IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2024-03-29T14:50:21ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2018-01-16T10:10:51Z2018-01-16T10:10:51Zhttp://eprints.imtlucca.it/id/eprint/3862This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/38622018-01-16T10:10:51ZMulti-parametric sensitivity analysis of the band structure for tetrachiral acoustic metamaterialsTetrachiral 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 an 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 tetrachiral acoustic 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.Marco LepidiAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2017-09-18T12:42:34Z2017-09-18T12:42:34Zhttp://eprints.imtlucca.it/id/eprint/3790This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37902017-09-18T12:42:34ZA lumped mass beam model for the wave propagation in anti-tetrachiral periodic latticesThe engineered class of periodic anti-tetrachiral materials is mainly characterized by
the unusual macroscopic property of a negative Poisson’s ratio. The auxetic behavior of the material
depends on the geometric and elastic features of the microstructure. In particular, the material symmetries
of the periodic cell govern the quadratic or orthotropic symmetry of the first-order elastic
tensor (i.e. auxetic quadratic or auxetic orthotropy). Under the assumption of uniform mass density
and elastic properties, one or the other case can be realized by a square or rectangular microstructure,
respectively. A beam lattice model with lumped masses is employed to analyse the effects
of different, usually small-valued, geometric and elastic parameters of the high- and low-frequency
dispersion curves and band gaps characterizing the free wave propagation.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itMarco Lepidi2017-09-18T12:26:07Z2017-09-18T12:26:07Zhttp://eprints.imtlucca.it/id/eprint/3789This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37892017-09-18T12:26:07ZPassive control of wave propagation in periodic anti-tetrachiral meta-materialsPeriodic anti-tetrachiral materials are strongly characterized by a marked auxeticity,
the unusual and fascinating mechanical property mathematically expressed by negative values
of the Poisson’s ratio. The auxetic behavior is primarily provided by pervasive rolling-up mechanisms
developed by the doubly-symmetric micro-structure of the periodic cell, composed by a
regular pattern of rigid rings connected by tangent flexible ligaments. Adopting a beam-lattice
model to describe the linear free dynamics of the elementary cell, the planar wave propagation
along the bi-dimensional material domain can be studied according to the Floquet-Bloch
theory. Parametric analyses of the dispersion curves, carried out with numerical or asymptotic
tools, typically reveal a highly-dense spectrum, with persistent absence of total band-gaps in the
low-frequency range. The paper analyses the wave propagation in the meta-material developed
by introducing rigid massive inserts, locally housed by all the rings and working as undamped
linear oscillators with assigned inertia and/or stiffness properties. The elastic coupling between
the cell microstructure and the oscillators, if properly tuned (inertial resonators), is found to
significantly modify the Floquet-Bloch spectrum of the material. The effects of the resonator
parameters (tuning frequency and mass ratio) on the low-frequency band structure of the metamaterial
are discussed, with focus on the valuable possibility to (i) open total band gaps, by
either the widening of an existing partial band gap or the avoidance of a crossing point between
adjacent dispersion curves, (ii) finely control the total band-gap amplification, in order to assess
the maximum achievable performance of the meta-material against the vibration propagationMarco LepidiAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2017-09-18T12:18:33Z2017-09-18T12:18:33Zhttp://eprints.imtlucca.it/id/eprint/3788This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37882017-09-18T12:18:33ZAnalytical and computational methods for modeling mechanical filters against bloch wave propagationThe free propagation of elastic waves through periodic microstructured materials
can be studied by the analytical formulation of beam lattice models for the elementary cell, in
combination with the Floquet-Bloch theory. Within this framework, the present paper deals
with periodic tetrachiral materials characterized by a monoatomic cell. Alternative analytical
formulations can be developed by continualization-homogenization techniques in micropolar
equivalent continua, characterized by overall elastic and inertial tensors. Valid approaches
for the solution of the wave propagation problems are offered by perturbation methods, numerical
continuation techniques, and – finally – computational analyses, suited to account for
some mechanical updates or improvements that can hardly be included in synthetic formulations.
Based on these considerations, the dispersion curves achievable by different formulations
are compared and discussed. The major interest is focused on the spectral effects
determined by changes in the geometry, inertia, elasticity of the microstructural elements and,
finally, by variations in the cellular symmetry. Some attention is paid to the parameter combinations,
which might open band gaps in the low-frequency range, useful to filter undesired
dynamic signals for vibration shielding purposes.Francesca VadalàAndrea Bacigalupoandrea.bacigalupo@imtlucca.itMarco LepidiLuigi Gambarotta2017-09-18T10:54:34Z2017-09-18T10:54:34Zhttp://eprints.imtlucca.it/id/eprint/3787This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37872017-09-18T10:54:34ZAsymptotic approximation of the band structure for tetrachiral metamaterialsTetrachiral 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. Therefore, 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 Floquet-Bloch spectrum (or band structure) governing the propagation of elastic waves through the tetrachiral material. By virtue of multiparametric perturbation techniques, an analytical asymptotic approximation is achieved for the dispersion surfaces in the Brillouin zone. Since different optimization strategies tend to fail in opening low-frequency band gaps in the material spectrum, this specific design purpose is commonly pursued by introducing interring inertial resonators. The paper demonstrates that multiparametric perturbation methods can efficiently deal with the consequent enlargement of the parameter space, necessary to describe the resulting inertial metamaterial. Indeed, paying due attention to the doubling of internal resonance conditions, an accurate parametric approximations of the enriched band structure can be achieved. From the applicative perspective, the research findings furnish suited analytical tools for the optimal design of pass and stop bands.Marco LepidiAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2017-08-04T09:59:14Z2017-08-04T09:59:14Zhttp://eprints.imtlucca.it/id/eprint/3741This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37412017-08-04T09:59:14ZMulti-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterialsTetrachiral 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)Marco LepidiAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2017-03-21T12:16:36Z2017-03-21T12:16:36Zhttp://eprints.imtlucca.it/id/eprint/3673This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36732017-03-21T12:16:36ZParametric design of the band structure for lattice materialsLattice 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.Marco LepidiAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2017-03-21T11:56:47Z2017-03-21T11:56:47Zhttp://eprints.imtlucca.it/id/eprint/3668This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36682017-03-21T11:56:47ZHigh-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materialsThe class of anti-tetrachiral cellular materials is phenomenologically characterized by a strong auxeticity of the elastic macroscopic response. The auxetic behavior is activated by rolling-up deformation mechanisms developed by the material microstructure, composed by a periodic pattern of stiff rings connected by flexible ligaments. A linear beam lattice model is formulated to describe the free dynamic response of the periodic cell, in the absence of a soft matrix. After a static condensation of the passive degrees-of-freedom, a general procedure is applied to analyze the wave propagation in the low-dimensional space of the active degrees-of-freedom. The exact dispersion functions are compared with explicit – although approximate – dispersion relations, obtained from asymptotic perturbation solutions of the eigenproblem governing the Floquet–Bloch theory. A general hierarchical scheme is outlined to formulate and solve the perturbation equations, taking into account the dimension of the perturbation vector. Original recursive formulas are presented to achieve any desired order of asymptotic approximation. For the anti-tetrachiral material, the fourth-order asymptotic solutions are found to approximate the dispersion curves with fine agreement over wide regions of the parameter space. The asymptotic eigensolutions allow an accurate sensitivity analysis of the material spectrum under variation of the key physical parameters, including the cell aspect ratio, the ligament slenderness and the spatial ring density. Finally, the explicit dependence of the dispersion functions on the mechanical parameters may facilitate the custom design of specific spectral properties, such as the wave velocities and band gap amplitudes.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itMarco Lepidi2017-03-21T11:05:10Z2017-09-21T14:56:38Zhttp://eprints.imtlucca.it/id/eprint/3666This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36662017-03-21T11:05:10ZOptimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materialsThe elastic wave propagation is investigated in a 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 number, placement and properties of the inertial resonators can be designed to open, shift and enlarge the band gaps between one or more pairs of consecutive branches in the frequency spectrum. In order to improve the meta-material performance, several nonlinear optimization problems are formulated. The largest among the band gap amplitudes in the low-frequency range is selected as suited objective function. Proper inequality constraints are introduced to restrict the admissible solutions within a compact set of mechanical and geometric parameters, including only physically realistic properties of both the lattice and the resonators. The optimization problems related to full and partial band gaps are solved by using a globally convergent version of the numerical method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique. The optimal solutions are numerically computed, discussed and compared from the qualitative and quantitative viewpoints, bringing to light the limits and potential of the meta-material performance. The clearest trends emerging from the numerical analyses are pointed out and interpreted from the physical viewpoint. Finally, some specific recommendations about the microstructural design of the meta-material are synthesized.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itGiorgio Gneccogiorgio.gnecco@imtlucca.itMarco LepidiLuigi Gambarotta2017-03-21T10:56:30Z2017-03-21T10:56:30Zhttp://eprints.imtlucca.it/id/eprint/3664This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36642017-03-21T10:56:30ZDesign of acoustic metamaterials through nonlinear programmingThe dispersive wave propagation in a periodic metamaterial with tetrachiral topology and inertial local resonators is investigated. The Floquet-Bloch spectrum of the metamaterial is compared with that of the tetrachiral beam lattice material without resonators. The resonators can be designed to open and shift frequency band gaps, that is, spectrum intervals in which harmonic waves do not propagate. Therefore, an optimal passive control of the frequency band structure can be pursued in the metamaterial. To this aim, a suitable constrained nonlinear optimization problem on a compact set of admissible geometrical and mechanical parameters is stated. According to functional requirements, the particular set of parameters which determines the largest low-frequency band gap between a pair of consecutive branches of the Floquet-Bloch spectrum is obtained. The optimization problem is successfully solved by means of a version of the method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique.
Subjects: Materials Science (cond-mat.mtrl-sci)
Cite as: arXiv:1603.07717 [cond-mat.mtrl-sci]
(or arXiv:1603.07717v2 [cond-mat.mtrl-sci] for this version)Andrea Bacigalupoandrea.bacigalupo@imtlucca.itGiorgio Gneccogiorgio.gnecco@imtlucca.itMarco LepidiLuigi Gambarotta2016-02-26T12:26:43Z2017-03-21T10:32:36Zhttp://eprints.imtlucca.it/id/eprint/3122This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/31222016-02-26T12:26:43ZOptimal design of auxetic hexachiral metamaterials with local resonatorsA parametric beam lattice model is formulated to analyse the propagation properties of elastic in-plane waves in an auxetic material based on a hexachiral topology of the periodic cell, equipped with inertial local resonators. The Floquet-Bloch boundary conditions are imposed on a reduced order linear model in the only dynamically active degrees-offreedom. Since the resonators can be designed to open and shift band gaps, an optimal design, focused on the largest possible gap in the low-frequency range, is achieved by solving a maximization problem in the bounded space of the significant geometrical and mechanical parameters. A local optimized solution, for a the lowest pair of consecutive dispersion curves, is found by employing the globally convergent version of the Method of Moving asymptotes, combined with Monte Carlo and quasi-Monte Carlo multi-start techniques.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itMarco LepidiGiorgio Gneccogiorgio.gnecco@imtlucca.itLuigi Gambarotta