Size-dependent wave propagation in two-dimensional functionally graded lattice materials

Abstract

Although the size-dependency of small-scale structures has limited the application of classic continuum theories to model their various mechanical properties, it has opened new avenues for the introduction of nonclassical continuum theories with the ability to capture the size effects. In this work, the modified strain gradient theory, for the first time, is used to model two-dimensional planar lattices of hexagonal and triangular architectures made of functionally graded materials. Using the finite element method and Bloch's theorem, the size-dependent wave propagation in such micro-lattices is investigated and the effect of the functionally graded distribution of materials on the wave-propagation and wave-filtering performances of such structures is studied. The results show that using the modified strain gradient theory, the dispersion curves and stop-bands are predicted at higher frequencies compared to the classical and modified couple stress theories. Additionally, by implementing functionally graded constituting elements, the location and width of stop-bands can be tuned.