Natural Frequencies in ETABS

[Tygra_1983]

Dear all

I am trying to simply compute the natural frequencies of a 4 storey structure in ETABS. I am also trying to validate them in MATLAB. However, I am getting drastic differences in the results. This is strange because a couple of years ago I did a dynamics of structures coursework (however using SAP2000) and I didn't have a problem of them matching.

These are the results from ETABS:



The first mode has a circular frequency of 15.7129 rads/sec.

Here is MATLAB

clear, clc, close all

% Structural Properties
E = 2.1E+08;
I = 11696/100^4;
L = 5;
h = 3;
c = 0.05;


% Stiffness of a single floor
kx = 4*(12*E*I)/h^3

% Stiffness Matrix
K = [2*kx -kx 0 0;
     -kx 2*kx -kx 0;
     0 -kx 2*kx -kx;
     0 0 -kx kx]

% Mass matrix
M = [1676.5 1676.5 1676.5 1366]
M = diag(M)

% Compute mode shapes and circular frequencies
[Phi w2] = eig(K,M)

% Circular frequencies
wf = sqrt(w2)

The first frequency is 1.8468 rads/sec. This is a massive difference! Perhaps I am doing something wrong in ETABS, but there must be something dreadfully wrong.

Could someone help please?

 

[GregLocock]

what do the etabs mode shapes look like?
You frequencies seem to be out by 2pi roughly.

Just by eye your second matlab modeshape doesn't pass the sniff test. I skipped stiffness matrix methods at uni so I don't know if your matlab is right, but you have defined L and not used it.

 

[Tygra_1983]

In modes 1,3,4,5 there is no shape. Etabs shows no displacement at all:



Here, are mode shapes 2, 6, 7 and 8.

 

[GregLocock]

Sorry that makes no sense, you can't have non zero eigenvalues with zero value eigenvectors. So it is a modelling problem. The second mode you posted bears only a cursory similarity to the matlab one.

 

[Tygra_1983]

Do you have any ideas what could be the problem then, Greg? I mean, I just build the model and run the modal analysis.

EDIT:

The reason there appears no shape is because it is oscillating in the direction into the screen, lol. I just discovered it.

 

[GregLocock]

No I haven't used ETABS and I don't have any experience with the stiffness matrix method in matlab. OTOH I have been using FEA since 1982, and measuring experimental mode shapes since 1983. your list of eigenvectors and eigenvalues from ETABS looks wrong, and mode 2 from matlab looks wrong, first floor is moving too much, top floor not enough.