Optimal synthesis of 2D phononic crystals for broadband frequency isolation

Hussein, Mahmoud I.; Hamza, Karim; Hulbert, Gregory M.; Saitou, Kazuhiro

doi:10.1080/17455030701501869

Cited by 87 publications

(27 citation statements)

References 16 publications

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“…The unique characteristics of phononic materials are currently exploited in a number of applications which include sensing devices based on resonators, acoustic logic ports, wave guides and filters based on surface acoustic waves (SAW). Synthesis of phononic materials with desired band gap and wave-guiding characteristics has achieved promising maturity, mostly through the application of topology and material optimization procedures [6][7][8]. Although very effective, such techniques may require intensive computations and may lead to complex geometries difficult to manufacture and whose performance may lack in robustness.…”

Section: Introductionmentioning

confidence: 99%

Phononic properties of hexagonal chiral lattices

et al. 2009

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a b s t r a c tThe manuscript reports the outcome of investigations on the phononic properties of a chiral cellular structure. The considered geometry features in-plane hexagonal symmetry, whereby circular nodes are connected through six ligaments tangent to the nodes themselves. In-plane wave propagation is analyzed through the application of Bloch theorem, which is employed to predict two-dimensional dispersion relations as well as illustrate dispersion properties unique to the considered chiral configuration. Attention is devoted to determining the influence of unit cell geometry on dispersion, band gap occurrence and wave directionality. Results suggest cellular lattices as potential building blocks for the design of meta-materials of interest for acoustic wave-guiding applications.

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Section: Introductionmentioning

confidence: 99%

Phononic properties of hexagonal chiral lattices

et al. 2009

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“…In the area of PnCs, the problem has been treated in a variety of settings and using several techniques. For example, unit cells have been optimized in one-dimension [18,19] and in two-dimensions (2D) [20][21][22][23][24][25], using gradient-based [21][22][23] as well as non-gradient-based [24,25] techniques. Interest in band-gap size maximation has also been treated outside the scope of the unit cell dispersion problem [21,26].…”

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confidence: 99%

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

2011

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We consider two-dimensional phononic crystals formed from silicon and voids, and present optimized unit cell designs for (1) out-of-plane, (2) in-plane and (3) combined out-of-plane and in-plane elastic wave propagation. To feasibly search through an excessively large design space (∼10 40 possible realizations) we develop a specialized genetic algorithm and utilize it in conjunction with the reduced Bloch mode expansion method for fast band structure calculations. Focusing on highsymmetry plain-strain square lattices, we report unit cell designs exhibiting record values of normalized band-gap size for all three categories. For the combined polarizations case, we reveal a design with a normalized band-gap size exceeding 60%.Phononic crystals (PnCs) are periodic materials that exhibit distinct frequency characteristics such as the possibility of formation of band gaps. In general, it is most advantagous to have the frequency range of a band gap maximized while pulling its midpoint as low as possible in order to keep the unit cell size to a minimum. Selecting the topological distribution of the material phases inside the unit cell provides a a powerful means towards reaching this target, and this has been the focus of numerous research studies not only on PnCs but also photonic crystals (PtCs).The exploration for optimal unit cell designs was initiated by Cox and Dobson in 1999 [15] (in the context of PtCs). The articles by Burger et al. [16] and Jensen and Sigmund [17] provide a review of subsequent studies concerned with band-gap widening in PtCs. In the area of PnCs, the problem has been treated in a variety of settings and using several techniques. For example, unit cells have been optimized in one-dimension [18,19] and in two-dimensions (2D) [20][21][22][23][24][25], using gradient-based [21][22][23] as well as non-gradient-based [24,25] techniques. Interest in band-gap size maximation has also been treated outside the scope of the unit cell dispersion problem [21,26]. In all these optimization studies the focus has been primarily on PnCs based on an infinite thickness model and a material composition consisting of two or more solid (or solid and fluid) phases with the exception of a few investigations that considered thin-plate singlephase models [22,23]. Recognizing the practical significance of solid-and-air PnCs with relatively large crosssectional thickness, some studies considered the configuraton of a 2D solid matrix with periodic cylindrical voids * Corresponding author; mih@colorado.edu.-modeled under 2D plain-strain conditons [27] or as a three-dimensional continuum with free surface boundary conditions [28] -and investigated the dependence of band-gap size upon the void radius. For combined out-of-plane and in-plane waves in 2D infinite-thickness PnCs formed from silicon and a square lattice of circular voids, it has been shown that the band-gap size normalized with respect to the mid-gap frequency cannot exceed 40% [27]. In this letter we utlize a specialized optimization algorithm in pursuit of ...

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“…2 Wave diffraction patterns depending on the shape of EFCs: a zero diffraction, b normal diffraction, c anti-diffraction. Arrows denote the directions of wave propagation in the wave vector space plane (k x , k y ) 2005; Halkjaer et al 2006;Rupp et al 2007;Hussein et al 2007;Stainko and Sigmund 2007;Wang et al 2011;Huang et al 2013), no topology optimization of self-collimating PCs has been carried out. Therefore, we need to newly set up a topology optimization formulation suitable for designing self-collimating PCs; we select the objective function to make zero curvature along the target portion of an EFC and the constraint function to make the slope of the target portion take a prescribed value.…”

Section: Introductionmentioning

confidence: 99%

Design of phononic crystals for self-collimation of elastic waves using topology optimization method

Park

Sik

Kim

2014

Struct Multidisc Optim

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Self-collimating phononic crystals (PCs) are periodic structures that enable self-collimation of waves. While various design parameters such as material property, period, lattice symmetry, and material distribution in a unit cell affect wave scattering inside a PC, this work aims to find an optimal material distribution in a unit cell that exhibits the desired selfcollimation properties. While earlier studies were mainly focused on the arrangement of self-collimating PCs or shape changes of inclusions in a unit cell having a specific topological layout, we present a topology optimization formulation to find a desired material distribution. Specifically, a finite element based formulation is set up to find the matrix and inclusion material distribution that can make elastic shear-horizontal bulk waves propagate along a desired target direction. The proposed topology optimization formulation newly employs the geometric properties of equi-frequency contours (EFCs) in the wave vector space as essential elements in forming objective and constraint functions. The sensitivities of these functions with respect to design variables are explicitly derived to utilize a gradient-based optimizer. To show the effectiveness of the formulation, several case studies are considered.

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Optimal synthesis of 2D phononic crystals for broadband frequency isolation

Cited by 87 publications

References 16 publications

Phononic properties of hexagonal chiral lattices

Phononic properties of hexagonal chiral lattices

Ultrawide phononic band gap for combined in-plane and out-of-plane waves

Design of phononic crystals for self-collimation of elastic waves using topology optimization method

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