Journal Article

# Homogenization and free-vibration analysis of elastic metamaterial plates by Carrera Unified Formulation finite elements

04 Mar 2021-Mechanics of Advanced Materials and Structures (Taylor & Francis)-Vol. 28, Iss: 5, pp 476-485
Abstract: This work focuses on the assessment of a novel so-called “homogenization method” allowing to transform a heterogeneous material with inclusions or holes into an equivalent homogeneous material with...

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Journal Article
Maria Cinefra1, G. D’Amico1, A. G. de Miguel1, Matteo Filippi1  +2 moreInstitutions (1)
01 Jul 2020-Applied Acoustics
Abstract: This work wants to investigate the soundproofing level of passive acoustic metamaterials made of Melamine Foam and cylindrical Aluminum inclusions. Latest research shows promising acoustical possibilities on controlling certain frequencies, varying their geometry or material configuration. Typically, acoustic metamaterials are plates with inclusions that resonate in low frequencies and block basses. Investigation is carried to use them for the improvement of aircraft cabin quietness. An homogenization method is adopted to study the metamaterial: this is modelled as viscoelastic material with inclusions, using a frequency-dependent approach, and the effective properties of the homogenized metamaterial are derived using a micromechanics-based method that allow us to prescribe the simplest mesh for periodical geometries (in this case, cylindrical) by reducing drastically the computation time. MSC Actran is used for vibro-acoustic simulations, in particular for the evaluation of Sound Transmission Loss in metamaterial panels with different volume fractions and in a sandwich panel with metamaterial core. This last has been compared with a classical sandwich panel used in aeronautics and it has been demonstrated that metamaterial gets higher transmission loss over all the frequency range.

8 Citations

Open access
01 Sep 2021-
Abstract: Since the introduction of the finite element approach, as a numerical solution scheme for structural and solid mechanics applications, various for mulation methodologies have been proposed. These ways offer different advantages and shortcomings. Among these techniques, the standard displacement-based approach has attracted more interest due to its straightforward scheme and generality. Investigators have proved that the other strategies, such as the force-based, hybrid, assumed stress, and as sumed strain provides special advantages in comparison with the classicfinite elements. For instance, the mentioned techniques are able to solve difficulties, like shear locking, shear parasitic error, mesh sensitivity, poor convergence, and rotational dependency. The main goal of this two-part study is to present a brief yet clear portrait of the basics and advantages of the direct strain-based method for development of high-performance plane finite elements. In this article, which is the first part of this study, assump tions and the basics of this method are introduced. Then, a detailed review of all the existing strain-based membrane elements is presented. Although the strain formulation is applicable for different types of structures, most of the existing elements pertain to the plane structures. The second part of this study deals with the application and performance of the reviewed elements in the analysis of plane stress/strain problems.

Topics: Plane stress (57%), Dependency (UML) (51%),

4 Citations

Journal Article
Abstract: This paper presents the static and mechanical buckling analyses of thick functionally graded (FG) plates. For this purpose, Carrera’s unified formulation (CUF) and the principle of virtual displace...

Topics: Finite strip method (58%), Buckling (51%), Static analysis (51%)

4 Citations

Journal Article
A. G. de Miguel1, M. Cinefra2, Matteo Filippi1, Alfonso Pagani1  +1 moreInstitutions (2)
Abstract: This work focuses on the study of composite metamaterials to be employed as possible lightweight insulation systems for noise and vibrations. In particular, the dispersion relations are derived by applying the Bloch-Floquet theory to the unit cell of the periodic microstructure. Advanced beam finite elements based on Carrera Unified Formulation are here extended, for the first time, to the dynamic characterization of these materials. Moreover, transmission curves are computed to validate the band gaps encountered in the analysis of dispersion behavior. The finite element model is first assessed by evaluating the dispersion behavior of some metamaterial configurations proposed in the literature. Finally, the model is applied to the parametric characterization of a composite metamaterial made of a melamine foam matrix and periodic distribution of cylindrical aluminium inclusions. The results show that it is possible to tune the band gaps of the metamaterial to lower frequencies by simply varying the dimensions of the unit cell and keeping constant its equivalent density.

Topics: Metamaterial (55%), ,

2 Citations

Journal Article
Abstract: Polysilazane-based ceramic coatings have ever-increasing applications in critical and high-power engineering. This paper analyzes the effects of the substrate grain size, the curvature of the coati...

Topics: Ceramic (60%), Coating (55%)

1 Citations

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Journal Article
R D Mindlin1, R D Mindlin2Institutions (2)

4,291 Citations

Open accessJournal Article
Guancong Ma1, Ping Sheng1Institutions (1)
Abstract: Within a time span of 15 years, acoustic metamaterials have emerged from academic curiosity to become an active field driven by scientific discoveries and diverse application potentials. This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors. We survey the more recent developments, which include compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians. Many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature.

Topics: , Metamaterial (60%), Acoustic wave (51%)

678 Citations

Open accessJournal Article
Abstract: Mechanical metamaterials exhibit properties and functionalities that cannot be realized in conventional materials. Originally, the field focused on achieving unusual (zero or negative) values for familiar mechanical parameters, such as density, Poisson's ratio or compressibility, but more recently, new classes of metamaterials — including shape-morphing, topological and nonlinear metamaterials — have emerged. These materials exhibit exotic functionalities, such as pattern and shape transformations in response to mechanical forces, unidirectional guiding of motion and waves, and reprogrammable stiffness or dissipation. In this Review, we identify the design principles leading to these properties and discuss, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami-based metamaterials), metamaterials harnessing instabilities and frustration, and topological metamaterials. We conclude by outlining future challenges for the design, creation and conceptualization of advanced mechanical metamaterials.

Topics: , Metamaterial (60%)

572 Citations

Open accessJournal Article
Charles Elachi1Institutions (1)
01 Dec 1976-
Abstract: The theory and recent applications of waves in periodic structures are reviewed. Both the Floquet and coupled waves approach are analyzed in some detail. The theoretical part of the paper includes wave propagation in unbounded and bounded active or passive periodic media, wave scatterring from periodic boundaries, source radiation (dipole, Cerenkov, transition, and Smith-Purcell) in-periodic media, and pulse transmission through a periodic slab. The applications part covers the recent development in a variety of fields: distributed feedback oscillators, filters, mode convertors, couplers, second-harmonic generators, deflectors, modulators and transducers in the fields of integrated optics and integrated surface acoustics. We also review the work on insect compound eyes, mehanical structures ocean waves, pulse compressions, temperature waves, and cholestric liquid crystals. Particles interaction with crystals is briefly reviewed, especially in the case of zeolite crystals and supelattices. Recent advances in fabrication techniques for very fine gratings me also covered. Finally, speculations about future problems and development in the field of waves in periodic structures are given.

Topics: Wave propagation (59%), Periodic function (55%), Wind wave (53%) ... show more

451 Citations

Journal Article
William J. Gordon1, Charles A. Hall2Institutions (2)
Abstract: In order to better conform to curved boundaries and material interfaces, curved finite elements have been widely applied in recent years by practicing engineering analysts. The most well known of such elements are the "isoparametric elements". As Zienkiewicz points out in [18, p. 132] there has been a certain parallel between the development of "element types" as used in finite element analyses and the independent development of methods for the mathematical description of general free-form surfaces. One of the purposes of this paper is to show that the relationship between these two areas of recent mathematical activity is indeed quite intimate. In order to establish this relationship, we introduce the notion of a "transfinite element" which, in brief, is an invertible mapping $$\vec T$$ from a square parameter domainJ onto a closed, bounded and simply connected region? in thexy-plane together with a "transfinite" blending-function type interpolant to the dependent variablef defined over?. The "subparametric", "isoparametric" and "superparametric" element types discussed by Zienkiewicz in [18, pp. 137---138] can all be shown to be special cases obtainable by various discretizations of transfinite elements Actual error bounds are derived for a wide class of semi-discretized transfinite elements (with the nature of the mapping $$\vec T$$ :J?? remaining unspecified) as applied to two types of boundary value problems. These bounds for semi-discretized elements are then specialized to obtain bounds for the familiar isoparametric elements. While we consider only two dimensional elements, extensions to higher dimensions is straightforward.