Probability that a band-gap extremum is located on the irreducible Brillouin-zone contour for the 17 different plane crystallographic lattices

Maurin, Florian; Claeys, Claus; Deckers, Elke; Desmet, Wim

doi:10.1016/j.ijsolstr.2017.11.006

Cited by 78 publications

(36 citation statements)

References 44 publications

(24 reference statements)

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“…In this work, modelling of wave propagation was restricted to the contour of the IBZ of the examined lattices. According to a statistical study by Maurin et al [56], restricting the detection of BGs to only the contour of the IBZ rather than the full IBZ provides accurate results for symmetric unit cells as well as savings in computation time. The IBZ of a cubic lattice is shown in Figure 7.…”

Section: Methodsmentioning

confidence: 99%

Multidimensional Phononic Bandgaps in Three-Dimensional Lattices for Additive Manufacturing

et al. 2019

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We report on numerical modelling of three-dimensional lattice structures designed to provide phononic bandgaps. The examined lattice structures rely on two distinct mechanisms for bandgap formation: the destructive interference of elastic waves and internal resonance. Further to the effect of lattice type on the development of phononic bandgaps, we also present the effect of volume fraction, which enables the designer to control the frequency range over which the bandgaps exist. The bandgaps were identified from dispersion curves obtained using a finite element wave propagation modelling technique that provides high computational efficiency and high wave modelling accuracy. We show that lattice structures employing internal resonance can provide transmissibility reduction of longitudinal waves of up to −103 dB. Paired with the manufacturing freedom and material choice of additive manufacturing, the examined lattice structures can be tailored for use in wide-ranging applications including machine design, isolation and support platforms, metrology frames, aerospace and automobile applications, and biomedical devices.

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Section: Methodsmentioning

confidence: 99%

Multidimensional Phononic Bandgaps in Three-Dimensional Lattices for Additive Manufacturing

et al. 2019

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“…The first Brillouin zone (FBZ) and irreducible Brillouin zone (IBZ) are depicted in Figure 6. The IBZ is the smallest part of the FBZ representing all the high-symmetry points in which the wave propagation is analyzed [33]. Figure 6.…”

Section: Wave Propagation Modelmentioning

confidence: 99%

“…Figure 6. The IBZ is the smallest part of the FBZ representing all the high-symmetry points in which the wave propagation is analyzed [33]. In this research, numerical simulations have been produced by employing an FE software.…”

Section: Wave Propagation Modelmentioning

confidence: 99%

Shape-Adaptive Metastructures with Variable Bandgap Regions by 4D Printing

et al. 2020

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This article shows how four-dimensional (4D) printing technology can engineer adaptive metastructures that exploit resonating self-bending elements to filter vibrational and acoustic noises and change filtering ranges. Fused deposition modeling (FDM) is implemented to fabricate temperature-responsive shape-memory polymer (SMP) elements with self-bending features. Experiments are conducted to reveal how the speed of the 4D printer head can affect functionally graded prestrain regime, shape recovery and self-bending characteristics of the active elements. A 3D constitutive model, along with an in-house finite element (FE) method, is developed to replicate the shape recovery and self-bending of SMP beams 4D-printed at different speeds. Furthermore, a simple approach of prestrain modeling is introduced into the commercial FE software package to simulate material tailoring and self-bending mechanism. The accuracy of the straightforward FE approach is validated against experimental observations and computational results from the in-house FE MATLAB-based code. Two periodic architected temperature-sensitive metastructures with adaptive dynamical characteristics are proposed to use bandgap engineering to forbid specific frequencies from propagating through the material. The developed computational tool is finally implemented to numerically examine how bandgap size and frequency range can be controlled and broadened. It is found out that the size and frequency range of the bandgaps are linked to changes in the geometry of self-bending elements printed at different speeds. This research is likely to advance the state-of-the-art 4D printing and unlock potentials in the design of functional metastructures for a broad range of applications in acoustic and structural engineering, including sound wave filters and waveguides. much attention due to their lower density, higher recoverable strain of up to 400%, lower cost, simple shape programming procedure, and excellent controllability over the recovery temperature [3,4].In the recent two decades, three-dimensional (3D) printing technology, also known as additive manufacturing (AM), has gained considerable attention as an advanced manufacturing technique that can create complex objects through depositing materials in a layer-by-layer manner [5][6][7][8][9]. With the introduction of active materials, 3D printing approaches have shown excellent potential for the fabrication of adaptive structures, namely four-dimensional (4D) printed structures, with the capability of reshaping their configuration and changing their properties over time [10][11][12]. For the first time, Tibbits [13] experimentally demonstrated how 4D-printed objects could transform over time and perform self-assemblies. While 3D printing methods can be used to fabricate static structures, 4D printing methods allow the fabrication of dynamically reconfigurable architectures with desired functionality and responsiveness. Considering a specific application, 4D-printed objects can be designed to respond to environmental...

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“…For two-and three-dimensional (2D and 3D) periodic structures, the symmetry of the unit cell can be taken into account to reduce the information contained in the first BZ to the one of a contour. The dispersion along the edge of the irreducible BZ contains all relevant wavepropagation information for an infinite assembly of unit cells [19].…”

Section: Introductionmentioning

confidence: 99%

Energy Distribution and Exchange Between Spatial Harmonics in Bending Wave Phononic Crystals

Damme

Zemp

2018

Phys. Rev. Applied

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Resonant metamaterials and phononic crystals are widely studied, with the aim of controlling and altering elastic wave propagation in solids. Beams with varying stiffness along the length are an archetypal example of a phononic crystal for bending waves, since the resulting nontrivial dispersion relation can be modeled analytically. In this work, the complex dispersion curve over the complete audible frequency range is measured using the inhomogeneous wave-correlation (IWC) technique, and compared to a unitcell model and an explicit model of the finite beam. Multiple band gaps, each with a different attenuation coefficient, are predicted and validated. An iterative implementation of IWC allows the identification of a spatial spectrum of wave numbers, responsible for the intricate beam displacement shape. The energy carried by the fundamental wave number and its Bloch (sub)harmonics are determined, showing that the main dispersion branch is monotonically increasing. It is shown that only a small fraction of the wave energy travels along branches with a negative slope in the first Brillouin zone. Additionally, in band gaps affecting only bending waves, energy is converted to other wave types, such as longitudinal waves. This approach offers some important insights into the physics of the wave propagation, which cannot be gathered from unit-cell modeling alone.

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Probability that a band-gap extremum is located on the irreducible Brillouin-zone contour for the 17 different plane crystallographic lattices

Abstract: Title: Probability that a band-gap extremum is located on the irreducible Brillouin-zone contour for the 17 different plane crystallographic lattices

Cited by 78 publications

References 44 publications

Multidimensional Phononic Bandgaps in Three-Dimensional Lattices for Additive Manufacturing

Multidimensional Phononic Bandgaps in Three-Dimensional Lattices for Additive Manufacturing

Shape-Adaptive Metastructures with Variable Bandgap Regions by 4D Printing

Energy Distribution and Exchange Between Spatial Harmonics in Bending Wave Phononic Crystals

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