2017
DOI: 10.1016/j.compositesb.2016.09.062
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Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials

Abstract: The elastic wave propagation is investigated in the beam lattice material characterized by a square periodic cell with anti-tetrachiral microstructure. With reference to the Floquet-Bloch spectrum, focus is made on the band structure enrichments and modifications which can be achieved by equipping the cellular microstructure with tunable local resonators. By virtue of its composite mechanical nature, the so-built inertial meta-material gains enhanced capacities of passive frequency-band filtering. Indeed the n… Show more

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Cited by 73 publications
(38 citation statements)
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“…where A is a 24 × 24 complex matrix, function of the dimensionless angular frequencyω 1 and wave vector K, slenderness λ 1 and λ 2 , aspect ratio α and geometric ratio χ. Vector c collects the 24 complex constants, C pq and D pq , appearing in the displacement field, Eqs. (5). Introducing the following normalization…”
Section: Dispersion Equationmentioning
confidence: 99%
“…where A is a 24 × 24 complex matrix, function of the dimensionless angular frequencyω 1 and wave vector K, slenderness λ 1 and λ 2 , aspect ratio α and geometric ratio χ. Vector c collects the 24 complex constants, C pq and D pq , appearing in the displacement field, Eqs. (5). Introducing the following normalization…”
Section: Dispersion Equationmentioning
confidence: 99%
“…This computational cost-saving target can be achieved by introducing acceptable simplifications, including -for instance -the adoption of machine-learning techniques for function interpolation or approximation. It has to be remarked that the considerations motivating the employment of machine-learning techniques are quite general, and their validity holds also for other optimizable topologies of periodic metamaterials [15], [16], [17].…”
Section: Motivations For Machine Learning In Spectral Design Problemsmentioning
confidence: 99%
“…Differently from [15], [16], [17], [22], the SLP algorithm is used instead of the Globally Convergent version of the Method of Moving Asymptotes (GCMMA) [33], [34], since some preliminary simulations suggest that, at least for the specific optimization problem, the performance of SLP does not depend strongly on the interpolation quality. Technical details about the mesh-free interpolation are reported in Appendix C; d) an iterative optimization algorithm is applied for a finite number s N of times, by adopting a Quasi-Monte Carlo multi-start initialization approach (identical to that employed in [15], [16], [17], [22]), which produces s N different starting points. In addition, a subset of the same input training points used for the construction of the interpolant is selected also to perform the Quasi-Monte Carlo multi-start initialization, since on such points the surrogate objective function reproduces exactly the true objective function, committing a zero approximation error therein.…”
Section: Surrogate Optimization In Spectral Designmentioning
confidence: 99%
“…where the O( 0 )-order combination parameter 2 s = 2 2 /χ 2 plays a key role. Indeed, it can be verified that the condition (18) is asymptotically equivalent to 2 s > 1 + 12 2 − δ 2 + 12 2 δ 2 (23) which essentially requires 2 s > 1, if higher orders are neglected. This low-order condition is fully consistent with the asymptotic approximation (19) obtained for the band gap amplitude.…”
Section: Pass and Stop Bandmentioning
confidence: 99%