Free Wave Propagation in Two-Dimensional Lattice Model of Textile Metamaterials

Abstract A parametric lattice model is formulated to describe the dispersion properties of harmonic elastic waves propagating in two-dimensional textile metamaterials. Within a weak nonlinear regime, the free undamped motion of the textile metamaterial, starting from a spatially periodic prestressed configuration, is governed by nonlinear differential difference equations, where nonlinearities arise from the elastic contact between plain woven yarns. Using Bloch’s theorem for periodic systems, the linear dispersion properties characterizing the regime of small oscillation amplitudes are obtained. Parametric analyses are carried out to study the influence of the mechanical parameters on wavefrequencies, waveforms and group velocities, respectively. As major spectral features, two distinct passbands are found to cover the low- and the high-frequency ranges, respectively, while a complete mid-frequency bandgap exists for large parameter regions.