Band-Gap Engineering of Elastic Waveguides Using Periodic Materials

2003 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Wave Attenuation ◽  
Material Interfaces ◽  
Band Gap Engineering ◽  
Attenuation Effect ◽  
Constituent Material ◽  
Unit Cells ◽  
Guide Wall ◽  
Forced Vibration Analysis ◽  
Periodic Materials ◽  
Elastic Waveguides

Within periodically heterogeneous materials, wave scattering takes place across constituent material interfaces in such a way that an overall wave attenuation effect arises at certain frequency ranges known as band gaps. This phenomenon can be utilized in developing structures with tailored dynamic characteristics. In this work, periodic materials are used to synthesize elastic waveguides within bounded structures. The underlying local-global design process is described, and the effect of the number of periodic cells used to form the guide “wall” is studied. Using forced vibration analysis, it is shown that with only three or four periodic unit cells, the desired wave attenuation capacity required to form a guide is attained.

Hierarchical Design of Phononic Materials and Structures

2005 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Wave Scattering ◽  
Design Methodology ◽  
Periodic Structures ◽  
Building Blocks ◽  
Hierarchical Design ◽  
Material Interfaces ◽  
Dynamical Characteristics ◽  
Constituent Material ◽  
Unit Cells ◽  
Damping Materials

Within periodically heterogeneous materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. A novel multiscale dispersive design methodology is presented by which periodic unit cells are designed for desired frequency band structures, and are used as building blocks for forming fully or partially periodic structures, typically at larger length scales. Structures resulting from this hierarchical design approach are tailored to desired dynamical characteristics without the necessity for altering the overall geometric shape of the structure nor employing dissipative damping materials. Case studies are presented for shock isolation and frequency sensing.

Computational design of resonant phononic crystal for aperiodic stress wave attenuation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chengcheng Luo ◽  
Shaowu Ning ◽  
Zhanli Liu ◽  
Xiang Li ◽  
Zhuo Zhuang
Keyword(s):  
Stress Wave ◽  
Wave Attenuation ◽  
Design Method ◽  
Phononic Crystal ◽  
Hard Core ◽  
Stress Waves ◽  
Physical Parameters ◽  
Attenuation Effect ◽  
Content Type ◽  
Soft Matrix

Purpose This paper aims to propose a design method for attenuating stress waves pressure using soft matrix embedded with particles. Design/methodology/approach Based on the phononic crystal theory, the particle composed of hard core and soft coating can form a spring oscillator structure. When the frequency of the wave is close to the resonance frequency of the spring oscillator, it can cause the resonance of the particle and absorb a lot of energy. In this paper, the resonant phononic crystal with three phases, namely, matrix, particle core and coating, is computationally designed to effectively mitigate the stress wave with aperiodic waveform. Findings The relationship between the center frequency and width of the bandgap and the geometric and physical parameters of particle core are discussed in detail, and the trend of influence is analyzed and explained by a spring oscillator model. Increasing the radius of hard core could effectively enhance the bandgap width, thus enhancing the effect of stress wave attenuation. In addition, it is found that when the wave is in the bandgap, adding viscosity into the matrix will not further enhance the stress attenuation effect, but will make the stress attenuation effect of the material worse because of the competition between viscous dissipation mechanism and resonance mechanism. Research limitations/implications This study will provide a reference for the design of stress wave protection materials with general stress waves. Originality/value This study proposes a design method for attenuating stress waves pressure using soft matrix embedded with particles.

scholarly journals Forced Vibration Analysis for a FGPM Cylindrical Shell

2013 ◽  
Vol 20 (3) ◽  
pp. 531-550 ◽  
Author(s):  
Hong-Liang Dai ◽  
Hao-Jie Jiang
Keyword(s):  
Cylindrical Shell ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Mechanical Load ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Constituent Material ◽  
Present Solution ◽  
Functionally Graded Piezoelectric ◽  
Forced Vibration Analysis

This article presents an analytical study for forced vibration of a cylindrical shell which is composed of a functionally graded piezoelectric material (FGPM). The cylindrical shell is assumed to have two-constituent material distributions through the thickness of the structure, and material properties of the cylindrical shell are assumed to vary according to a power-law distribution in terms of the volume fractions for constituent materials, the exact solution for the forced vibration problem is presented. Numerical results are presented to show the effect of electric excitation, thermal load, mechanical load and volume exponent on the static and force vibration of the FGPM cylindrical shell. The goal of this investigation is to optimize the FGPM cylindrical shell in engineering, also the present solution can be used in the forced vibration analysis of cylindrical smart elements.

scholarly journals Effect of non-ionizing reaction rate (assumed to be controllable) on the plasma generation mechanism and communication around RAMC vehicle during atmospheric reentry

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wenchong Ouyang ◽  
Qi Liu ◽  
Zheng Zhang ◽  
Tao Jin ◽  
Zhengwei Wu
Keyword(s):  
Reaction Rate ◽  
Wave Attenuation ◽  
Plasma Sheath ◽  
Generation Mechanism ◽  
Transmission Model ◽  
Attenuation Effect ◽  
Plasma Generation ◽  
Atmospheric Reentry ◽  
Communication Signal ◽  
Ionization Reaction

AbstractRadio frequency (RF) blackout occurs during radio attenuation measurement C (RAMC) vehicle reentry due to the attenuation effect of the plasma sheath on the communication signal. In recent years, the mitigation mechanism of chemical reaction for RF blackout problem has gradually been studied numerically and experimentally. However, the effect of non-ionization reaction rate has been ignored because it does not directly involve the generation of electrons. In the present study, the influence of non-ionizing reaction rate on the plasma generation mechanism and EM wave attenuation was numerically solved by the plasma flow and multilayer transmission model. According to the simulation results, only the reaction rate of $$NO \rightleftharpoons N + O$$ N O ⇌ N + O has a significant effect on the electron number density in all non-ionizing reactions, and the degree of influence is less than the ionization reaction rate. The EM wave attenuation decreases with the decrease of the reaction rate of $$NO \rightleftharpoons N + O$$ N O ⇌ N + O . When the reaction rate is reduced by 25 times, the maximum attenuation of electromagnetic wave can be reduced by 12 dB. Finally, a potential scheme by reducing the reaction rate of $$NO \rightleftharpoons N + O$$ N O ⇌ N + O was proposed to mitigate the RF blackout problem.

scholarly journals Optimization of a type of elastic metamaterial for broadband wave suppression

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210337
Author(s):  
Kun Wu ◽  
Haiyan Hu ◽  
Lifeng Wang
Keyword(s):  
Vibration Isolation ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Dispersion Analysis ◽  
Mass Unit ◽  
Super Cell ◽  
Unit Cells ◽  
Sequential Quadratic Programming Method ◽  
Continuous Frequency ◽  
Quadratic Programming Method

The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling multiple separate narrow bandgaps into a broad bandgap. A new objective function is proposed in the optimization process for a continuous bandgap. Then, the continuous frequency range with low-wave transmissibility is optimized to achieve the maximal width of bandgap. The stiffness optimization of super-cell gives the broad bandgap from 10 Hz to 22.9 Hz at low-frequency ranges. In addition, numerical simulations are conducted for a type of dissipative metamaterial composed of a finite number of periodicities. The level of vibration isolation can be tuned by adjusting a critical value in the optimization scheme. The wave suppression in the numerical simulation well coincides with the obtained bandgaps and verifies the optimization results.

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.

Surface water waves over a shallow canopy

2015 ◽  
Vol 768 ◽  
pp. 572-599 ◽  
Author(s):  
Benlong Wang ◽  
Xiaoyu Guo ◽  
Chiang C. Mei
Keyword(s):  
Water Waves ◽  
Wave Attenuation ◽  
Multiple Scale ◽  
Small Scale ◽  
Vegetation Canopy ◽  
Unit Cells ◽  
Surface Water Waves ◽  
Slow Evolution ◽  
Scale Motion ◽  
Vertical Cylinders

The dynamics of water waves passing over a vegetation canopy is modelled theoretically. To simplify the geometry, we examine a periodic array of vertical cylinders fixed on a slowly varying seabed. The macroscale behaviour of wave attenuation is predicted based on microscale dynamics between plants. Interstitial turbulence is modelled by Reynolds equations with a locally constant eddy viscosity determined by energy considerations. Using the asymptotic method of multiple-scale expansions, the slow evolution of waves is derived by considering the coupling with the small-scale motion in the canopy. After numerical solution of the canonical boundary-value problem in a few unit cells, predictions of macroscale effects such as wave attenuation are made and compared with laboratory experiments. The counteracting effects of shoaling and dissipation are discussed for different vegetation densities.

Effects of “Finiteness” on Wave Propagation and Vibration in Elastic Periodic Structures

Aerospace ◽  
2004 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Frequency Band ◽  
Vibration Isolation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Stop Band ◽  
Forced Response ◽  
Band Frequency ◽  
Mode Localization ◽  
Unit Cells ◽  
Frequency Behavior

The dynamics of finite elastic periodically layered structures is compared to that of the constituent periodic media. The focus is on both the frequency behavior and the spatial response. Through simulations of harmonically induced wave motion within a finite number of unit cells, the frequency band structure and attenuation characteristics of infinite and finite periodic systems are shown to conform under certain conditions. It is concluded that only one or two unit cells of a periodic material are required for “frequency bandness” to carry through to a finite structure, and only three to four unit cells are necessary for significant wave attenuation to take place when the structure is excited at a stop-band frequency. Furthermore, vibration analyses are conducted on a bounded fully periodic structure. The natural frequency spread is shown to conform with the frequency band layout of the infinite periodic material, and the steady-state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium. These results could be used for setting guidelines for the design of periodic structures for vibration isolation and frequency filtering.

Band gap optimization of one-dimension elastic waveguides using spatial Fourier plane wave expansion coefficients

2021 ◽  
pp. 095440622098683
Author(s):  
Vinícius D Lima ◽  
Luis GG Villani ◽  
Juan F Camino ◽  
José RF Arruda
Keyword(s):  
Plane Wave ◽  
Band Gap ◽  
Fourier Coefficients ◽  
Wave Attenuation ◽  
Optimization Technique ◽  
Band Gaps ◽  
Plane Wave Expansion ◽  
Frequency Bands ◽  
Wave Expansion ◽  
Elastic Waveguides

Periodic elastic waveguides, such as rods, beams, and shafts, exhibit frequency bands where wave reflections at impedance discontinuities cause strong wave attenuation by Bragg scattering. Such frequency bands are known as stop bands or band gaps. This work presents a shape optimization technique for one-dimensional periodic structures. The proposed approach, which aims to maximize the width of the first band gap, uses as tuning parameters the spatial Fourier coefficients that describe the shape of the cell cross-section variation along its length. Since the optimization problem is formulated in terms of Fourier coefficients, it can be directly applied to the Plane Wave Expansion (PWE) method, commonly used to obtain the dispersion diagrams, which indicate the presence of band gaps. The proposed technique is used to optimize the shape of a straight bar with both solid and hollow circular cross-sections. First, the optimization is performed using the elementary rod, the Euler-Bernoulli and Timoshenko beam, and the shaft theoretical models in an independent way. Then, the optimization is conducted to obtain a complete band gap in the dispersion diagrams, which includes the three wave types, i.e., longitudinal, bending, and torsional. All numerical results provided feasible shapes that generate wide stop bands in the dispersion diagrams. The proposed technique can be extended to two- and three-dimensional periodic frame structures, and can also be adapted for different classes of cost functions.

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