Modal Nodal Forces-FEM-Matlab

[E2015]

Hi,
I am looking at natural frequencies and mode shapes of Timoshenko beam in Matlab. For the analysis I used FEM. I had translation and rotation at each node, 4DOF per element.
I need to calculate MODAL NODAL FORCES, expressions: k[sub]e[/sub] * phi and K * PHI.
k[sub]e[/sub] * phi refers to element level and K * PHI refers to the whole system. k[sub]e[/sub] is the element stiffness matrix, K is system stiffness matrix, PHI is matrix that stores mode shapes of the system, and phi I don't know how to name it(amplitude of the mode shape at each node for translational and rotational DOF?).

If I want to calculate k[sub]e[/sub] * phi, dimension of k[sub]e[/sub] is 4by4, but what is the dimension of phi? 4by1?

Lets say I had 10 finite elements, so my system stiffness matrix K was at the end 22by22. If I want to look at first three modes, the matrix that stores mode shapes is 22by3. Usually I omit mode shapes corresponding to rotational degrees of freedom. So at the end the matrix that stores mode shapes is 11by3. But if I do that here I can not calculate the expression K * PHI because the dimensions of matrices do not match.
Should I omit the mode shapes that correspond to rotational degrees of freedom? If yes, how could I write the expression K * PHI?

Any advise or suggestion would help.

Thanks!

 

[LRJ]

Sorry if this counts as thread necromancy - I was looking for another topic and came across this one which looked interesting.

My question is why have you removed the rotation? Why not just leave it in there? It makes life a whole lot easier and you don't have to do anything with that information if you don't want to.