Plane wave propagation in a rotating anisotropic medium with voids under the action of a uniform magnetic field

In this paper, plane wave propagation in a rotating anisotropic material of general nature under the action of a magnetic field of constant magnitude has been investigated. The material is supposed to be porous in nature and contains voids. Following the concept of [Cowin S. C. and Nunziato, J. W. [1983] “Linear elastic materials with voids,” J. Elasticity 13, 125–147.] the governing equations of motion have been written in tensor notation taking account of rotation, magnetic field effect and presence of voids in the medium and the possibility of plane wave propagation has been examined. A number of particular cases have been derived from our general results to match with previously obtained results in this area. Effects of various parameters on the velocity of wave propagation have been presented graphically.

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

Journal of Vibration and Acoustics ◽

10.1115/1.4052748 ◽

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.

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Generalized magneto-hydrodynamic formulae

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100028395 ◽

1953 ◽

Vol 49 (2) ◽

pp. 299-307 ◽

Cited By ~ 27

Author(s):

C. O. Hines ◽

H. Bondi

Keyword(s):

Magnetic Field ◽

Wave Propagation ◽

Plane Wave ◽

Dispersion Equation ◽

Hydrodynamic Theory ◽

Initial Work ◽

The Subject ◽

Plane Wave Propagation

AbstractThe formulae for current and force which were employed in some of the initial work on magneto-hydrodynamic theory are not valid over the whole range of phenomena which the subject itself embraces. Generalized formulae, suitable for wider application, are derived by an extension of the magneto-ionic approach, and are applied to the simple case of plane-wave propagation in the direction of a primary magnetic field. The dispersion equation which results, as well as the basic current and force formulae, are reduced by approximations in a variety of limiting circumstances. Some earlier results are thereby regained and, in particular, the region of known validity of Alfvén's propagation relation is extended.

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Pedagogical tool to teach electromagnetic plane wave propagation in various media environments

European Journal of Physics ◽

10.1088/1361-6404/abf89d ◽

2021 ◽

Author(s):

Anqi Li ◽

Chengyou Yin ◽

Yongji Gan ◽

Qianqian Zhang ◽

Wei Wu

Keyword(s):

Wave Propagation ◽

Plane Wave ◽

Electromagnetic Plane Wave ◽

Pedagogical Tool ◽

Media Environments ◽

Plane Wave Propagation ◽

Electromagnetic Plane

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Plane Wave Propagation

Radio Propagation and Remote Sensing of the Environment ◽

10.1201/9780203022856.ch2 ◽

2004 ◽

pp. 31-52

Keyword(s):

Wave Propagation ◽

Plane Wave ◽

Plane Wave Propagation

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

Advances in Acoustics and Vibration ◽

10.1155/2018/3276548 ◽

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.

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