ELASTIC WAVES IN TRIGONAL CRYSTALS

1961 ◽  
Vol 39 (1) ◽  
pp. 65-80 ◽  
Author(s):  
G. W. Farnell
Keyword(s):  
Elastic Waves ◽  
Energy Flow ◽  
Pure Mode ◽  
Sound Waves ◽  
Propagation Characteristics ◽  
Three Solutions ◽  
Transverse Waves ◽  
Plane Wavefront ◽  
Wave Normal ◽  
Quasi Longitudinal Wave

In non-isotropic single crystals the normals to the wavefronts of elastic waves are not colinear with the vectors representing either the energy flow or the particle displacement. Calculations have been carried out on the propagation characteristics of sound waves in two particular trigonal crystals, α-quartz and sapphire.The development of the eigenvalue equation for the velocity and the formulae for the components of the displacement and energy-flow vectors are summarized. The assumption that the wave has a plane wavefront normal to a given direction leads to three solutions, one representing a quasi-longitudinal wave and the other two representing quasi-transverse waves. The velocities of propagation, directions of displacement, and directions of energy flow for the three waves have been calculated for many orientations of the wave normal. Detailed results for propagation near one of the pure-mode axes are presented.

scholarly journals Elastic waves in a prestressed Mooney material

1972 ◽  
Vol 7 (1) ◽  
pp. 135-160 ◽  
Author(s):  
J.A. Belward
Keyword(s):  
Simple Form ◽  
Fourier Transforms ◽  
Secular Equation ◽  
Sufficient Conditions ◽  
Axially Symmetric ◽  
Transverse Waves ◽  
Wave Speeds ◽  
Impulsive Forces ◽  
Plane Wavefront ◽  
Necessary And Sufficient

The dynamic response of a prestressed incompressible Mooney material is studied by investigating plane wave propagation and the response of the material to impulsive lines of force. The choice of an initial deformation which is axially symmetric gives a particularly simple form for the secular equation for the plane wavefront velocities. The speeds of propagation and the amplitudes of the two permissible transverse waves are found and necessary and sufficient conditions for there to exist two real wave speeds in all directions are established. The simple form of the secular equation enables the response of the material to concentrated disturbances to be readily solved using Fourier transforms. The motions caused by a line of impulsive forces is examined in some detail.

Antiferromagnetic Conic Refraction of Sound in Hematite

2010 ◽  
Vol 168-169 ◽  
pp. 173-176
Author(s):  
S.A. Migachev ◽  
M.F. Sadykov ◽  
M.M. Shakirzyanov ◽  
D.A. Ivanov
Keyword(s):  
Magnetic Field ◽  
Elastic Waves ◽  
Energy Flow ◽  
Deflection Angle ◽  
Easy Plane ◽  
Magnetoelastic Interaction ◽  
Basis Plane ◽  
Field Dependent ◽  
The Deflection Angle ◽  
The Magnetic Field

In a trigonal easy-plane -Fe2O3 antiferromagnet magnetic-field-dependent conic refraction due to the renormalization of the coefficients of elasticity effective magnetoelastic interaction is experimentally found in addition to the conventional internal conic refraction of the transverse elastic waves propagating along the trigonal C3 axis. It is shown that the deflection angle () of the energy flow from the C3 axis upon the internal conic refraction does not depend on the value of the magnetic field applied in the basis plane (HC3) and is a constant value determined by the correlation of the C14 and C44 coefficients of elasticity. The deflection angle of the energy flow upon the antiferromagnetic conic refraction () increases with increase in the field and tends to the  value at large H values. The obtained results agree well with the theory of this phenomenon in antiferromagnets and support its conclusions.

The torque on an infinite strip exposed to plane sound waves

1957 ◽  
Vol 53 (1) ◽  
pp. 234-247 ◽  
Author(s):  
Harold Levine
Keyword(s):  
Incident Wave ◽  
Unit Length ◽  
Equilibrium Density ◽  
Infinite Strip ◽  
Sound Waves ◽  
Plane Sound ◽  
Oscillatory Character ◽  
The Mean ◽  
Image Position ◽  
Wave Normal

ABSTRACTThe mean torque on an infinite fixed strip due to plane harmonic sound waves is calculated, employing simple acoustical theory as a basis and neglecting viscosity. In the range of wavelength λ small compared to the strip width δ, the torque per unit length iswhere α denotes the angle between the incident wave normal and that of the strip and ρο the equilibrium density of the medium. This oscillatory character of the torque in its dependence on δ/λ is not to be found at long wavelengths where, as is well known, the torque acts only in the sense of aligning the strip broadside to the incident wave normal.

scholarly journals Acousto-optic devices using acoustic waves refraction

2021 ◽  
Vol 2127 (1) ◽  
pp. 012039
Author(s):  
N V Polikarpova ◽  
I K Chizh
Keyword(s):  
Elastic Waves ◽  
Acoustic Waves ◽  
Energy Flow ◽  
Anisotropic Media ◽  
Generation Process ◽  
Practical Applications ◽  
Technical Parameters ◽  
Acousto Optic Device ◽  
Materials Used ◽  
Flow Propagation

Abstract The methods of acousto-optics provide multiple techniques for controlling optical beam. The technical parameters of corresponding acousto-optic devices are largely determined by the efficiency of acoustic waves generation. In present work we examine the features of elastic waves generation in materials used in acousto-optics. In most of practical applications the elastic wave generation process is implemented through the refraction of elastic waves at the boundary between two anisotropic media. We present a detailed study of the refraction of elastic waves in strongly anisotropic media. We report new refractive effects such as “extraordinary” refraction. In the latter case the change in the direction of the incident acoustic wave does not influence the direction of the energy flow propagation for refracted elastic waves. The configuration of an acousto-optic device using the geometry of unusual refraction in an anisotropic medium is discussed.

scholarly journals The Influence of Crack Modes on the Elastic Wave Propagation Characteristics in a Non-uniform Rotating Shaft

2018 ◽  
Author(s):  
Yimin Wei ◽  
Xuan Shi ◽  
Qi Liu ◽  
Wenhua Chen
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Transverse Crack ◽  
Propagation Characteristics ◽  
Mode Iii ◽  
Transverse Cracks ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Local Flexibility ◽  
The Media

The vibration propagates in a media such as a shaft in the form of elastic waves. The propagation characteristics of the waves are affected by the geometry of the media, the material properties as well as the cracks. The study to elastic waves propagating in a shaft with transverse cracks can help to detect them. The transverse crack possesses different crack modes due to different external loads. The influence of the crack mode, the location and the depth to the propagation characteristics is investigated in this paper. Firstly, the local flexibility coefficients with three different modes are deduced. And then, the transfer matrix of the elastic wave can be obtained. Finally, the influence of the crack mode, the location and the depth of the transverse crack as well as the rotating speed to the propagation characteristics is then studied, both in a numerical and an experimental way. It’s found that mode III is the most suitable mode in this paper, the location of the crack will make the stopbands fluctuating, the depth mainly affects the bandwidth of the stopbands, and the increase of the rotating speed will shift up the stopbands without changing their bandwidths.

A Novel Technique With a Magnetostrictive Transducer for In Situ Length Monitoring of a Distant Specimen

2003 ◽  
Author(s):  
Michael Pedrick ◽  
Michael Heckman ◽  
B. R. Tittmann
Keyword(s):  
High Precision ◽  
Temperature Effects ◽  
Sound Propagation ◽  
Sound Waves ◽  
Propagation Characteristics ◽  
Novel Technique ◽  
Flight Measurement ◽  
Magnetostrictive Sensor ◽  
Magnetostrictive Transducer

A Magnetostrictive sensor was used to generate sound waves in a specimen through thirty feet of wire. Many hardware aspects are discussed such as boundaries, materials, acoustic horn design, and sound propagation characteristics which facilitated the generation of sound energy in the specimen. Temperature effects on velocity and length were calculated and a model was developed to determine length from a time of flight measurement. The specimen was heated in an oven to various temperatures and times of flight were measured and compared to the model. Results show agreement between the measured values and the model as well as the ability for a high precision length measurement.

A New Ballistic-Diffusive Model for Heat Pulse Propagation

2012 ◽  
Author(s):  
Yanbao Ma
Keyword(s):  
Heat Flux ◽  
Pulse Propagation ◽  
Dielectric Materials ◽  
Heat Pulse ◽  
Second Sound ◽  
Sound Waves ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Diffusive Model ◽  
Diffusive Part

In this paper, we reported a new ballistic-diffusive model for heat pulse propagation in dielectric materials. The internal energy and heat flux are split into ballistic part originating from the boundaries and diffusive part originating from inside medium. The ballistic part is modeled based on analytical solutions while the diffusive part is described by Guyer-Krumhansl equations. To validate this model, heat pulse propagation in pure NaF at low temperature is studied. The observed longitudinal waves, transverse waves, second sound waves, and diffusive waveforms from the experiments conducted in early 1970s are numerically reconstructed. There is qualitative agreement between numerical results and experimental observation.

Modeling and Analysis of Nonlinear Wave Propagation in One-Dimensional Phononic Structures

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
M. Liu ◽  
W. D. Zhu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Band Structure ◽  
Band Gap ◽  
Nonlinear Wave ◽  
Elastic Waves ◽  
Propagation Characteristics ◽  
Nonlinear Wave Propagation ◽  
Weakly Nonlinear

Different from elastic waves in linear periodic structures, those in phononic crystals (PCs) with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot accurately predict band-gap variations under finite-amplitude wave motions; creating nonlinear PCs remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler–Bernoulli beam using their exact Green–Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval (BSWI) finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear PCs.

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