the energy velocity of a lossless elastic plane wave, the vector C_ijkl p_j n_k p_l / (rho v)

Syntax

vp, vs1, vs2, pp, ps1, ps2 = velocity(C, n)

E = energyVector(C, n, vp, pp)

The energy velocity of the p wave in the direction n.

E = energyVector(C, n, vs1, ps1, density=rho)

Of the faster s wave, with another density.

vp, vs1, vs2, pp, ps1, ps2 = velocity(C)

E = energyVector(C, None, vp, pp)

As a vector field on the sphere.

Description

The energy velocity is the velocity at which a plane wave carries its energy through a medium without attenuation, a good proxy for the group velocity. It is Ve_i = C_ijkl p_j n_k p_l / (rho v), with n the propagation direction, v the phase speed and p the polarisation of one of the three waves velocity returns.

Its projection onto n is the phase speed, so its length is at least v. Pass the speed and the polarisation of the same wave, at the same directions.

Given a speed function and a polarisation field, they are evaluated at the directions n; without directions the result is the vector field on the sphere.

Input

`C`	stiffnessTensor in GPa
`n`	vector3d, the propagation directions, or None for the vector field
`speed`	the phase speed of the wave in km/s, vp, vs1 or vs2 of velocity, or an S2Fun
`polarization`	vector3d, the polarisation of the wave, pp, ps1 or ps2 of velocity, or an S2AxisField

Keywords

keyword	default	description
`density`	`None`	the density in g/cm^3; by default the density stored on the tensor

Output

`E`	vector3d, the energy velocity in km/s; S2VectorField without a direction

References

F. I. Fedorov, Theory of Elastic Waves in Crystals, Plenum Press, New York (1968)

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/stiffnessTensor.energyVector_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

stiffnessTensor.energyVector