Axially moving materials with granular microstructure. (October 2019) - Nejadsadeghi, Nima; Misra, Anil
Highlights: Axially moving materials with granular microstructures is modeled. Granular micromechanics model with enriched kinematic description is utilized. Elastic wave dispersion asymmetries is investigated. Emergence of frequency band gaps and negative group velocities is predicted. Abstract: The mechanics of axially moving media is significant because of their broad engineering applications. In many engineering applications, it is beneficial to understand the dynamical material response from a microstructural viewpoint. Here we focus upon wave propagation in axially moving materials with granular microstructure. To this end, the granular micromechanics approach is utilized since the resulting continuum model is known to predict wave dispersion. To consider axially moving materials, this approach is enhanced to account for the axial velocity using an Eulerian description of the system accounting for convective terms in the material derivatives and utilizing variational approach. The dispersive behavior of axially moving 1D materials are then derived and compared with the dispersive behavior of non-moving materials. In the absence of microstructure, the axially moving material model simplifies to published literature and shows non-dispersive non-symmetric forward and backward waves. In the case of axially moving materials with granular microstructure, the model predicts dispersive non-symmetric waves. In this case, there are two acoustic and two optical wave branches. Axial velocity leads to narrowing and widening in the frequency band gaps in the forward and backward waves, respectively. Negative group velocity is also observed in certain wavenumber ranges. Clearly, the stopbands created by the axial velocity and the non-symmetric dispersive behavior studied here should be considered in engineering designs for vibration control when the axially moving material possesses granular microstructure. The results presented here can also be used to help obtain parameters needed for axially moving granular metamaterials to be designed for particular applications. Graphical abstract: Image, graphical abstract