The goal of this work is to develop a physically-based measure of the evanescence of wave propagation in phononic crystals (PCs) which can be used to quantitatively predict the behavior of finite PC-based systems. PCs have been widely reported to exhibit band gaps, which for non-dissipative systems are well-defined from the dispersion relation as a frequency range in which no propagating (i.e. non-decaying) wave modes exist. However, the notion of a band gap is less clear in dissipative systems, as all wave modes exhibit attenuation. Interpreting the dispersion relation is difficult because complex frequencies and/or wavenumbers must be taken into account. To overcome this difficulty, various measures have been proposed to quantify the "evanescence" of frequency ranges and/or wave propagation directions, but these measures lack a rigorous physical motivation. Furthermore, in finite systems created by truncating a PC, wave propagation is strongly attenuated but not completely forbidden, and a quantitative measure that predicts wave transmission in a finite viscoelastic PC from the infinite dispersion relation is elusive. Motivated by our prior study of wave propagation in magneto-active elastomeric metastructures, we propose a physically-based "evanescence indicator" that relates the decay component of the Bloch wavevector to the transmitted wave amplitude through a finite viscoelastic PC. When plotted over a frequency range of interest, this indicator reveals frequency regions of strongly attenuated wave propagation, which are dubbed "fuzzy band gaps" due to the smooth (rather than abrupt) frequency transition between evanescent and propagating wave characteristics. We apply this indicator to accurately predict measured band gaps in highly viscoelastic and finite phononic crystals, fabricated out of a magneto-active elastomer. 

"Fuzzy band gaps": quantifying Bloch wave evanescence in viscoelastic phononic crystals

The Virtual Technical Meeting of the Society of Engineering Science 2020 is the first fully virtual meeting of the SES community to envision and connect during the hiatus created by Covid-19, providing a platform for the exchange of ideas, and to showcase the latest research in the field of engineering science.

[Visit the Programme](https://drive.google.com/file/d/1BoCPBzrr1IQFANuzQI8a-paXCJoOcCkB/view?usp=sharing) | [Visit the Prerecorded Video/Poster List](https://drive.google.com/file/d/1XHLeEXJxEFjCSsNScuLDfMwy1X7oy7oJ/view?usp=sharing) | [View the Session Grid](https://drive.google.com/file/d/1VeDOC-Ev5m_ymYjXnjaXSZHR3_DARiLt/view?usp=sharing)