Elastic wave dispersion in microstructured membranes

The effect of microstructural properties on the wave dispersion in linear elastic membranes is addressed in this paper. The periodic spring-mass lattice at the lower level of observation is continualised and a gradient-enriched membrane model is obtained to account for the characteristic microstructural length scale of the material. In the first part of this study, analytical investigations show that the proposed model is able to capture correctly the physical phenomena of wave dispersion in microstructured membrane which is overlooked by classical continuum theories. In the second part, a finite element discretisation of microstructured membrane is formulated by introducing the pertinent inertia and stiffness terms. Importantly, the proposed modifications do not increase the size of the problem with respect to the classical elasticity. Numerical simulations are included for validation purposes. The results confirm that the structural characteristics of the material can have a huge impact on the vibrational properties, particularly in the high-frequency range.