Multi-scale wave propagation modelling for two-dimensional periodic textile composites

In this article, a method allowing vibro-acoustic and ultrasonic wave propagation analysis of highly anisotropic textile composites at a mesoscopic level is presented for the first time. The method combines the advantages of mode-based Component Mode Synthesis (CMS) that allows reduction of the size of the Dynamic Stiffness Matrix (DSM) of a textile unit cell, and of a Wave Finite Element Method (WFEM), which associates the Periodic Structure Theory (PST) with standard Finite Element Method (FEM). The scheme presented allows the study of the wave propagation properties of a periodic structure by modelling only a unit cell. A multi-scale approach is used to enable the comparison of standard vibrational analysis of textile composite structures, using homogenised properties, with a more complex analysis, where the mesoscale properties of the structure are preserved. It is shown for two different types of weaves that using a standard homogenised model results in significant errors in the dispersion curves. Also band-gap behaviour within specific frequency ranges are successfully predicted using the mesoscale models, whereas it was not observed in the macroscale ones.