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

Park, Jun Hyeong; Sik, Pyung; Kim, Yoon Young

doi:10.1007/s00158-014-1206-8

Cited by 46 publications

(20 citation statements)

References 37 publications

(50 reference statements)

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“…In terms of the material uncertainty for the obtained deterministic design, the design has a mean band gap of 34.68 kHz and a standard deviation of 2.41 kHz. Although the deterministic design has a larger mean value of the band gap, the robust design still has better stochastic performance in terms of the objective function (23) and is less sensitive to uncertainty in the input material distribution. A remarkable difference can be found between the robust design in Figure 7 and the deterministic design in Figure 8.…”

Section: Robust Topology Optimization Resultsmentioning

confidence: 99%

Robust topology optimization of phononic crystals with random field uncertainty

Zhang

Takezawa

et al. 2018

Numerical Meth Engineering

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Summary The uncertain spatial variation of material properties can remarkably affect the band gap characteristics of phononic crystals (PnCs). It is necessary to consider this issue when designing and manufacturing PnC materials/structures. This paper investigates a robust topology optimization method for designing the microstructures of PnCs by considering random‐field material properties. Herein, the spatial distribution of the material properties is first represented by a random field and then discretized into uncorrelated stochastic variables with the expansion optimal linear estimation method; stochastic band gap analysis is then conducted with polynomial chaos expansion. Furthermore, a robust topology optimization formulation of PnCs is proposed on the basis of the relative elemental density, where a weighted objective function handles the compromise of the mean value and standard deviation of the PnC band gap. The band gap response is analyzed, employing the finite element method for each sample of polynomial chaos expansion. In this context, the sensitivities of the stochastic band gap behaviors to the design variables are also derived. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of PnCs with a relatively large width and less sensitive band gap. Additionally, the effects of the weight factors in the objective function and the variation coefficient of material properties are discussed.

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Section: Robust Topology Optimization Resultsmentioning

confidence: 99%

Robust topology optimization of phononic crystals with random field uncertainty

Zhang

Takezawa

et al. 2018

Numerical Meth Engineering

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“…Accordingly, a working frequency of 19 kHz is suitable for both structures considered in this work. Moreover, to enable 3-D focusing with each composite lens, the equifrequency contours (EFCs) in the x-z plane were computed by sweeping the wavevector through all positions in the unit cell [34][35][36] . As shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

Design and characterization of an acoustic composite lens with high-intensity and directionally controllable focusing

Sun

Wang

Huang

et al. 2020

Sci Rep

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Acoustic orientation and bunching methods, which include the radiation surface expansion, ultrasonic demodulation, multiunit coherence, phased arrays and acoustic lenses, can be used to manipulate and focus sound waves. Recently, focusing systems composed of acoustic lenses have been found to offer high controllability and focusing intensity. in this paper, a newly designed composite acoustic lens that can achieve wave convergence is proposed by assembling a lattice array of concave hexagonal (cH)-shaped rods. in comparison with the latest published work, the new cH structure improves upon the focusing capability of traditional acoustic lenses while retaining their advantages in terms of 3-D underwater focusing. Simulated and experimental results show that a lens with the cH structure has good focusing intensity and can focus acoustic waves over a wide range of incidence angles without losing its functionality. With its good focusing capabilities, this new composite lens may open the door to a broad range of applications, including high-precision nondestructive testing (NDT), high-efficiency medical treatment and multidirectional underwater focusing.Over the past three decades, man-made materials that can control wave characteristics have been proposed and endowed with capabilities beyond those of materials that exist in nature 1-4 . Periodic composites that act as special unnatural structures such as photonic 5 or phononic crystal arrays have been theoretically developed and experimentally verified 6,7 . In contrast to metamaterial-based negative refractive index devices with deep-subwavelength resolution 8-13 , periodic crystal structures introduce acoustic waves into phononic crystals resulting from Bragg scattering and occurring in passbands with a negative group velocity 14,15 . However, in practice, for usage in medical treatment and nondestructive testing (NDT), high-performance acoustic composite materials are required, such as acoustic superlens or hyperlens 16 . To overcome the limitations of such materials for these potential applications, the focusing of acoustic waves using phononic crystals has been systematically studied in both air and water 17,18 , and a broad variety of applications for acoustic focusing have been demonstrated.In the literature, in the field of acoustic focusing with composite lens structures, resonant units for convergent lenses have been designed and developed with various shapes, such as rigid cylinders [19][20][21][22] , Helmholtz resonators 23,24 , cross structures [25][26][27] , and concentric rings 28 , or with the use of multiphase materials to reduce impedance mismatch 29 . Acoustic lenses with rigid cylinders are commonly designed as gradient index (GRIN) homogenized 2-D sonic crystals based on Bragg reflection 30 . To modify the local refraction index (or filling fraction) to achieve sound focusing, a particular calculated radial distribution or crystal material must be used for the cylinders, as seen from both theory and experiment 31 . However, 2-D GRIN acoustic len...

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“…Extraordinary features of heterogeneous lattice structures in controlling acoustic and elastodynamic waves have attracted a great deal of research and motivated development of design optimization methods. The destructive interaction of waves within these structures when the wavelength is comparable to the lattice periodicity, enables self-collimation, negative refraction and even total reflection of particular frequencies (Deymier 2011;Lin 2012;Nemat-Nasser 2015a;Park, Ma & Kim 2015). Frequency ranges over which successive in-phase (Bragg) reflection of waves at the interface of periodic heterogeneities causes exponential decay of the wave amplitude are called phononic bandgaps.…”

Section: Introductionmentioning

confidence: 99%

Maximizing bandgap width and in-plane stiffness of porous phononic plates for tailoring flexural guided waves: Topology optimization and experimental validation

Hedayatrasa

Kersemans

Abhary

et al. 2017

Mechanics of Materials

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Phononic crystal plates (PhPs) with porous heterogeneities manufactured through perforation of a uniform plate comprise effective wave reflecting interfaces and are free from complexities and interfacial imperfections associated with fabricating bi-material designs. However, numerical optimization of such porous PhPs for maximized bandgap efficiency naturally leads to topologies with isolated solid domains, or disconnected island-like features. Requiring PhPs to exhibit an adequate stiffness is, therefore, an important design consideration. This paper presents a multi-objective topology optimization study with experimental validation to explore the relationship between bandgap efficiency and effective in-plane stiffness, introducing topologies exhibiting superior properties compared to those reported in earlier works. Topology optimization is performed in two stages: first, at a relatively coarse resolution followed by a topology optimization on a refined mesh. The minimum allowable length scale of features is maintained across the mesh refinement, and thus the refined stage primarily leads to optimization of the feature boundaries, which is shown to significantly enhance response. Bandgap of fundamental flexural guided wave modes is studied herein, and it is shown how bandgap efficiency is degraded by increasing the in-plane stiffness. Distinct stiff and compliant topology modes are realized in the intermediate section of the optimized Pareto fronts which offer variation of structural stiffness while having almost the same bandgap efficiency, with potential application as base cells in design of gradient phononic lattices. A subset of promising stiff and compliant optimized topologies are manufactured by water-jetting of an aluminum plate and experimentally tested to validate the calculated bandgap efficiencies and effective elastic properties.

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

Cited by 46 publications

References 37 publications

Robust topology optimization of phononic crystals with random field uncertainty

Robust topology optimization of phononic crystals with random field uncertainty

Design and characterization of an acoustic composite lens with high-intensity and directionally controllable focusing

Maximizing bandgap width and in-plane stiffness of porous phononic plates for tailoring flexural guided waves: Topology optimization and experimental validation

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