Wave Propagation in Periodic Piezoelectric Elastic Waveguides

2012 ◽  
Author(s):  
D. G. Piliposyan ◽  
K. B. Ghazaryan ◽  
G. T. Piliposian ◽  
A. S. Avetisyan
Keyword(s):  
Wave Propagation ◽  
Stop Band ◽  
Transmission Conditions ◽  
Band Gaps ◽  
Full System ◽  
One Dimensional ◽  
Dynamic Setting ◽  
Floquet Waves ◽  
Wide Range ◽  
Shear Horizontal

The prorogation of electro-magneto-elastic coupled shear-horizontal waves in one dimensional infinite periodic piezoelectric waveguides is considered within a full system of the Maxwell’s equations. Such setting of the problem allows to investigate the Bloch-Floquet waves in a wide range of frequencies. Two different conditions along the guide walls and three kinds of transmission conditions at the interfaces between the laminae of waveguides have been studied. Stop band structures have been identified for Bloch-Floquet waves both at acoustic and optical frequencies. The results demonstrate the significant effect of piezoelectricity on the widths of band gaps at acoustic frequencies and confirm that it does not affect the band structure at optical frequencies. The results show that under electrically shorted transmission conditions Bloch-Floquet waves exist only at acoustic frequencies. For electrically open interfaces the dynamic setting provides solutions only for photonic crystals. In this case the piezoelectricity has no effect on band gaps.

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.

Wave Propagation in One-Dimensional Structure of Periodic Inelasticity Composites

2011 ◽  
Author(s):  
Helio Aparecido Navarro ◽  
Meire Pereira de Souza Braun
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Stop Band ◽  
Dimensional Structure ◽  
Material Models ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Structural Problems ◽  
Plastic Damage ◽  
Non Linear

This study involves the analysis of elastic-plastic-damage dynamics of one-dimensional structures comprising of periodic materials. These structures are composed by multilayer unit cells with different materials. The dynamical characteristics of the composite material present distinct frequency ranges where wave propagation is blocked. The steady-state forced analyses are conducted on a structure constructed from a periodic inelasticity material. The material models have a linear dependence for elasticity problems and non-linear for elastoplasticity-damage problems. This paper discusses the pass and stop-band dispersive behavior of material models on temporal and spatial domains. For this purpose, some structural problems are composed of periodic and damping materials for analysis of vibration suppression have been simulated. This work brings a formulation of Galerkin method for one-dimensional elastic-plastic-damage problems. A time-stepping algorithm for non-linear dynamics is also presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spatial discretization the standard finite element method is used. The procedure proposed in this work can be extended to multidimensional problems, analysis of strain localization, and for others material models.

Elastic Wave Propagation in a Bio-Inspired Phononic Crystal

2020 ◽  
Vol 1012 ◽  
pp. 9-13
Author(s):  
H.V. Cantanhêde ◽  
E.J.P. Miranda Jr. ◽  
J.M.C. dos Santos
Keyword(s):  
Wave Propagation ◽  
Band Structure ◽  
Vibrational Energy ◽  
Periodic Structures ◽  
Chemical Elements ◽  
Phononic Crystal ◽  
Stop Band ◽  
Elastic Vibration ◽  
Band Gaps ◽  
Sound Waves

The wave propagation in a two-dimensional bio-inspired phononic crystal (PC) is analysed. When composite materials and structures consist of two or more different materials periodically, there will be stop band characteristic, in which there are no mechanical propagating waves. These periodic structures are known as PCs. PCs have shown an excellent potential in many disciplines of science and technology in the last decade. They have generated lots of interests due to their ability to manipulate mechanical waves like sound waves and thermal properties which are not available in nature. The physical properties of PCs are not essentially determined by chemical elements and bonds in the materials, but rather on the internal specific structures. Structures of this type have the ability to inhibit the propagation of vibrational energy over certain ranges of frequencies forming band gaps. The main purpose of this study is to investigate the band structure and especially the location and width of band gaps. For this analysis, it is used the finite element method (FEM) and plane wave expansion (PWE). The results are shown in the form of band structure and wave modes. Band structures calculated by FEM and PWE present good agreement. We suggest that the bio-inspired PC considered should be feasible for elastic vibration control.

Structural Intensity Analysis of Periodic Elastic Structures With Frequency Stop Bands

2016 ◽  
Author(s):  
M. Nouh
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Periodic Structures ◽  
External Disturbance ◽  
Stop Band ◽  
Bloch Wave ◽  
Periodic Medium ◽  
Elastic Structures ◽  
Structural Intensity ◽  
Wide Range

Periodic elastic structures consisting of self-repeating geometric or material arrangements exhibit unique wave propagation characteristics culminating in frequency stop bands, i.e. ranges of frequency where elastic waves can propagate the periodic medium. Such features make periodic structures appealing for a wide range of vibration suppression and noise control applications. Stop bands in periodic media are achieved via Bragg scattering of elastic which is attributed to impedance mismatches between the different constituents of the self-repeating cells. Stop band frequencies can be numerically predicted using mathematical models which generally utilize the Bloch wave theorem and a transfer matrix method to track the spatial and temporal parameters of the propagating waves from one cell to the next. Such analysis generates what is referred to as the band structure (or the dispersion curves) of the periodic medium which can be used to predict the location of the pass and stop bands. Although capable, these models become significantly more involved when analyzing structures with dissipative constituents and/or material damping and need further adjustments to account for complex elastic moduli and frequency dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power and energy transmission paths. It is shown that the steady-state spatial propagation of vibrational power caused by an external disturbance accurately reflects the wave propagation pattern in the periodic medium, and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The developed framework is mathematically applied to a one-dimensional periodic rod to validate the proposed method.

Band structure of surface flexural–gravity waves along periodic interfaces

1998 ◽  
Vol 369 ◽  
pp. 333-350 ◽  
Author(s):  
TOM CHOU
Keyword(s):  
Wave Propagation ◽  
Excitation Frequency ◽  
Band Gaps ◽  
Bragg Scattering ◽  
Solid State Physics ◽  
One Dimensional ◽  
Propagating Waves ◽  
Infinite Array ◽  
Flexural Gravity Waves ◽  
Bloch’S Theorem

We extend Floquet's Theorem, similar to that used in calculating electronic and optical band gaps in solid state physics (Bloch's Theorem), to derive dispersion relations for small-amplitude water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one-dimensional periodicity (stripes), we find band gaps for wavevectors in the direction of periodicity corresponding to frequency ranges which support only non-propagating standing waves, as a consequence of multiple Bragg scattering. The dependence of these gaps on scatterer strength, density, and water depth is analysed. In contrast to band gap behaviour in electronic, photonic, and acoustic systems, we find that the gaps here can increase with excitation frequency ω. Thus, higher-order Bragg scattering can play an important role in suppressing wave propagation. In simple two-dimensional periodic geometries no complete band gaps are found, implying that there are always certain directions which support propagating waves. Evanescent modes offer one qualitative reason for this finding.

Comparative Study of Viscoelastic Arterial Wall Models in Nonlinear One-Dimensional Finite Element Simulations of Blood Flow

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Rashmi Raghu ◽  
Irene E. Vignon-Clementel ◽  
C. Alberto Figueroa ◽  
Charles A. Taylor
Keyword(s):  
Finite Element ◽  
Blood Flow ◽  
Wave Propagation ◽  
Comparative Study ◽  
Abdominal Aorta ◽  
Elastic Model ◽  
One Dimensional ◽  
Viscoelastic Models ◽  
Wide Range ◽  
Wall Models

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein et al. in 1980 (model V1) and Valdez-Jasso et al. in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.

scholarly journals Wave Propagation in an Optimized Tunable Multi-channel Flter based on One-dimensional Nano Superconductor Photonic Crystal

2021 ◽  
Author(s):  
Ali Baseri ◽  
Alireza Keshavarz
Keyword(s):  
Wave Propagation ◽  
Low Temperature ◽  
Defect Layer ◽  
Band Gaps ◽  
Defect Modes ◽  
One Dimensional ◽  
Lattice Constants ◽  
Space Industry ◽  
Polarized Waves ◽  
Central Defect

Abstract Although there has been a focus on THz lters so far, there is a signifcant defciency in advancing low-temperature THz lters. According to the needs, we proposed a tunable THz lter that selectively permits the desired incident frequencies to be propagated in relevance with our purpose. The presence of a low-temperature nano superconductor and an undoped semiconductor layers in the proposed structure resulted in a multi-channel THz lter, which could be highly tuned with several parameters such as lattice constants, applied temperature, etc. The achieved transmittance spectra revealed that the emerged transmittance couples and stacks follow exact regulations. Furthermore, the structure exhibited omnidirectional band-gaps for both TE and TM polarized waves. Moreover, the use of a central defect layer gave some transmittance defect modes in the forbidden areas. This structure could be used in some THz devices such as switches, optimized sensors as well as in space industry and telecommunications.

GENERALIZED EIGENPROBLEM FOR ACOUSTIC WAVE PROPAGATION IN PERIODICALLY LAYERED ANISOTROPIC MEDIA

2008 ◽  
Vol 16 (01) ◽  
pp. 1-10 ◽  
Author(s):  
ENG LEONG TAN
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Anisotropic Media ◽  
Acoustic Wave Propagation ◽  
High Frequencies ◽  
Generalized Eigenproblem ◽  
Floquet Waves ◽  
Wide Range ◽  
Numerical Difficulty ◽  
Stable Matrix

A stable matrix method is presented for studying acoustic wave propagation in thick periodically layered anisotropic media at high frequencies. The method enables Floquet waves to be determined reliably based on the solutions to a generalized eigenproblem involving scattering matrix. The method thus overcomes the numerical difficulty in the standard eigenproblem involving cell transfer matrix, which occurs when the unit cell is thick or the frequency is high. With its numerical stability and reliability, the method is useful for analysis of periodic media with wide range of thickness at high frequencies.

Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yaroslava E. Poroshyna ◽  
Aleksander I. Lopato ◽  
Pavel S. Utkin
Keyword(s):  
Wave Propagation ◽  
Detonation Wave ◽  
Model Comparison ◽  
Approximation Order ◽  
Transition Regime ◽  
Stage Model ◽  
Two Stage ◽  
One Dimensional ◽  
Kinetics Of ◽  
Detonation Wave Propagation

Abstract The paper contributes to the clarification of the mechanism of one-dimensional pulsating detonation wave propagation for the transition regime with two-scale pulsations. For this purpose, a novel numerical algorithm has been developed for the numerical investigation of the gaseous pulsating detonation wave using the two-stage model of kinetics of chemical reactions in the shock-attached frame. The influence of grid resolution, approximation order and the type of rear boundary conditions on the solution has been studied for four main regimes of detonation wave propagation for this model. Comparison of dynamics of pulsations with results of other authors has been carried out.

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