Hello All
I am new here. Please forgive any dumbness. I can sort of understand partial differential equations, but not those tensor equations.
I am looking for equations that work for a three dimensional elastic medium. I came across articles such as "Governing Equations of Three Dimensional Elasticity" http://homepages.engineering.auckla...asticity/07_3DElasticity_03_3D_Elasticity.pdf which is too difficult for me.
In one set of equations that I saw they used three extra variables to x, y, z which were the displacements from the original positions. That makes sense to me.
As to what I am trying to do, it is to link to understanding in another area. I want to consider such things as spherical rotation (not cylindrical rotation) in an elastic medium. http://www.rwgrayprojects.com/WSM/SphericalRotations/SR.html
In an elastic medium, this type of rotation will cause a stretching of the medium near the centre of the wave in addition to the standing waves that exist. I want to understand whether a linear medium will cause apparently non-linear effects due to this rotation.
This is some work that I did years ago using linear equations. I wonder whether non-linearity is needed. Where the medium is stretched, it seems to me that the local wave speed will be greater.
Thanks for your consideration
Ray Tomes
I am new here. Please forgive any dumbness. I can sort of understand partial differential equations, but not those tensor equations.
I am looking for equations that work for a three dimensional elastic medium. I came across articles such as "Governing Equations of Three Dimensional Elasticity" http://homepages.engineering.auckla...asticity/07_3DElasticity_03_3D_Elasticity.pdf which is too difficult for me.
In one set of equations that I saw they used three extra variables to x, y, z which were the displacements from the original positions. That makes sense to me.
As to what I am trying to do, it is to link to understanding in another area. I want to consider such things as spherical rotation (not cylindrical rotation) in an elastic medium. http://www.rwgrayprojects.com/WSM/SphericalRotations/SR.html
In an elastic medium, this type of rotation will cause a stretching of the medium near the centre of the wave in addition to the standing waves that exist. I want to understand whether a linear medium will cause apparently non-linear effects due to this rotation.
This is some work that I did years ago using linear equations. I wonder whether non-linearity is needed. Where the medium is stretched, it seems to me that the local wave speed will be greater.
Thanks for your consideration
Ray Tomes