scholarly journals Longitudinal wave propagation in a one-dimensional quasi-periodic waveguide

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190392
Author(s):  
Vladislav S. Sorokin
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Periodic Waveguide ◽  
One Dimensional ◽  
Vibration Attenuation ◽  
Direct Separation ◽  
Longitudinal Wave Propagation ◽  
Spatial Modulations

The paper deals with the analysis of wave propagation in a general one-dimensional (1D) non-uniform waveguide featuring multiple modulations of parameters with different, arbitrarily related, spatial periods. The considered quasi-periodic waveguide, in particular, can be viewed as a model of pure periodic structures with imperfections. Effects of such imperfections on the waveguide frequency bandgaps are revealed and described by means of the method of varying amplitudes and the method of direct separation of motions. It is shown that imperfections cannot considerably degrade wave attenuation properties of 1D periodic structures, e.g. reduce widths of their frequency bandgaps. Attenuation levels and frequency bandgaps featured by the quasi-periodic waveguide are studied without imposing any restrictions on the periods of the modulations, e.g. for their ratio to be rational. For the waveguide featuring relatively small modulations with periods that are not close to each other, each of the frequency bandgaps, to the leading order of smallness, is controlled only by one of the modulations. It is shown that introducing additional spatial modulations to a pure periodic structure can enhance its wave attenuation properties, e.g. a relatively low-frequency bandgap can be induced providing vibration attenuation in frequency ranges where damping is less effective.

Elastic wave propagation in metamaterial rods with periodic shunted piezo-patches

2021 ◽  
Vol 263 (2) ◽  
pp. 4303-4311
Author(s):  
Edson J.P. de Miranda ◽  
Edilson D. Nobrega ◽  
Leopoldo P.R. de Oliveira ◽  
José M.C. Dos Santos
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Band Gaps ◽  
Low Frequencies ◽  
Periodic Arrays ◽  
Extended Plane ◽  
Elastic Metamaterials ◽  
Piezoelectric Structures

The wave propagation attenuation in low frequencies by using piezoelectric elastic metamaterials has been developed in recent years. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 1-D elastic metamaterial rod with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial rod is capable of filtering the propagation of longitudinal elastic waves over a specified range of frequency, called band gaps. The complex dispersion diagrams are obtained by the extended plane wave expansion (EPWE) and wave finite element (WFE) approaches. The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

scholarly journals Vibration Attenuation Optimization in a Rod With Different Periodic Piezoelectric Shunting Configurations

2021 ◽  
Vol 26 (3) ◽  
pp. 212-220
Author(s):  
Hui Guo ◽  
Yaru Zhang ◽  
Tao Yuan ◽  
Pei Sun Qian ◽  
Qian Cheng ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Wave Propagation ◽  
Numerical Model ◽  
Elastic Wave ◽  
Vibration Control ◽  
Wave Attenuation ◽  
Broad Band ◽  
Band Gaps ◽  
Attenuation Constant ◽  
Vibration Attenuation

Wave propagation control in piezoelectric meta-materials has been extensively investigated in recent years due to its significant effects on elastic wave attenuation. In this work, a novel piezoelectric meta-material rod connected to three configurations of shunting circuits is proposed for broad band gaps. The numerical model is constructed to predict the band gap, attenuation constant, and vibration transmission. For larger attenuation within the band gaps, the shunting circuit parameters are optimized with a genetic algorithm. The result shows that the structure with the optimized parameters provides prominent vibration control ability. Both the attenuation constant and the width of the band gaps are enlarged.

Flexural waves in elastically coupled telescopic metabeams

2021 ◽  
pp. 1-28
Author(s):  
Rajan Prasad ◽  
Arnab Banerjee
Keyword(s):  
Wave Propagation ◽  
Band Gap ◽  
Wave Attenuation ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Length Ratio ◽  
Beam Equation ◽  
Flexural Wave ◽  
Constitutive Components

Abstract This paper investigates the flexural wave propagation through elastically coupled metabeams. It is assumed that the metabeam is formed by connecting successive beams with each other using distributed elastic springs. The equations of motion of a representative unit of the above mentioned novel structural form is established by dividing it into three constitutive components that are two side beams, modeled employing Euler-Bernoulli beam equation and an elastically coupled articulated distributed spring connection (ECADSC) at middle. ECADSC is modeled as parallel double beams connected by distributed springs. The underlying mechanics of this system in context of elastic wave propagation is unique when compared with the existing state of art in which local resonators, inertial amplifiers etc. are attached to the beam to widen the attenuation bandwidth. The dynamic stiffness matrix is employed in conjunction with Bloch-Floquet theorem to derive the band-structure of the system. It is identified that the coupling coefficient of the distributed spring layer and length ratio between the side beams and the elastic coupling plays the key role in the wave attenuation. It has been perceived that a considerable widening of the attenuation band gap in the low-frequency can be achieved while the elastically distributed springs are weak and distributed in a small stretch. Specifically, 140% normalized band gap can be obtained only by tuning the stiffness and the length ratio without adding any added masses or resonators to the structure.

Models for thermoelastic attenuation of waves in heterogeneous solids

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1032-1040 ◽  
Author(s):  
Baxter H. Armstrong
Keyword(s):  
Temperature Variation ◽  
Wave Attenuation ◽  
Homogeneous Equation ◽  
Low Frequency ◽  
Temperature Wave ◽  
Heterogeneous Solids ◽  
One Dimensional ◽  
Thermal Current ◽  
Periodic Arrangement ◽  
Heterogeneous Solid

Some one‐dimensional models of a heterogeneous solid are presented consisting of a succession of slabs with different anharmonic properties. The equation for the temperature variation in these models due to passage of a longitudinal elastic wave can be solved exactly in the approximation of weak attenuation. The solutions are given in terms of the forced oscillation plus the temperature wave solutions to the homogeneous equation needed to match the boundary conditions of continuity of temperature and thermal current. Thermoelastic attenuation due to this temperature variation is compared to that of Zener’s classical approach. For periodic arrangement of slab properties or upon use of Zener’s boundary condition of vanishing thermal current, the temperature‐wave approach reproduces Zener‐type attenuation. However, a succession of slabs with a random, uncorrelated distribution of the Gruneisen constant leads to a new result with attenuation proportional to the three‐halves power of the wave frequency in the low‐frequency limit. The results are discussed in the context of seismoacoustic wave attenuation.

Wave Propagation in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling

1964 ◽  
Vol 31 (3) ◽  
pp. 423-429 ◽  
Author(s):  
Robert C. Petrof ◽  
Serge Gratch
Keyword(s):  
Wave Propagation ◽  
Elastic System ◽  
Thermomechanical Coupling ◽  
Temperature Dependent ◽  
Stress Variation ◽  
Single Degree Of Freedom ◽  
One Dimensional ◽  
Stress Strain Relation ◽  
Longitudinal Wave Propagation ◽  
Temperature Dependent Properties

A numerical method is developed for the analysis of one-dimensional wave propagation in viscoelastic media with temperature-dependent properties when thermomechanical coupling is significant. The method is applied to a specific case of longitudinal wave propagation in a finite rod with essentially sinusoidal stress variation at the two ends. The results show that, contrary to the usual assumption, such a system does not have the same response as a single-degree-of-freedom elastic system with viscous damping, as long as a realistic stress-strain relation is used.

Pressure Waves Propagation in an Elastic Shell with Polydisperse Liquid-Gas Mixture

2011 ◽  
Vol 105-107 ◽  
pp. 259-262
Author(s):  
Semyon Levitsky ◽  
Rudolf Bergman ◽  
Jehuda Haddad
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Elastic Shell ◽  
Wall Friction ◽  
Pressure Waves ◽  
Friction Heat ◽  
Longitudinal Wave Propagation ◽  
Waves Propagation ◽  
Acoustic Losses ◽  
Surrounding Liquid

The target of the paper is modeling of the influence of small amount of free gas on pressure wave propagation in a cylindrical elastic shell, filled with viscous liquid. Heterogeneity of the bubble population and the basic sources of wave attenuation (wall friction, heat exchange between gas in microbubbles and surrounding liquid, viscous and acoustic losses) are taken into account. The dispersion equation for the waveguide is studied numerically and effect of the bubble size distribution on the longitudinal wave propagation is discussed.

On the use of localization theory to characterize elastic wave propagation in randomly stratified 1-D media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 177-179 ◽  
Author(s):  
John A. Scales
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Seismic Data ◽  
Effective Medium Theory ◽  
Low Frequency ◽  
Elastic Wave Propagation ◽  
Well Log ◽  
Medium Theory ◽  
One Dimensional ◽  
Localization Theory

In a series of papers Benjamin White, Ping Sheng, George Papanicolaou and others have described the application of localization theory to the study of elastic wave propagation in randomly stratified one‐dimensional (1-D) media. They describe methods for computing the localization parameters and apply the results to sonic well‐log data. In this note, I will show that, at least in the seismic band, the results of their calculations disagree with effective medium theory. This disagreement may to be due to the lack of low‐frequency information in exploration seismic data.

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