scholarly journals Phase-resonance Exploitation in Full-Metal 3D Periodic Structures for Single- and Multi- Wideband Applications

2021 ◽  
Author(s):  
Carlos Molero Jiménez
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
Circuit Model ◽  
Unit Cell ◽  
Equivalent Circuits ◽  
Cell Architecture ◽  
Complex Unit Cell ◽  
Phase Resonance

This paper presents a versatile full-metal 3D periodic structure based on square waveguides with non-closed resonators perforated on their walls. The complex unit-cell architecture is modelled via accurate equivalent circuits, previously characterized. The circuit model predicts the excitation of phase resonance, which will be used to optimize and design different functionalities, such as polarisation converters or absorption.

scholarly journals Phase-resonance Exploitation in Full-Metal 3D Periodic Structures for Single- and Multi- Wideband Applications

2021 ◽  
Author(s):  
Carlos Molero Jiménez
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
Circuit Model ◽  
Unit Cell ◽  
Equivalent Circuits ◽  
Cell Architecture ◽  
Complex Unit Cell ◽  
Phase Resonance

This paper presents a versatile full-metal 3D periodic structure based on square waveguides with non-closed resonators perforated on their walls. The complex unit-cell architecture is modelled via accurate equivalent circuits, previously characterized. The circuit model predicts the excitation of phase resonance, which will be used to optimize and design different functionalities, such as polarisation converters or absorption.

Broadband Seismic Isolation of Periodic Ladder Frame Structure

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rajan Prasad ◽  
Abhijit Sarkar
Keyword(s):  
Periodic Structure ◽  
Seismic Isolation ◽  
Periodic Structures ◽  
Stop Band ◽  
Design Guidelines ◽  
Unit Cell ◽  
Frame Structure ◽  
Design Parameters ◽  
Pictorial Presentation ◽  
Selection Of

Abstract Ladder frame structures are used as models for multistorey buildings. These periodic structures exhibit alternating propagating and attenuating frequency bands. Of the six different wave modes of propagation, two modes strongly attenuate at all frequencies. The other four modes have nonoverlapping stop band characteristics. Thus, it is challenging to isolate such structures when subjected to broadband, multimodal base excitation. In this study, we seek to synthesize a periodic ladder frame structure that has attenuation characteristics over the maximal range of frequencies for all the modes of wave propagation. We synthesize a unit cell of the periodic structure, which comprises two distinct regions having different inertial, stiffness, and geometric properties. The eigenvalues of the transfer matrix of the unit cell determines the attenuating or the nonattenuating characteristics of the structure. A novel pictorial presentation in the form of eigenvalue map is developed. This is used to synthesize the optimal unit cell. Also, design guidelines for suitable selection of the design parameters are presented. It is shown that a large finite periodic structure comprising a unit cell synthesized using the present approach has significantly better isolation characteristics in comparison to the homogeneous or any other arbitrarily chosen periodic structure.

Broadband Vibration Isolation for Rods and Beams Using Periodic Structure Theory

2018 ◽  
Vol 86 (2) ◽  
Author(s):  
Rajan Prasad ◽  
Abhijit Sarkar
Keyword(s):  
Periodic Structure ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Stop Band ◽  
Extreme Case ◽  
Unit Cell ◽  
Structure Theory ◽  
Seismic Excitations ◽  
Stiffness Properties ◽  
Selection Of

The alternating stop-band characteristics of periodic structures have been widely used for narrow band vibration control applications. The objective of this work is to extend this idea for broadband excitations. Toward this end, we seek to synthesize a longitudinal and a flexural periodic structure having the largest fraction of the frequencies falling in the attenuation bands of the structure. Such a periodic structure when subjected to broadband excitation has minimal transmission of the response away from the source of excitation. The unit cell of such a periodic structure is constituted of two distinct regions having different inertial and stiffness properties. We derive guidelines for suitable selection of inertial and stiffness properties of the two regions in the unit cell such that the maximal frequency region corresponds to attenuation bands of the periodic structure. It is found that maximal dissimilarity between the neighboring regions of the unit cell leads to maximal attenuating frequencies. In the extreme case, it is found that more than 98% of the frequencies are blocked. For seismic excitations, it is shown that large, finite periodic structures corresponding to the optimal unit cell derived using the infinite periodic structure theory has significant vibration isolation benefits in comparison to a homogeneous structure or an arbitrarily chosen periodic structure.

Excitation of Rotationally Periodic Structures

1979 ◽  
Vol 46 (4) ◽  
pp. 878-882 ◽  
Author(s):  
S. J. Wildheim
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
Resonance Condition ◽  
Forced Response ◽  
Closed Ring ◽  
Additional Resonance ◽  
Rotationally Symmetric ◽  
Deformation Patterns ◽  
Frequency Diagram ◽  
Rotationally Periodic Structure

A rotationally periodic structure consists of a finite number of identical substructures forming a closed ring. The vibrational behavior of such structures is considered, especially the forced response due to a rotating force. It is known that for a rotationally symmetric structure, excited by a rotating force, resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is ωn = nΩ, where Ω is the angular velocity of the force. This resonance condition also holds for a rotationally periodic structure. But then additional resonance possibilities exist, given by ωn = (kN ± n)Ω, where N is the number of substructures and k = 0, 1, 2,… These resonance conditions give a zigzag line in the nodal diameters versus frequency diagram, which here is introduced as the ZZENF diagram. The deformation patterns at the resonances are both forward and backward traveling waves.

scholarly journals Метод моделирования диэлектрической проницаемости анизотропного иерархически построенного нанокомпозита с периодической структурой

2021 ◽  
Vol 47 (16) ◽  
pp. 3
Author(s):  
С.А. Корчагин ◽  
Д.В. Терин
Keyword(s):  
Dielectric Constant ◽  
Electromagnetic Radiation ◽  
Periodic Structure ◽  
High Frequency ◽  
Resonance Absorption ◽  
Complex Dielectric Constant ◽  
Quantum Mechanical ◽  
Equivalent Circuits ◽  
Quantum Mechanical Calculations ◽  
Effective Medium Model

A method is proposed for modeling the complex dielectric constant of an anisotropic hierarchically constructed nanocomposite with a periodic structure, based on the complex application of quantum mechanical calculations, an effective medium model, and equivalent equivalent circuits. The dielectric constant of the TiO2 - Al2O3 nanocomposite under the action of external high-frequency electromagnetic radiation has been investigated. The wavelength ranges at which resonance bursts are observed are determined. The possibility of controlling the maxima of difference losses and resonance absorption maxima by changing the geometric parameters of the nanocomposite is shown.

Design of Three-Dimensional, Triply Periodic Unit Cell Scaffold Structures for Additive Manufacturing

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Mazher Iqbal Mohammed ◽  
Ian Gibson
Keyword(s):  
Additive Manufacturing ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Unit Cell ◽  
Final Size ◽  
Fused Filament Fabrication ◽  
Cell Structures ◽  
Triply Periodic ◽  
Unit Cells ◽  
Scaffold Structure

Highly organized, porous architectures leverage the true potential of additive manufacturing (AM) as they can simply not be manufactured by any other means. However, their mainstream usage is being hindered by the traditional methodologies of design which are heavily mathematically orientated and do not allow ease of controlling geometrical attributes. In this study, we aim to address these limitations through a more design-driven approach and demonstrate how complex mathematical surfaces, such as triply periodic structures, can be used to generate unit cells and be applied to design scaffold structures in both regular and irregular volumes in addition to hybrid formats. We examine the conversion of several triply periodic mathematical surfaces into unit cell structures and use these to design scaffolds, which are subsequently manufactured using fused filament fabrication (FFF) additive manufacturing. We present techniques to convert these functions from a two-dimensional surface to three-dimensional (3D) unit cell, fine tune the porosity and surface area, and examine the nuances behind conversion into a scaffold structure suitable for 3D printing. It was found that there are constraints in the final size of unit cell that can be suitably translated through a wider structure while still allowing for repeatable printing, which ultimately restricts the attainable porosities and smallest printed feature size. We found this limit to be approximately three times the stated precision of the 3D printer used this study. Ultimately, this work provides guidance to designers/engineers creating porous structures, and findings could be useful in applications such as tissue engineering and product light-weighting.

(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials

2021 ◽  
Vol 263 (4) ◽  
pp. 2102-2113
Author(s):  
Vanessa Cool ◽  
Lucas Van Belle ◽  
Claus Claeys ◽  
Elke Deckers ◽  
Wim Desmet
Keyword(s):  
Dispersion Curve ◽  
Periodic Structures ◽  
Cell Model ◽  
Stop Band ◽  
Computational Cost ◽  
Order Reduction ◽  
Element Model ◽  
Unit Cell ◽  
Reduction Techniques ◽  
Bloch Mode

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

Parametric Study on Rectangular Sonic Crystal

2012 ◽  
Vol 152-154 ◽  
pp. 281-286 ◽  
Author(s):  
Arpan Gupta ◽  
Kian Meng Lim ◽  
Chye Heng Chew
Keyword(s):  
Band Gap ◽  
Periodic Structure ◽  
Parametric Study ◽  
Sound Propagation ◽  
Periodic Structures ◽  
Sound Attenuation ◽  
Experimental Results ◽  
Center Frequency ◽  
Sonic Crystal ◽  
Sonic Crystals

Sonic crystals are periodic structures made of sound hard scatterers which attenuate sound in a range of frequencies. For an infinite periodic structure, this range of frequencies is known as band gap, and is determined by the geometric arrangement of the scatterers. In this paper, a parametric study on rectangular sonic crystal is presented. It is found that geometric spacing between the scatterers in the direction of sound propagation affects the center frequency of the band gap. Reducing the geometric spacing between the scatterers in the direction perpendicular to the sound propagation helps in better sound attenuation. Such rectangular arrangement of scatterers gives better sound attenuation than the regular square arrangement of scatterers. The model for parametric study is also supported by some experimental results.

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