Wave Characteristics of Two-Dimensional Hierarchical Hexagonal Lattice Structures

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Y. L. Xu ◽  
C. Q. Chen ◽  
X. G. Tian
Keyword(s):  
Lattice Structure ◽  
Hexagonal Lattice ◽  
Low Frequency ◽  
Hierarchical Structures ◽  
Wave Mode ◽  
Periodic Lattice ◽  
Lattice Structures ◽  
Two Dimensional ◽  
Dispersion Surface ◽  
Mode Dispersion

Hierarchical structures are structures that themselves contain structural elements. Hierarchical lattice structures are counterparts of the traditional lattice structures, whose walls are replaced by some kind of structure. In this paper, wave propagation in two-dimensional hierarchical hexagonal lattice structures is calculated by the finite element method with the Bloch theory. Attention is devoted to the comparison of the band gap, wave mode, dispersion surface, and phase and group velocities between the second-order hierarchical hexagonal lattice structures and their first-order traditional counterpart. The results show that the former structures have more band gaps and similar isotropic wave behavior in the low frequency compared to the latter structure. The structure hierarchy is favorable for the periodic lattice structure to filtering or guiding wave at some circumstances to meet the demands of engineering.

scholarly journals Determination of the molecular structure and (m,n) index assignment to the constituent walls of MWCNTs with undetermined diameters and chirality

2020 ◽  
Author(s):  
Viktor Andonovic ◽  
Aleksandar T Dimitrov ◽  
Perica Paunovic ◽  
Beti Andonovic
Keyword(s):  
Lattice Structure ◽  
Structural Parameters ◽  
Hexagonal Lattice ◽  
Low Frequency ◽  
Graph Representation ◽  
Mathematical Representation ◽  
Multi Wall Carbon Nanotubes ◽  
Cell Parameters ◽  
Index Assignment ◽  
Python Programming

Each carbon nanotube (CNT) has its own mathematical representation due to its hexagonal lattice structure. The subjects of research are multi-wall carbon nanotubes (MWCNTs) and determining their structural parameters: innermost and outermost diameters, chiral indices m and n, number of walls and their unit cell parameters. Within this paper low frequency region and corresponding high frequency parts of Raman spectra of three experimentally produced CNTs are considered, as well as use of Python programming for the most accurate (m,n) assignment. Determining the chirality of these samples enables calculation of other structural properties which are performed hereby. Furthermore, this author’s work enables future studies on the samples, as are calculation of different topological indices using the graph representation and the chirality of the studied CNT samples.

Wave Manipulation of Two-Dimensional Periodic Lattice by Parametric Excitation

2019 ◽  
Vol 87 (1) ◽  
Author(s):  
Xiao-Dong Yang ◽  
Qing-Dian Cui ◽  
Wei Zhang
Keyword(s):  
Parametric Excitation ◽  
Elastic Waves ◽  
High Frequency ◽  
Low Frequency ◽  
Waveguide Structure ◽  
Phononic Crystals ◽  
Periodic Lattice ◽  
Two Dimensional ◽  
Time Dynamic ◽  
Mechanical Waves

Abstract Phononic crystals composed of delicately designed periodic units are used to control spatial and spectral properties of acoustic or elastic waves. The ability to manipulate transmitting waves in a real-time dynamic manner provides a new concept in programable phononic crystals and metamaterials. In this study, the mechanical waves and bandgaps in a two-dimensional spring-mass array loaded by high-frequency parametric excitation have been investigated by both analytical and numerical methods. It is found that the high-frequency parametric excitation provides an equivalent additional stiffness which leads to low-frequency bandgaps. By tuning the parametric excitation, the versatility of such a dynamic modulating technique has been presented. The waveguide structure has also been designed and studied by non-uniformly distributed parametric excitations.

Elastic Properties and Nonlinear Elasticity of the Noncarbon Hexagonal Lattice Nanomaterials Based on the Multiscale Modeling

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Sandeep Singh ◽  
B. M. Ravi Raj ◽  
Kiran D. Mali ◽  
Gaurav Watts
Keyword(s):  
Elastic Properties ◽  
Nonlinear Elasticity ◽  
Interatomic Potential ◽  
Lattice Structure ◽  
Hexagonal Lattice ◽  
Experimental Investigations ◽  
Continuum Approximation ◽  
Two Dimensional ◽  
Bending Rigidity ◽  
Bending Modulus

Abstract This study presents the elastic properties and nonlinear elasticity of the two-dimensional noncarbon nanomaterials of hexagonal lattice structures having molecular structure XY. Four nitride-based and two phosphide-based two-dimensional nanomaterials, having graphene-like hexagonal lattice structure, are considered in the present study. The four empirical parameters associated with the attractive and repulsive terms of the Tersoff–Brenner potential are calibrated for noncarbon nanomaterials and tested for elastic properties, nonlinear constitutive behavior, bending modulus, bending and torsional energy. The mathematical identities for the tangent constitutive matrix in terms of the interatomic potential function are derived through an atomistic–continuum coupled multiscale framework of the extended version of Cauchy–Born rule. The results obtained using newly calibrated empirical parameters for cohesive energy, bond length, elastic properties, and bending rigidity are compared with those reported in the literature through experimental investigations and quantum mechanical calculations. The continuum approximation is attained through the finite element method. Multiscale evaluations for elastic properties and nonlinear stretching of the nanosheets under in-plane loads are also compared with those obtained from atomistic simulations.

Fabrication of Two-Dimensional Photonic Crystals on N-Type Silicon Substrate Using Holographic and Wet Etching Techniques

2007 ◽  
Author(s):  
Han Lin ◽  
Shou Liu ◽  
Xiangsu Zhang
Keyword(s):  
Porous Silicon ◽  
Photonic Crystals ◽  
Silicon Substrate ◽  
Lattice Structure ◽  
Hexagonal Lattice ◽  
Cost Effective ◽  
Wet Etching ◽  
Etching Time ◽  
Two Dimensional ◽  
Photoresist Mask

Technique of fabricating two-dimensional (2D) photonic crystals (PCs) in silicon wafers using the combination of holographic lithography and wet etching is described in the paper. The fabricated silicon material is suitable to be used as porous silicon for Ge/Si quantum dots growth or other applications. Single exposure holographic method was adopted to fabricate the photoresist mask with the pattern of 2D hexagonal lattice structure. HF:HNO3:CH3COOH = 4:4:3 solution was used to etch circular pores with bowl-shaped bottom into silicon substrate at room temperature with 30 s etching time. Periodic structure in silicon with 1 μm lattice constant and 200 nm pore depth was obtained in the experiment. The fabrication process is fast and cost-effective thus having the potential for industrial mass production of porous silicon.

Support vector machines for predicting the compressive response of defected 3D printed polymeric sandwich structures

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Khameel Mustapha ◽  
Jamal Alhiyafi ◽  
Aamir Shafi ◽  
Sunday Olusanya Olatunji
Keyword(s):  
Nonlinear Response ◽  
Lattice Structure ◽  
Structural Defects ◽  
Periodic Lattice ◽  
Support Vector ◽  
Fused Deposition Modelling ◽  
Lattice Structures ◽  
Compression Tests ◽  
Content Type ◽  
Fused Deposition

Purpose This study aims to investigate the prediction of the nonlinear response of three-dimensional-printed polymeric lattice structures with and without structural defects. Unlike metallic structures, the deformation behavior of polymeric components is difficult to quantify through the classical numerical analysis approach as a result of their nonlinear behavior under mechanical loads. Design/methodology/approach Geometric models of periodic lattice structures were designed via PTC Creo. Imperfections in the form of missing unit cells are introduced in the replica of the lattice structure. The perfect and imperfect lattice structures have the same dimensions – 10 mm × 14 mm × 30 mm (w × h × L). The fused deposition modelling technique is used to fabricate the parts. The fabricated parts were subjected to physical compression tests to provide a measure of their transverse compressibility resistance. The ensuing nonlinear response from the experimental tests is deployed to develop a support vector machine surrogate model. Findings Results from the surrogate model’s performance, in terms of correlation coefficient, rose to as high as 99.91% for the nonlinear compressive stress with a minimum achieved being 98.51% across the four datasets used. In the case of deflection response, the model accuracy rose to as high as 99.74% while the minimum achieved is 98.56% across the four datasets used. Originality/value The developed model facilitates the prediction of the quasi-static response of the structures in the absence and presence of defects without the need for repeated physical experiments. The structure investigated is designed for target applications in hierarchical polymer packaging, and the methodology presents a cost-saving method for data-driven constitutive modelling of polymeric parts.

scholarly journals Model Calibration of 3D Printed Lattice Structures

2021 ◽  
Author(s):  
Edoardo Mancini ◽  
Mattia Utzeri ◽  
Emanuele Farotti ◽  
Marco Sasso
Keyword(s):  
Lattice Structure ◽  
Periodic Lattice ◽  
Lattice Structures ◽  
Compression Tests ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
Triply Periodic Minimal Surface ◽  
3D Printed ◽  
Energy Absorbers ◽  
Experimental Findings

Nowadays cellular materials are receiving great attention for their excellent mechanical properties, being applied in energy absorbers or in structural components having optimized mass distribution. In this paper stretch-dominated lattice structures have been considered. A 3D periodic lattice structure of different cell size, TPMS (triply periodic minimal surface), made of epoxy resin by DLP technology was studied. Compression tests at different strain rate (10-3 to 103 1/s) have been performed and a constitutive model to assess the experimental findings has been calibrated.

Band Gap Properties of Two-Dimensional Photonic Crystal Structures with Rectangular Lattice

2015 ◽  
Vol 36 (2) ◽  
Author(s):  
Hamed Alipour-Banaei ◽  
Somaye Serajmohammadi ◽  
Farhad Mehdizadeh ◽  
Alireza Andalib
Keyword(s):  
Band Gap ◽  
Lattice Structure ◽  
Band Gaps ◽  
The Other ◽  
Square Lattice ◽  
Rectangular Lattice ◽  
Lattice Structures ◽  
Two Dimensional ◽  
Two Dimensional Photonic Crystal ◽  
Polarization Independent

AbstractIn this paper we proposed a new structure of two-dimensional photonic crystals with rectangular lattice. After deducing the primitive lattice vectors and first Brillouin zone of the structures, we studied the band gap properties of horizontal and vertical rectangular lattice structures and compared them with conventional square lattice structure. The most excellent characteristic of these structures is their joint band gap regions, which make them suitable for designing polarization-independent devices. The other advantage of these structures is having band gaps at higher normalized frequencies.

scholarly journals Experimental study on the high-damping properties of metallic lattice structures obtained from SLM

2020 ◽  
Author(s):  
Federico Scalzo ◽  
Giovanni Totis ◽  
Emanuele Vaglio ◽  
Marco Sortino
Keyword(s):  
Dynamic Behaviour ◽  
Acoustic Noise ◽  
Lattice Structure ◽  
Low Frequency ◽  
Weight Ratio ◽  
Damping Capacity ◽  
Lattice Structures ◽  
Frequency Range ◽  
Global Dynamic ◽  
Manufacturing Technologies

Modern additive manufacturing technologies allow the creation of parts characterized by complex geometries that cannot be created using conventional production techniques. Among them the Selective Laser Melting (SLM) technique is very promising. By using SLM it is possible to create lightweight lattice structures that may fill void regions or partially replace bulk regions of a given mechanical component. As a consequence, the overall mechanical properties of the final component can be greatly enhanced, such as the resistance to weight ratio and its damping capacity against undesired vibrations or acoustic noise. Nevertheless, only a few research works focused on the characterization of the dynamic behaviour of lattice structures, that were mainly investigated in the low frequency range or directly tested on some specific applications. In this work the dynamic behaviour of lattice structures in the medium-high frequency range was experimentally investigated and then modelled. For this purpose, different types of lattice structures made of AlSi10Mg and AISI 316L were measured. Experimental modal analysis was performed on the obtained specimens in order to assess the influence of lattice material and unit cell geometry on their global dynamic behaviour. Experimental results revealed that lattice structures have superior damping characteristics compared to solid materials having an equivalent static stiffness. Eventually, the classic Rayleigh model was found to be adequate - with some approximation - to explain the damping behaviour of a generic lattice structure.

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