The mechanical behaviour of periodic three-dimensional nonhomogeneous solids can be functionally designed by optimizing their cellular composite microstructure. The present contribution aims at establishing a theoretical and methodological framework to determine the dispersion properties of periodicCauchy materials, characterized by a generic microstructured repetitive cell. First, two conceptually alternative strategies are formulated to state the continuous complex-valued eigenproblem, governing the free undamped propagation ofBlochwaves, in the finite domain of the periodic cell. Second, a consistent mathematical procedure to convert the governing field equations into an equivalent discrete eigenproblem, suited to be computationally attacked through the finite element method, is outlined.
Free Bloch Wave Propagation in Periodic Cauchy Materials: Analytical and Computational Strategies
Bacigalupo A.;Lepidi M.;
2022-01-01
Abstract
The mechanical behaviour of periodic three-dimensional nonhomogeneous solids can be functionally designed by optimizing their cellular composite microstructure. The present contribution aims at establishing a theoretical and methodological framework to determine the dispersion properties of periodicCauchy materials, characterized by a generic microstructured repetitive cell. First, two conceptually alternative strategies are formulated to state the continuous complex-valued eigenproblem, governing the free undamped propagation ofBlochwaves, in the finite domain of the periodic cell. Second, a consistent mathematical procedure to convert the governing field equations into an equivalent discrete eigenproblem, suited to be computationally attacked through the finite element method, is outlined.File | Dimensione | Formato | |
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Current Trends and Open Problems in Computational Mechanics (2022) pp.41-49 Springer, Cham.pdf
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