Topology optimization for phononic band gap maximization considering a target driving frequency

Yi, Guilian; Shin, Yong Chang; Yoon, Heonjun; Jo, Soo-Ho; Youn, Byeng D.

doi:10.1007/s42791-019-00019-y

Cited by 20 publications

(7 citation statements)

References 11 publications

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“…All of the structures show a reinforcement on their corners, which use tungsten for those elements. A similar behavior was reported in previous literature for 2D structures [ 13 , 25 , 26 , 32 ].…”

Section: Resultssupporting

confidence: 90%

“…Li et al [ 25 ] proposed a new optimization approach based a bidirectional evolutionary structural optimization (BESO) for bandgap maximization of two-dimensional structures. A gradient-based optimization algorithm was used by Yi et al [ 26 ] to maximize the bandgap at a given frequency for two-dimensional solid materials. This approach makes it possible to design a bandgap with the maximum width for a target frequency.…”

Section: Introductionmentioning

confidence: 99%

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Phononic Bandgap Optimization in Sandwich Panels Using Cellular Truss Cores

et al. 2021

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The development of custom cellular materials has been driven by recent advances in additive manufacturing and structural topological optimization. These contemporary materials with complex topologies have better structural efficiency than traditional materials. Particularly, truss-like cellular structures exhibit considerable potential for application in lightweight structures owing to their excellent strength-to-mass ratio. Along with being light, these materials can exhibit unprecedented vibration properties, such as the phononic bandgap, which prohibits the propagation of mechanical waves over certain frequency ranges. Consequently, they have been extensively investigated over the last few years, being the cores for sandwich panels among the most important potential applications of lattice-based cellular structures. This study aims to develop a methodology for optimizing the topology of sandwich panels using cellular truss cores for bandgap maximization. In particular, a methodology is developed for designing lightweight composite panels with vibration absorption properties, which would bring significant benefits in applications such as satellites, spacecraft, aircraft, ships, automobiles, etc. The phononic bandgap of a periodic sandwich structure with a square core topology is maximized by varying the material and the geometrical properties of the core under different configurations. The proposed optimization methodology considers smooth approximations of the objective function to avoid non-differentiability problems and implements an optimization approach based on the globally convergent method of moving asymptotes. The results show that it is feasible to design a sandwich panel using a cellular core with large phononic bandgaps.

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Section: Resultssupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Phononic Bandgap Optimization in Sandwich Panels Using Cellular Truss Cores

et al. 2021

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“…8 and 9, we observe that the optimized topologies depend on the initial layouts. This phenomenon of dependency on the initial layouts for the unconstrained band gap maximization problem has been previously described in the literature (Yi et al, 2019;Li et al, 2016b) and is somewhat expected in gradient-based optimization. From the plots of the iteration histories of the objective function, we observe that the objective function increases rapidly at the starting stage of the topology optimization process and then the convergence rate becomes significantly slowed down over the iterations.…”

Section: Topology Optimization Resultssupporting

confidence: 53%

“…The use of topology optimization for maximizing phononic band gaps was pioneered by Sigmund & Søndergaard Jensen (2003). Their work was followed by many studies employing optimization techniques for synthesizing phononic crystals such that desired band gap characteristics are obtained (Halkjaer & Jensen, 2006;Gazonas et al, 2006;Hussein et al, 2007;Bilal & Hussein, 2011;Liu et al, 2014Liu et al, , 2016aLi et al, 2016a;Liu et al, 2016b;Xie et al, 2017;Lu et al, 2017;Xie et al, 2017;Chen et al, 2018;Yi et al, 2019;Liu et al, 2020;Quinteros et al, 2021;Zhang et al, 2021). Detailed reviews on topology optimization of phononic crystals were provided by Yi & Youn (2016) and Li et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

Sharma

Kosta

Gal

et al. 2022

Composite Structures

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Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable.To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method for maximizing the width of the band gaps in an exemplary case study. We employ a finite element formulation of the governing equations, and use the properties of each element as the design variables. In order to iteratively update the design variables, we employ gradient-based optimization, namely the Method of Moving Asymptotes. We carry out and implement fully analytical sensitivity analysis for computing the gradient of the objective function with respect to each one of the design variables. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider that those that were generated using metaheuristics-based topology optimization, while the computational cost to identify them is reduced by orders of magnitude.

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“…[1,2] In the prior few years, a substantial amount of theoretical, numerical, and experimental studies have been conducted on metamaterials with peculiar applications, for example, wave guidance and filtering, [3][4][5] acoustic, [6][7][8] energy harvesting, [9][10][11] and vibration isolation. [12][13][14] Accordingly, many research groups committed to finding effective methods to realize wave propagation along a predetermined pathway using metamaterials, for example, local resonance methods, [15,16] Bragg scattering methods, [17,18] topology optimization methods, [19][20][21] and wave interference-based methods. [22] However, to the best of the authors' knowledge, although the existing methods for manipulating wave propagation have been widely investigated, most of them are limited to acting on longitudinal waves and little research work has focused on the shear waves.…”

Section: Introductionmentioning

confidence: 99%

Functionally Graded Phononic Crystals with Broadband Gap for Controlling Shear Wave Propagation

Liu

Yoon

et al. 2020

Adv Eng Mater

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Metamaterials that can be used in manipulating wave propagation have been shown in previous research. However, existing methods for controlling the propagation of shear waves remain a challenge. By combining the principle of wave destructive interference and the design concept of the gradient‐index phononic crystals, here new functionally graded phononic crystals with broadband gap for controlling shear wave propagation are presented. The proposed functionally graded phononic crystals are formed by an array of unit cells with different topological geometries, where the topological geometries of the unit cell are tailored to obtain the frequency bandgap guided by the wave destructive interference. Meanwhile, the frequency bandgap with a target width is obtained by combining the design concept of the gradient‐index phononic crystals. This work presents an approach to control the propagation of shear waves, and the advantages of the method reported in this work can be useful in engineering applications, such as bridges, railways, and buildings.

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Topology optimization for phononic band gap maximization considering a target driving frequency

Cited by 20 publications

References 11 publications

Phononic Bandgap Optimization in Sandwich Panels Using Cellular Truss Cores

Phononic Bandgap Optimization in Sandwich Panels Using Cellular Truss Cores

Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

Functionally Graded Phononic Crystals with Broadband Gap for Controlling Shear Wave Propagation

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