Elastic wave dispersion in microstructured membranes

The effect of microstructural properties on the wave dispersion in linear elastic membranes is addressed in this paper. A periodic spring-mass lattice at the lower level of observation is continualized 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 correctly capture the physical phenomena of wave dispersion in microstructured membrane which is overlooked by classical continuum theories. In the second part, a finite-element discretization 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 compared wiith classical elasticity. Numerical simulations confirm that the vibrational properties are affected by the microstructural characteristics of the material, particularly in the high-frequency regime.