Design and Additive Manufacturing of 3D Phononic Band Gap Structures Based on Gradient Based Optimization

Wormser, Maximilian; Wein, Fabian; Stingl, Michael; Körner, Carolin

doi:10.3390/ma10101125

Cited by 64 publications

(34 citation statements)

References 46 publications

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“…These systems have a particular dispersion relation with the presence of band gaps [3]. Recently, with the advent of 3D printing, more complex and efficient designs are allowed [4][5][6][7]. In the particular case of rigid scatterers embedded in a fluid host, the system is known as sonic crystal because they are particularly suited for sound waves [8].…”

Section: Introductionmentioning

confidence: 99%

“…s . ∆ slit = ∆l 1 + ∆l 2 is the length correction, where ∆l 1 is the length correction given by the pressure radiation at the discontinuity from the neck duct to the cavity of the Helmholtz resonator, and ∆l 2 comes from the radiation at the discontinuity from the neck to the principal waveguide (see reference [38]) given by Equation (4) and Equation (5). It is important to note that, due to the symmetry of each resonator, the radiation correction of the slit to the free space must be applied at both sides of the structure.…”

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confidence: 99%

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Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators

et al. 2020

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We report a theoretical and experimental study of an array of Helmholtz resonators optimized to achieve both efficient sound absorption and diffusion. The analysis starts with a simplified 1D model where the plane wave approximation is used to design an array of resonators showing perfect absorption for a targeted range of frequencies. The absorption is optimized by tuning the geometry of the resonators, i.e., by tuning the viscothermal losses of each element. Experiments with the 1D array were performed in an impedance tube. The designed system is extended to 2D by periodically replicating the 1D array. The 2D system has been numerically modeled and experimentally tested in an anechoic chamber. It preserves the absorption properties of the 1D system and introduces efficient diffusion at higher frequencies due to the joint effect of resonances and multiple scattering inside the discrete 2D structure. The combined effect of sound absorption at low frequencies and sound diffusion at higher frequencies, may play a relevant role in the design of noise reduction systems for different applications.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators

et al. 2020

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“…There are two formation mechanisms of the elastic band gap in PCs: one is the Bragg scattering mechanism [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and the other is the locally resonant mechanism. The wave length corresponding to the elastic band gap formed by Bragg scattering is generally equal to the lattice size or lattice constant, which restricts its application in engineering practice.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

et al. 2019

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The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields.

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“…Further developments include substantial material research to optimize different metallic powders and minimize the grain size to improve resolution and surface roughness [28]. SLS and SLM have recently been successfully employed to build 3D phononic crystals for lower frequency operation [16,19].…”

Section: Choice Of Fabrication Technologymentioning

confidence: 99%

“…Numerical analysis usually focuses on the formation of a complete band gap between all types of propagation modes in an infinite lattice, or on a specific type of wave propagation through a semi-infinite lattice. Experimental acoustic transmission analysis is then often limited to only one primary propagation direction [16][17][18][19]. As early phononic crystal research has already shown, the band structure and transmission behavior will yield drastically different results for the complete, omnidirectional band gap and more application oriented directional band gaps for specific acoustic modes.…”

Section: Introductionmentioning

confidence: 99%

Design and Fabrication Challenges for Millimeter-Scale Three-Dimensional Phononic Crystals

Lucklum

Vellekoop

2017

Crystals

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While phononic crystals can be theoretically modeled with a variety of analytical and numerical methods, the practical realization and comprehensive characterization of complex designs is often challenging. This is especially important for the nearly limitless possibilities of periodic, three-dimensional structures. In this contribution, we take a look at these design and fabrication challenges of different 3D phononic elements based on recent research using additive manufacturing. Different fabrication technologies introduce specific limitations in terms of, e.g., material choices, minimum feature size, aspect ratios, or support requirements that have to be taken into account during design and theoretical modeling. We discuss advantages and disadvantages of additive technologies suitable for millimeter and sub-millimeter feature sizes. Furthermore, we present comprehensive experimental characterization of finite, simple cubic lattices in terms of wave polarization and propagation direction to demonstrate the substantial differences between complete phononic band gap and application oriented directional band gaps of selected propagation modes.

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Design and Additive Manufacturing of 3D Phononic Band Gap Structures Based on Gradient Based Optimization

Cited by 64 publications

References 46 publications

Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators

Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

Design and Fabrication Challenges for Millimeter-Scale Three-Dimensional Phononic Crystals

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