Optimal Design Approach for One-dimensional Rubber-Concrete Periodic Foundations based on Analytical Approximations of Band Gaps

2021 ◽  
Author(s):  
Zhifeng Xu
Keyword(s):  
Optimal Design ◽  
Periodic Structures ◽  
Analytical Approximation ◽  
Band Gaps ◽  
Design Approach ◽  
One Dimensional ◽  
Frequency Responses ◽  
Analytical Approximations ◽  
Resonance Frequencies ◽  
Rubber Concrete

This research investigates band gaps and frequency responses of one-dimensional periodic structures and further presents an optimal design approach for one-dimensional rubber-concrete periodic foundations based on the proposed analytical formulas for approximating the first few band gaps. The presented design approach is optimal for being able of globally searching the best solution which effectively cooperates the band gaps with the superstructure’s resonance frequencies. Firstly, frequency responses of one-dimensional periodic structures and the corresponding approximation method are studied. Furthermore, analytical approximation formulas for the first few band gaps, localization factor, attenuation coefficient, and frequency responses of one-dimensional rubber-concrete periodic foundations are proposed and verified. Lastly, inspired by the proposed analytical approximation for computing band gaps, an optimal design approach for one-dimensional rubber-concrete periodic foundations is presented and applied to a practical example, whose optimality is verified theoretically and numerically.

scholarly journals Complete Band Gaps in One-Dimensional Left-Handed Periodic Structures

2005 ◽  
Vol 95 (19) ◽  
Author(s):  
Ilya V. Shadrivov ◽  
Andrey A. Sukhorukov ◽  
Yuri S. Kivshar
Keyword(s):  
Periodic Structures ◽  
Band Gaps ◽  
One Dimensional ◽  
Left Handed

Two-dimensional complete band gaps in one-dimensional metal-dielectric periodic structures

2008 ◽  
Vol 92 (5) ◽  
pp. 053104 ◽  
Author(s):  
Jin-long Zhang ◽  
Hai-tao Jiang ◽  
Stefan Enoch ◽  
Gérard Tayeb ◽  
Boris Gralak ◽  
...  
Keyword(s):  
Periodic Structures ◽  
Band Gaps ◽  
Two Dimensional ◽  
One Dimensional

Thickness-Modulated One-Dimensional Periodic Phononic Crystal

2013 ◽  
Vol 750-752 ◽  
pp. 1207-1210 ◽  
Author(s):  
Ya Zhuo Xie ◽  
Hai Feng Qi ◽  
Min Zhao ◽  
Hui Fang ◽  
Jian Gao ◽  
...  
Keyword(s):  
Periodic Structures ◽  
Phononic Crystal ◽  
Dispersion Curves ◽  
Band Gaps ◽  
Plane Wave Expansion ◽  
Modulated Structure ◽  
One Dimensional ◽  
Periodic Model ◽  
Engineering Requirement ◽  
Media Layer

We have studied the dispersion curves of the thickness-modulated one-dimensional (1D) periodic phononic crystal. The dispersion curves of acoustic wave propagating perpendicular to the surfaces of the models are calculated based on the plane wave expansion (PWE) method. By compared the band gaps in thickness-modulated structure with the simple periodic structure, we have found that the band gaps in simple periodic model split into many sub-band gaps when the thickness of media layer is modulated periodically. This can be explained that the thickness-modulated structure can be considered to be made up of many periodic structures with different lattice spacing. It provides flexible choices for real engineering requirement.

Investigations on the band-gap characteristics of one-dimensional flexural periodic structures with varying geometries

2021 ◽  
pp. 107754632110368
Author(s):  
Sachchidanand Das ◽  
Murtaza Bohra ◽  
Sabareesh Geetha Rajasekharan ◽  
Yendluri Venkata Daseswara Rao
Keyword(s):  
Band Gap ◽  
Frequency Band ◽  
Periodic Structures ◽  
Band Gaps ◽  
One Dimensional ◽  
Vibration Attenuation ◽  
Gap Characteristics ◽  
Novel Concept ◽  
Selection Of ◽  
Shape And Size

Periodic structures have been studied extensively for their wave-filtering capabilities as they exhibit frequency band-gaps. The band-gap characteristics of flexural periodic structures, consisting of periodic cavities, depend on the geometry (shape and size) of cavities. The present work brings out experimental and numerical investigation of the effect of geometry of periodicity on the vibration characteristics of one-dimensional periodic structures. A procedure for prediction of the experimentally observed frequency band-gaps, with the help of eigenfrequency analysis, has been presented. Further, a novel concept of ‘real’ and ‘pseudo’ band-gaps has been theorized. Based on the experimental and numerical results, the best configuration of a periodic structure for maximum vibration attenuation has been arrived at. The work can find application in the design of frames and channels, made of periodic structures, where periodicity can be introduced to reduce vibration transmission in desired frequency bands. It can also reduce the requirement of extensive prototype trials for the selection of suitable periodic geometry.

Momentum exchange impact damper design methodology for object-wall-collision problems

2017 ◽  
Vol 24 (14) ◽  
pp. 3206-3218
Author(s):  
Yohei Kushida ◽  
Hiroaki Umehara ◽  
Susumu Hara ◽  
Keisuke Yamada
Keyword(s):  
Optimal Design ◽  
Design Methodology ◽  
Design Parameters ◽  
Momentum Exchange ◽  
Impact Damper ◽  
One Dimensional ◽  
Practical Design ◽  
Wall Collision ◽  
Damper Design ◽  
And Control

Momentum exchange impact dampers (MEIDs) were proposed to control the shock responses of mechanical structures. They were applied to reduce floor shock vibrations and control lunar/planetary exploration spacecraft landings. MEIDs are required to control an object’s velocity and displacement, especially for applications involving spacecraft landing. Previous studies verified numerous MEID performances through various types of simulations and experiments. However, previous studies discussing the optimal design methodology for MEIDs are limited. This study explicitly derived the optimal design parameters of MEIDs, which control the controlled object’s displacement and velocity to zero in one-dimensional motion. In addition, the study derived sub-optimal design parameters to control the controlled object’s velocity within a reasonable approximation to derive a practical design methodology for MEIDs. The derived sub-optimal design methodology could also be applied to MEIDs in two-dimensional motion. Furthermore, simulations conducted in the study verified the performances of MEIDs with optimal/sub-optimal design parameters.

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

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.

Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials

2004 ◽  
Vol 70 (16) ◽  
Author(s):  
A. Mandatori ◽  
C. Sibilia ◽  
M. Bertolotti ◽  
S. Zhukovsky ◽  
J. W. Haus ◽  
...  
Keyword(s):  
Periodic Structures ◽  
One Dimensional
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