Limits of the Kelvin Voigt Model for the Analysis of Wave Propagation in Monoatomic Mass Spring Chains

Abstract

In this study, the effect of energy dissipation on harmonic waves propagating in onedimensional monoatomic linear viscoelastic massspring chains is investigated. In particular, first dispersion laws in terms of wavenumber, attenuation, and wave propagation velocities (phase, group, and energy) for a generic viscoelastic massspring chain are derived from the homologous linear elastic (LE) expressions in force of the correspondence principle. A new formula for the energy velocity is introduced to account for energy dissipation. Next, such relations are specified for the Kelvin Voigt (KV) and the standard linear solid (SLS) rheological models. The analysis of the KV massspring chain in the highfrequency regime proves that the socalled wavenumbergap is not related to energy dissipation, as assumed in previous studies, but is due to the nonphysical rigid behavior of the model at high frequencies. The SLS massspring chain, in fact, does not show any wavenumbergap and at high frequencies recovers the wavenumber dispersion curve of the LE system. The behavior of the energy velocity for the different massspring chains confirms this conclusion.