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How to recover eigenvector components for specified displacements ?


I have a problem visualising specified displacements from a modal/buckling analysis. 

When solving the algebraic system of equations [K]{u}={f} resulting from FEA discretization, the vector {u} does not have components for the specified displacements, zero or not zero, because the corresponding degrees of freedon (dof) have been eliminated. To visualize all the displacements, even the ones that are specified, we recover them from the input data to create a longer vector {u|u*} where {u} are the active dof and {u*} are the specified dof, zero or not zero. 

My problem is what to do when the vector {u} is an eigenvector from modal or buckling analysis? In such case, the eigenvector is undertermined by a constant, and most of the time normalized so that its larger component is equal to one. Then, the scale of the eigenvector is inconsistent with the non-zero specified displacements of the problem.

I have no idea about the magnitude of the eigenvector components for the dof that were specified because they were eliminated. 

Does anybody know about a reference where to read about this, or do you know the solution outright? 



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