete and continuous metamaterials. Exploiting this asymmetric viscoelastic metamaterial, an exceptional point with UZR for longitudinal waves in the non-Hermitian system is achieved by tuning the masses of two oscillators in the unit. The proposed multifunctional metamaterial may have significant potential in vibration/wave control and guided wave based non-destructive testing.