LOMBARDO, M. and ASKES, H., 2010. Elastic wave dispersion in microstructured membranes. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466 (2118), pp.1789-1807.
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.
This article was accepted for publication in the Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences: http://rspa.royalsocietypublishing.org/