eprintid: 3741
rev_number: 9
eprint_status: archive
userid: 69
dir: disk0/00/00/37/41
datestamp: 2017-08-04 09:59:14
lastmod: 2017-08-04 09:59:14
status_changed: 2017-08-04 09:59:14
type: monograph
metadata_visibility: show
creators_name: Lepidi, Marco
creators_name: Bacigalupo, Andrea
creators_id: 
creators_id: andrea.bacigalupo@imtlucca.it
title: Multi-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterials
ispublished: submitted
subjects: T1
subjects: TA
divisions: CSA
full_text_status: public
monograph_type: working_paper
abstract: Tetrachiral materials are characterized by a cellular microstructure made by a periodic pattern of stiff rings and flexible ligaments. Their mechanical behaviour can be described by a planar lattice of rigid massive bodies and elastic massless beams. The periodic cell dynamics is governed by a monoatomic structural model, conveniently reduced to the only active degrees-of-freedom. The paper presents an explicit parametric description of the band structure governing the free propagation of elastic waves. By virtue of multiparametric perturbation techniques, sensitivity analyses are performed to achieve analytical asymptotic approximation of the dispersion functions. The parametric conditions for the existence of full band gaps in the low-frequency range are established. Furthermore, the band gap amplitude is analytically assessed in the admissible parameter range. In inertial tetrachiral metamaterials, stop bands can be opened by the introduction of intra-ring resonators. Perturbation methods can efficiently deal with the consequent enlargement of the mechanical parameter space. Indeed high-accuracy parametric approximations are achieved for the band structure, enriched by the new optical branches related to the resonator frequencies. In particular, target stop bands in the metamaterial spectrum are analytically designed through the asymptotic solution of inverse spectral problems.
Subjects:	Materials Science (cond-mat.mtrl-sci)
Cite as:	arXiv:1706.08754 [cond-mat.mtrl-sci]
 	(or arXiv:1706.08754v1 [cond-mat.mtrl-sci] for this version)
date: 2017
date_type: published
publisher: arXiv
pages: 21
id_number: arXiv:1706.08754
institution: IMT Institute for Advanced Studies Lucca
official_url: https://arxiv.org/abs/1706.08754
citation:   Lepidi, Marco and Bacigalupo, Andrea  Multi-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterials.  Working Paper   arXiv       (Submitted)   
document_url: http://eprints.imtlucca.it/3741/1/1706.08754.pdf