Phonons in diatomic linear viscoelastic chains

In this study waves propagating in a diatomic linear viscoelastic periodic system are investigated with the aim of understanding the operative range of some commonly adopted rheological models. Dispersion laws of a diatomic viscoelastic periodic system under prescribed harmonic motion, i.e. real angular frequency and complex wavenumber (wavenumber and attenuation), are derived. It is shown that such relations can be easily obtained from the linear elastic counterpart in force of the correspondence principle. The complex band structures and energy velocity for the one-dimensional diatomic periodic chains are computed considering both the Kelvin Voigt and the Standard Linear Solid models. It is proven that unusual dispersive behaviors already observed by other researchers when using the Kelvin Voigt model, such as wavenumber-gaps and strong band shifting, are only caused by its nonphysical rigid behavior at high frequencies, since they disappear once the Standard Linear Solid model is adopted. The comparison between the energy velocity of the Kelvin Voigt and Standard Linear Solid discrete systems provides a further confirmation of these findings.