Phononic properties of hexagonal chiral lattices

Spadoni, Alessandro; Ruzzene, Massimo; Gonella, Stefano; Scarpa, Fabrizio

doi:10.1016/j.wavemoti.2009.04.002

Cited by 289 publications

(183 citation statements)

References 26 publications

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“…The size and position of phononic band gaps in cellular solids can be controlled via the topology 13 and dimension 14 of the underlying unit cell. Apart from the chosen geometry 9,15 , the slenderness ratio of the struts 8 and the angle between the struts 16 were identified as key parameters for controlling the band structure.…”

Section: 2mentioning

confidence: 99%

Single phase 3D phononic band gap material

Warmuth

Wormser

Körner

2017

Sci Rep

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Phononic band gap materials are capable of prohibiting the propagation of mechanical waves in certain frequency ranges. Band gaps are produced by combining different phases with different properties within one material. In this paper, we present a novel cellular material consisting of only one phase with a phononic band gap. Different phases are modelled by lattice structure design based on eigenmode analysis. Test samples are built from a titanium alloy using selective electron beam melting. For the first time, the predicted phononic band gaps via FEM simulation are experimentally verified. In addition, it is shown how the position and extension of the band gaps can be tuned by utilizing knowledge-based design.Materials with complete phononic band gaps show frequency intervals in which the propagation of mechanical waves is not possible for any direction 1 . A lot of studies have been dedicated to phononic crystal systems with periodic variation of density and large mismatches in wave speed periodically modulated on a length scale comparable to the desired wavelength based on multi-phase systems [1][2][3][4] . We present a novel approach of designing the unit cell of a single phase three-dimensional cellular structure leading to complete and tunable phononic band gaps. Additive manufacturing is used to fabricate samples and verify the numerical predictions. This, in turn, opens completely new ways to adjust the vibrational and damping properties of structural components.Materials with phononic band gaps are either phononic crystals or acoustic metamaterials. Croënne et al. 5defined phononic crystals as systems in which the periodic arrangement of scatterers in a matrix is responsible for the emergence of phononic band gaps. Acoustic metamaterials, however, rely on the characteristics of the single inclusions inside the medium 5 . Different phononic band gap formation mechanisms have been described in literature 5 . The most common one relies on Bragg scattering of the waves in phononic crystals at the periodic inclusions and their destructive interference, hence they are called Bragg gaps 6 . Furthermore, hybridization gaps are caused by coupling of the rigid-body resonances of individual inclusions as well as the propagating mode in the embedding medium and do not need a periodic arrangement of inclusions 3,7 . Another mechanism appears only in systems in which masses are elastically bonded: in such a mechanism the resonant modes of the masses interact via the elastic bonding and passbands are generated Based on theoretical and numerical methods, the existence of phononic band gaps has been predicted in lattice topologies 8,9 , undulated lattices 10 and three-dimensional lattices 9,11,12 . The size and position of phononic band gaps in cellular solids can be controlled via the topology 13 and dimension 14 of the underlying unit cell. Apart from the chosen geometry 9, 15 , the slenderness ratio of the struts 8 and the angle between the struts 16 were identified as key parameters for controlling the band structu...

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Section: 2mentioning

confidence: 99%

Single phase 3D phononic band gap material

Warmuth

Wormser

Körner

2017

Sci Rep

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“…In this work, a representative auxetic structural network with internal rotational units, known as the chiral lattice is investigated with an equivalent, micropolar-continuum model in an attempt to remove the indeterminacy n ¼ À1 encountered so far (Prall and Lakes, 1997;Spadoni, 2008;Spadoni et al, 2009). A detailed microstructural analysis of the chiral lattice is also employed to describe the repercussions of auxetic behavior on the relationship between Young's modulus, shear modulus and Poisson's ratio.…”

Section: Introductionmentioning

confidence: 99%

Elasto-static micropolar behavior of a chiral auxetic lattice

Spadoni

Ruzzene

2012

Journal of the Mechanics and Physics of Solids

292

158

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a b s t r a c tAuxetic materials expand when stretched, and shrink when compressed. This is the result of a negative Poisson's ratio n. Isotropic configurations with n % À1 have been designed and are expected to provide increased shear stiffness G. This assumes that Young's modulus and n can be engineered independently. In this article, a micropolarcontinuum model is employed to describe the behavior of a representative auxetic structural network, the chiral lattice, in an attempt to remove the indeterminacy in its constitutive law resulting from n ¼ À1. While this indeterminacy is successfully removed, it is found that the shear modulus is an independent parameter and, for certain configurations, it is equal to that of the triangular lattice. This is remarkable as the chiral lattice is subject to bending deformation of its internal members, and thus is more compliant than the triangular lattice which is stretch dominated. The derived micropolar model also indicates that this unique lattice has the highest characteristic length scale l c of all known lattice topologies, as well as a negative first Lamé constant without violating bounds required for thermodynamic stability. We also find that hexagonal arrangements of deformable rings have a coupling number N ¼1. This is the first lattice reported in the literature for which couple-stress or Mindlin theory is necessary rather than being adopted a priori.

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“…A global stability criterion that purely depends onz was first determined by Maxwell for pin-joined lattices comprising spring-like ligaments 1 , and then modified to account for the nature (pin or welded) of the joints 6 , the bending stiffness of the struts 7,8 , self-stresses 9 , dislocation defects 10 , collapse mechanisms 11 and boundary modes [12][13][14][15] . In recent years, the dynamic response of periodic lattices has also attracted considerable interest [16][17][18][19] because of their ability to tailor the propagation of elastic waves through directional transmissions [20][21][22][23] and bandgaps (frequency ranges of strong wave attenuation) [21][22][23][24] . However, though several studies have shown that the wave propagation properties of periodic lattices are highly sensitive to the architecture of the network [20][21][22][23][24] , a global criterion connecting the frequency and size of bandgaps to the lattice topology is still not yet in place.…”

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confidence: 99%