Dear Bilal Khan:

If I appropriately understood your question, you might need to:

1. Obtain the eigenvector matrix for FE analysis

With FE analysis, now you have modal displacements in u1 and u2. Actually, eigenvector matrix V is calculated by equation V(K-ω2M) =0. Essentially, V is a table of the modal displacement. Here, every column corresponds to a certain mode shape while every row corresponds to a certain DOF(degree of freedom).

If you have u1 and u2 displacements for modes you interested, you may arrange them as:

           [u11 u12    ... u1n ]

VFE= [u21 u22    ... u2n ]

           [...                .... ...   ]

           [un1 un2    ... unn ]

Where the first subscript represents the number of DOF and the second represents the number of mode.

2. Appropriately match the DOF(degree of freedom) between experimental and FE model.

In this step, you need to find the DOFs that corresponding to points with sensors in Experiment. Record them as S={i,j,...,k}. Then delete rows in VFE that not recorded.

For example, you have {1,2}. Then you have a new VFE:

           [u11 u12    ... u1n ]

           [u21 u22    ... u2n ]

Then you also need to delete the columns in the new VFE that corresponding to modes that you are not interested in the experiment. 

For example, you only care about the first three modes, you have a new VFE:

           [u11 u12  u13 ]

           [u21 u22  u23 ]

This is the eigenvector matrix that you can use to compare with experimental results.

3. Arrange experimental results in eigenvector matrix form.

With S vector and the number of  modes you interested, you can write a corresponding experimental eigenvector matrix VE as:

            1st      2nd    3rd

VE= [u11e u12e u13e]      1

         [u21e u22e u23e]      n

Where subscript e means results obtained from experiment.

You can compare VFE and VE.

Best regards,

Bowei.

You might be interested in the following papers

The Modal Assurance Criterion (MAC): Twenty Years of Use and Abuse

www.sandv.com/downloads/0308alle.pdf

http://www.sciencedirect.com/science/article/pii/S1877705812046140

Dear Bilal Khan:

If I appropriately understood your question, you might need to:

1. Obtain the eigenvector matrix for FE analysis

With FE analysis, now you have modal displacements in u1 and u2. Actually, eigenvector matrix V is calculated by equation V(K-ω2M) =0. Essentially, V is a table of the modal displacement. Here, every column corresponds to a certain mode shape while every row corresponds to a certain DOF(degree of freedom).

If you have u1 and u2 displacements for modes you interested, you may arrange them as:

           [u11 u12    ... u1n ]

VFE= [u21 u22    ... u2n ]

           [...                .... ...   ]

           [un1 un2    ... unn ]

Where the first subscript represents the number of DOF and the second represents the number of mode.

2. Appropriately match the DOF(degree of freedom) between experimental and FE model.

In this step, you need to find the DOFs that corresponding to points with sensors in Experiment. Record them as S={i,j,...,k}. Then delete rows in VFE that not recorded.

For example, you have {1,2}. Then you have a new VFE:

           [u11 u12    ... u1n ]

           [u21 u22    ... u2n ]

Then you also need to delete the columns in the new VFE that corresponding to modes that you are not interested in the experiment. 

For example, you only care about the first three modes, you have a new VFE:

           [u11 u12  u13 ]

           [u21 u22  u23 ]

This is the eigenvector matrix that you can use to compare with experimental results.

3. Arrange experimental results in eigenvector matrix form.

With S vector and the number of  modes you interested, you can write a corresponding experimental eigenvector matrix VE as:

            1st      2nd    3rd

VE= [u11e u12e u13e]      1

         [u21e u22e u23e]      n

Where subscript e means results obtained from experiment.

You can compare VFE and VE.

Best regards,

Bowei.

You may refer to u1 and u2 as displacements of your degrees of freedom DOFs of each node and not as eigen vectors. Eigen vectors contain displacements of every single DOF of your system that correspond to a mode of vibration.

Dear Bilal Khan,

The eigenvectors matrix [Phi] of (nxm) order is obtained from the calculated {Phi} (nx1) eigenvectors (columns in {Phi] matrix) of each mode obtained from the solving process after an assumption of one d.o.f  where m