TY  - INPR
JF  - Meccanica
UR  - http://dx.doi.org/10.1007/s11012-017-0644-y
KW  - Lattice materials; Band structure; Parametric design; Inverse problem; Perturbation methods
Y1  - 2017///
AV  - none
TI  - Parametric design of the band structure for lattice materials
SP  - 1
N2  - Lattice materials are often investigated to determine how small parameter variations in the periodic microstructrure can influence the elastic wave propagation. A general hierarchical scheme, based on asymptotic perturbation techniques, is outlined to analytically assess the parametric sensitivity of the material band structure to a generic multi-parametric perturbation (direct problem). Modeling refinements, parameters updates, microstructural damages and manufacturing irregularities can be treated indifferently and simultaneously. According to a converse strategy, based on the inversion of the sensitivity problem, a hierarchical scheme is sketched to identify the parameter combinations which realize a design band structure (inverse problem). The direct and inverse problem are applied to the sensitivity analysis and band structure design of the anti-tetrachiral lattice material. Despite the high spectral density and the high-dimensional parameter space, the multi-parameter perturbation technique demonstrates its suitability in, first, analytically---although asymptotically---describe the material spectrum and, second, designing the material microstructure to obtain the desired spectral components. The inverse problem solution is discussed in terms of existence, uniqueness, asymptotic consistency and physical admissibility.
PB  - Springer
SN  - 0025-6455
A1  - Lepidi, Marco
A1  - Bacigalupo, Andrea
EP  - 16
ID  - eprints3673
ER  -