Elastic Plane Waves in Homogeneous Materials

2012 ◽  
pp. 237-308
Keyword(s):  
Plane Waves ◽  
Elastic Plane ◽  
Homogeneous Materials

Magneto-thermo-elastic plane waves in rotating media

1983 ◽  
Vol 21 (2) ◽  
pp. 155-163 ◽  
Author(s):  
S.K Roy Chaudhuri ◽  
Lokenath Debnath
Keyword(s):  
Plane Waves ◽  
Elastic Plane

Magneto-thermo-elastic plane waves

1965 ◽  
Vol 61 (4) ◽  
pp. 939-944 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Shear Wave ◽  
Wave Velocity ◽  
Compression Wave ◽  
Thermal Field ◽  
Plane Waves ◽  
Elastic Plane ◽  
Magnetic Diffusivity ◽  
The Magnetic Field

AbstractThe combined effects of uniform thermal and magnetic fields on the propagation of plane waves in a homogeneous, initially unstressed, electrically conducting elastic medium have been investigated.When the magnetic field is parallel to the direction of wave propagation, the compression wave is purely thermo-elastic and the shear wave is purely magneto-elastic in nature. For a transverse magnetic field, the shear waves remain elastic whereas the compression wave assumes magneto-thermo-elastic character due to the coupling of all the three fields—mechanical, magnetic and thermal. In the general case, the waves polarized in the plane of the direction of wave propagation and the magnetic field are not only coupled but are also influenced by the thermal field, once again exhibiting the coupling of the three fields. The shear wave polarized transverse to the plane retains its magneto-elastic character.Notation.Hi = primary magnetic field components,ht = induced magnetic field components,To = initial thermal field,θ = induced thermal field,C = compression wave velocity.S = shear wave velocity,ui = displacement components,cv = specific heat at constant volume,k = thermal conductivity,η = magnetic diffusivity,μe = magnetic permeability,λ, μ = Lamé's constants,β = ratio of coefficient of volume expansion to isothermal compressibility.

On the propagation of elastic waves in aeolotropic media I. General principles

1954 ◽  
Vol 226 (1166) ◽  
pp. 339-355 ◽  
Keyword(s):  
Continuous Medium ◽  
Equations Of Motion ◽  
Plane Waves ◽  
Elastic Plane ◽  
Wave Surface ◽  
Least Action ◽  
Phase Velocities ◽  
Principle Of Least Action ◽  
Propagation Of Elastic Waves ◽  
General Method

Using the principle of least action the equations of motion and momentum conditions for elastic disturbances in any continuous medium are derived. Consideration of energy flux defines the form of the wave surface as the first negative pedal of the surface of phase velocities for elastic plane waves in the medium . A general method for obtaining the forms of these surfaces and an associated inverse surface is given and general conclusions about the propagation of disturbances are drawn.

The propagation of magneto-elastic plane waves

1966 ◽  
Vol 62 (1) ◽  
pp. 91-94 ◽  
Author(s):  
A. J. Willson
Keyword(s):  
Thermal Effects ◽  
Present Author ◽  
Thermal Field ◽  
Plane Waves ◽  
Elastic Field ◽  
Principal Result ◽  
Elastic Plane ◽  
Preferred Direction ◽  
Small Change ◽  
Elastic Strains

The propagation of magneto-elastic plane waves is a topic which has recently aroused much interest. Thus Paria ((l)), for example, and the present author ((2)), have studied in some detail the interaction between the magneto-elastic field and the thermal field. Analyses published so far, however, have neglected the effects due to the passage of the wave upon the magnetic permeability of the medium. It is the object of the present paper to consider these effects and it will be shown that although the elastic strains induced cause but a small change in the numerical values of the permeability, nevertheless the effects upon wave propagation may be very considerable. The principal result is the demonstration that the effects considered are equivalent so far as the dispersion equation is concerned, to an anisotropic rescaling of the primary magnetic field, the direction of propagation of the wave being a preferred direction. For simplicity, thermal effects are not considered here.

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