Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Surface Energy, Transverse Shear and Rotational Inertia Effects

2018 ◽  
Author(s):  
R. Z. Gao ◽  
G. Y. Zhang ◽  
T. Ioppolo
Keyword(s):  
Surface Energy ◽  
Band Gap ◽  
Volume Fraction ◽  
Classical Model ◽  
Band Gaps ◽  
Rotational Inertia ◽  
Beam Structure ◽  
Inertia Effects ◽  
Periodic Composite ◽  
Beam Thickness

A new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Timoshenko beam model that incorporates the surface energy, transverse shear and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when the surface energy effect is not considered. It is shown that the band gaps predicted by the current model depend on the surface elastic constants of each constituent material, beam thickness, unit cell size, and volume fraction. The numerical results reveal that the band gap based on the current non-classical model is always larger than that given by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.

Elastic wave propagation in a periodic composite beam structure: A new model for band gaps incorporating surface energy, transverse shear and rotational inertia effects

2018 ◽  
Vol 03 (03n04) ◽  
pp. 1840005 ◽  
Author(s):  
R. Z. Gao ◽  
G. Y. Zhang ◽  
T. Ioppolo ◽  
X.-L. Gao
Keyword(s):  
Surface Energy ◽  
Band Gap ◽  
Volume Fraction ◽  
Classical Model ◽  
Band Gaps ◽  
Rotational Inertia ◽  
Inertia Effects ◽  
New Model ◽  
Periodic Composite ◽  
Beam Thickness

A new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Timoshenko beam model that incorporates the surface energy, transverse shear and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when the surface energy effect is not considered. It is shown that the band gaps predicted by the current model depend on the surface elastic constants of each constituent material, beam thickness, unit cell size, and volume fraction. The numerical results reveal that the band gap based on the current non-classical model is always larger than that given by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.

scholarly journals Phoamtonic designs yield sizeable 3D photonic band gaps

2019 ◽  
Vol 116 (47) ◽  
pp. 23480-23486 ◽  
Author(s):  
Michael A. Klatt ◽  
Paul J. Steinhardt ◽  
Salvatore Torquato
Keyword(s):  
Band Gap ◽  
Volume Fraction ◽  
Photonic Band Gap ◽  
Three Dimensional ◽  
Band Gaps ◽  
Photonic Band Gaps ◽  
Photonic Networks ◽  
Photonic Waveguides ◽  
High Degree ◽  
Photonic Band

We show that it is possible to construct foam-based heterostructures with complete photonic band gaps. Three-dimensional foams are promising candidates for the self-organization of large photonic networks with combinations of physical characteristics that may be useful for applications. The largest band gap found is based on 3D Weaire–Phelan foam, a structure that was originally introduced as a solution to the Kelvin problem of finding the 3D tessellation composed of equal-volume cells that has the least surface area. The photonic band gap has a maximal size of 16.9% (at a volume fraction of 21.6% for a dielectric contrast ε=13) and a high degree of isotropy, properties that are advantageous in designing photonic waveguides and circuits. We also present results for 2 other foam-based heterostructures based on Kelvin and C15 foams that have somewhat smaller but still significant band gaps.

Tailoring of Two-Dimensional Band-Gap Materials for Broadband Frequency Isolation

2007 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Karim Hamza ◽  
Gregory M. Hulbert ◽  
Kazuhiro Saitou
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Optimization Techniques ◽  
Band Gaps ◽  
Two Dimensional ◽  
Frequency Bandwidth ◽  
Periodic Composite ◽  
Unit Cells ◽  
Periodic Materials ◽  
Broadband Frequency

The spatial distribution of material phases within a periodic composite can be engineered to produce band gaps in its frequency spectrum. Applications for such composite materials include vibration and sound isolation. Previous research focused on utilizing topology optimization techniques to design two-dimensional periodic materials with a maximized band gap around a particular frequency or between two particular dispersion branches. While sizable band gaps can be realized, the possibility remains that the frequency bandwidth of the load that is to be isolated might significantly exceed the size of the band gap. In this paper, genetic algorithms are used to design squared bi-material unit cells with a maximized sum of relative band-gap widths over a prescribed frequency range of interest. The optimized unit cells therefore exhibit broadband frequency isolation characteristics. The effects of the ratios of contrasting material properties are also studied. The designed cells are subsequently used, with varying levels of material damping, to form a finite vibration isolation structure, which is subjected to broadband loading conditions. Excellent isolation properties of the synthesized material are demonstrated for this structure.

Design of Band Gap Formation in Periodic Rotors via Optimization

2021 ◽  
Author(s):  
Patrick B. Lamas ◽  
Rodrigo Nicoletti
Keyword(s):  
Frequency Response ◽  
Band Gap ◽  
Optimization Procedure ◽  
Band Gaps ◽  
Rotational Inertia ◽  
Gap Formation ◽  
Central Frequency ◽  
Periodic Condition

Abstract Rotors are usually composed of rotating elements (e.g. disks, impellers, blade stages) which add mass and rotational inertia to the system. When this additional inertia of the rotating elements is evenly distributed along the rotor, inertia periodicity appears and the system presents considerably large band gaps in its frequency response, where no resonances appear. The present work shows that we can change the central frequency of these band gaps, without significantly affecting its bandwidth, by changing the distribution of the inertia along the rotor to a quasi-periodic condition. Such designing of the rotor, and consequently of the band gap, is achieved by an optimization procedure.

Study on Band Gap Varying of Diamond Photonic Crystals by Fabricating to Bring the Error of Dielectric Volume Fraction

2014 ◽  
Vol 670-671 ◽  
pp. 101-104
Author(s):  
Shi Bin Chen ◽  
Yun Shi Yao ◽  
Xiao Hui Li ◽  
Min Jie Wang
Keyword(s):  
Photonic Crystals ◽  
Band Gap ◽  
Volume Fraction ◽  
Band Gaps ◽  
Band Width ◽  
Photonic Band Gaps ◽  
Frequency Range ◽  
Gel Casting ◽  
Diamond Crystals ◽  
Photonic Band

To avoid the effect of the error of dielectric volume fraction brought by fabricating process on band gap, the diamond crystals with different the error of dielectric volume fraction were designed and fabricated to investigate the fluctuation of band gaps. Theses photonic crystals with a diamond structure were fabricated using alumina by stereolithography, gel-casting and sintering. The photonic band gaps were observed along <100> direction and the photonic band gaps were formed in different frequency range. Increasing the radius from 4.2mm to 4.32mm and changing band width from 0.8 to 1.39GHz, the radius is increased by 2.86%, and corresponding band width increased by 73.75%. Therefore, the fabrication error in mold and fabrication process including injecting mold, sintering should be maintained under the same conditions, which can retain the error of band gap.

scholarly journals The Band-Gap Studies of Short-Period CdO/MgO Superlattices

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Ewa Przeździecka ◽  
P. Strąk ◽  
A. Wierzbicka ◽  
A. Adhikari ◽  
A. Lysak ◽  
...  
Keyword(s):  
Band Gap ◽  
Layer Thickness ◽  
Energy Gap ◽  
Band Gaps ◽  
Short Period ◽  
Wide Range ◽  
Salt Structure ◽  
Short Period Superlattices ◽  
Direct Band ◽  
Sublayer Thickness

AbstractTrends in the behavior of band gaps in short-period superlattices (SLs) composed of CdO and MgO layers were analyzed experimentally and theoretically for several thicknesses of CdO sublayers. The optical properties of the SLs were investigated by means of transmittance measurements at room temperature in the wavelength range 200–700 nm. The direct band gap of {CdO/MgO} SLs were tuned from 2.6 to 6 eV by varying the thickness of CdO from 1 to 12 monolayers while maintaining the same MgO layer thickness of 4 monolayers. Obtained values of direct and indirect band gaps are higher than those theoretically calculated by an ab initio method, but follow the same trend. X-ray measurements confirmed the presence of a rock salt structure in the SLs. Two oriented structures (111 and 100) grown on c- and r-oriented sapphire substrates were obtained. The measured lattice parameters increase with CdO layer thickness, and the experimental data are in agreement with the calculated results. This new kind of SL structure may be suitable for use in visible, UV and deep UV optoelectronics, especially because the energy gap can be precisely controlled over a wide range by modulating the sublayer thickness in the superlattices.

Effect of Double Defects on Transmission Spectra of One-Dimensional Photonic Crystals

2010 ◽  
Vol 663-665 ◽  
pp. 725-728 ◽  
Author(s):  
Yuan Ming Huang ◽  
Qing Lan Ma ◽  
Bao Gai Zhai ◽  
Yun Gao Cai
Keyword(s):  
Photonic Crystals ◽  
Band Gap ◽  
Theoretical Calculations ◽  
Stop Band ◽  
Band Gaps ◽  
Characteristic Matrix ◽  
Frequency Range ◽  
Defect Band ◽  
One Dimensional ◽  
The One

Considered the model of the one-dimensional photonic crystals (1-D PCs) with double defects, the refractive indexes (n2’, n3’ and n2’’, n3’’) of the double defects were 2.0, 4.0 and 4.0, 2.0 respectively. With parameter n2=1.5, n3=2.5, by theoretical calculations with characteristic matrix method, the results shown that for a certain number (14 was taken) of layers of the 1-D PCs, when the double defects abutted, there was a defect band gap in the stop band gap, while when the double defects separated, there occurred two defect band gaps in the stop band gap; besides, with the separation of the two defects, the transmittance of the double defect band gaps decreased gradually. In addition, in this progress, the frequency range of the stop band gap has a little increase from 0.092 to 0.095.

Sign in / Sign up

Export Citation Format

Share Document