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This work presents a generalized physical interpretation of unconventionaldispersion asymmetries associated moving elastic solids. By shifting the notionfrom systems with time-variant material fields to physically travelingmaterials, the newly adopted paradigm provides an eloquent take on thedispersion problem and, in the process, highlights discrepancies between bothschemes. Equations governing the motion of an elastic rod with a prescribedmoving velocity observed from a stationary reference frame are used to predictpropagation patterns and asymmetries in wave velocities induced as a result ofthe induced linear momentum bias. Three distinct scenarios corresponding to amoving rod with a constant modulus, a spatially varying one, and one thatvaries in space and time are presented. These cases are utilized to extract andinterpret correlations pertaining to directional velocities, dispersionpatterns, as well as nature of band gaps between moving periodic media andtheir stationary counterparts with time-traveling material properties. A linearvertical shear transformation is derived and utilized to thoroughly neutralizethe effect of the moving velocity on the resultant dispersion characteristics.Finally, dispersion contours associated with the transient response of a finitemoving medium are used to validate the entirety of the presented framework.

Generalized Analysis of Elastic Wave Dispersion Asymmetries in Moving Periodic Media