A Dispersive Nonlocal Model for In-Plane Wave Propagation in Laminated Composites With Periodic Structures

2015 ◽  
Vol 82 (3) ◽  
Author(s):  
H. Brito-Santana ◽  
Yue-Sheng Wang ◽  
R. Rodríguez-Ramos ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Phase Velocity ◽  
Incident Angle ◽  
Unit Cell ◽  
Wave Number ◽  
Periodic Distribution ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
Plane Wave Propagation

In this paper, the problem of in-plane wave propagation with oblique incidence of the wave in an isotropic bilaminated composite under perfect contact between the layers and periodic distribution between them is studied. Based on an asymptotic dispersive method for the description of the dynamic processes, the dispersion equations were derived analytically from the average model. Numerical examples show that the dispersion curves obtained from the present model agree with the exact solutions for a range of wavelengths. Detailed numerical simulations are provided to illustrate graphically the phase and group velocities. Such illustrations allow the identification and comparison of the effects of the unit cell size, wave number and incident angle. It was observed that, as the incident angle increases, the dimensionless quasi-longitudinal phase velocity increases, and the dimensionless quasi-shear phase velocity decreases. In addition, the phase and group velocities decrease as the size of the unit cell increases. The frequency band structure, as a function of the wave-vector components is calculated.

Locally resonant effective phononic crystals for subwavelength vibration control of torsional cylindrical waves

2021 ◽  
pp. 1-30
Author(s):  
Ignacio Arretche ◽  
Kathryn Matlack
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Effective Properties ◽  
Equations Of Motion ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Unit Cell ◽  
Periodic Coefficients ◽  
Bloch Theorem ◽  
Plane Wave Propagation

Abstract Locally resonant materials allow for wave propagation control in the sub-wavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this paper, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially-varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e. its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.

Effects of Ions on the Propagation of Langmuir Oscillations in Cold Quantum Electron-Ion Plasmas

2008 ◽  
Vol 63 (7-8) ◽  
pp. 400-404 ◽  
Author(s):  
Hyun-Jae Rhee ◽  
Young-Dae Jung
Keyword(s):  
Phase Velocity ◽  
Quantum Effect ◽  
Frequency Mode ◽  
Wave Number ◽  
Propagation Mode ◽  
Quantum Electron ◽  
Quantum Plasmas ◽  
Phase And Group Velocities ◽  
Lower Frequency Mode ◽  
Group Velocities

The effects of ions on the propagation of Langmuir oscillations are investigated in cold quantum electron-ion plasmas. It is shown that the higher and lower frequency modes of the Langmuir oscillations would propagate in cold quantum plasmas according to the effects of ions. It is also shown that these two propagation modes merge into one single propagation mode if the contribution of ions is neglected. It is found that the quantum effect enhances the phase and group velocities of the higher frequency mode of the propagation. In addition, it is shown that the phase velocity of the lower frequency mode is saturated with increasing the quantum wavelength and further that the group velocity of the lower frequency mode has a maximum position in the domains of the wave number and quantum wavelength.

scholarly journals VELOCITIES AND TRAJECTORIES OF WAVE MOTION IN A TWO-LAYER HYDRODYNAMIC SYSTEM

2020 ◽  
pp. 30-37
Author(s):  
Y. Hurtovyi ◽  
O. Kuharenko
Keyword(s):  
Surface Tension ◽  
Phase Velocity ◽  
Internal Waves ◽  
Lower Layer ◽  
World Ocean ◽  
Capillary Waves ◽  
Wave Number ◽  
Hydrodynamic System ◽  
Phase And Group Velocities ◽  
Group Velocities

The paper deals with studying trajectories of motion of individual liquid particles in a two-layer hydrodynamic system with a finite layer thickness as well as analyzing phase and group velocities of internal waves in the system. The problem is modeled for an inviscid incompressible fluid under action of the gravity and surface tension forces in a dimensionless form. Solutions of the problem are sought in the form of progressive waves using the multi-scale method. The solutions are expanded in terms of the nonlinearity coefficient. Dependence of the dispersion ratio of the wavenumber is investigated for different values of the surface tension coefficient and the ratio of the layer densities. Formulas are obtained for the group and phase velocities for internal gravity-capillary waves as well as in the limiting case for capillary waves. A comparison of the values of the phase and group velocities of internal waves for different values of the wave number is carried out. It is proved that with an increase in the wave number, the group velocity begins to outstrip the phase velocity, and their equality occurs at the minimum phase velocity. It is shown that the trajectories are ellipses in which the horizontal semi axes are larger than the vertical ones. Formulas are obtained for the semi axes of elliptic trajectories for each of the layers. The character of the change in the semi axes of elliptical trajectories is analyzed depending on the distance from the interface between two liquid layers as well as on the values of the wave number. It is proved that the semi axes of ellipses decrease unevenly with increasing distance from the boundary. The asymmetry of the particle trajectories of each of the layers is shown for the case when the thickness of the lower layer differs from the thickness of the lower layer. The study of the kinematic characteristics of the particle motion makes it possible to simulate real physical wave processes in the World Ocean. The results are also relevant for creating a theoretical basis for experiments.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

Period equation for Rayleigh waves in a layer overlying a half space with a sinusoidal interface

1962 ◽  
Vol 52 (4) ◽  
pp. 807-822 ◽  
Author(s):  
John T. Kuo ◽  
John E. Nafe
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Length ◽  
Linear Equations ◽  
Wave Number ◽  
Interface Plane ◽  
Period Equation ◽  
Phase And Group Velocities

abstract The problem of the Rayleigh wave propagation in a solid layer overlying a solid half space separated by a sinusoidal interface is investigated. The amplitude of the interface is assumed to be small in comparison to the average thickness of the layer or the wave length of the interface. Either by applying Rayleigh's approximate method or by perturbating the boundary conditions at the sinusoidal interface, plane wave solutions for the equations which satisfy the given boundary conditions are found to form a system of linear equations. These equations may be expressed in a determinant form. The period (or characteristic) equations for the first and second approximation of the wave number k are obtained. The phase and group velocities of Rayleigh waves in the present case depend upon both frequency and distance. At a given point on the surface, there is a local phase and local group velocity of Rayleigh waves that is independent of the direction of wave propagation.

scholarly journals Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Daniel Omondi Onyango ◽  
Robert Kinyua ◽  
Abel Nyakundi Mayaka
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Plane Wave ◽  
Acoustic Pressure ◽  
Three Dimensional ◽  
The Other ◽  
Expansion Chamber ◽  
Central Tube ◽  
Simple Expansion ◽  
Plane Wave Propagation

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

Plane wave propagation in microstretch thermoelastic medium with microtemperatures

2014 ◽  
Vol 21 (16) ◽  
pp. 3403-3416
Author(s):  
Rajneesh Kumar ◽  
Mandeep Kaur ◽  
SC Rajvanshi
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Thermoelastic Medium ◽  
Plane Wave Propagation
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