Modal analysis of a pin-jointed frameworks

[jackcolebrook]

Hi

I'm trying to find the modal frequencies of a pin-jointed frames, to validate an ansys model.

So far I've used direct stiffness method to generate a global stiffness matrix for the framework in Matlab. Is it as simple as mutiplying the stiffness matrix with an inverted mass matrix and finding the eigenvalues?

My gut geeling tells me I'm missing a step. Any help would be great.

 

[skeleton]

When:
Mass = M
Stiffness = K

Then:
vector(modal frequencies) = sqrt(eigenvals(K * M^-1))

 

[jackcolebrook]

Thanks for the help skeleton,

Could you take a look at my workings as see if I am talking cobblers.

If I use direct stiffness method, I can obtain a global stiffness for a framework. This is done by decomposing the frame into sperate trusses. Calulating the stiffness in local co-ordinates, then tranfering into global co-ordinates. Each truss is then arranged into a global stiffness matrix.

This global stiffness matrix now releates forces at each node with a displacements in x and y. Ordinarily I would then use this as a simple method to calulate displacements/stresses in a framework.

Ok, so this is where I get confused.

In my example I have 3 elements with 2 possible displacements at each node. This gives a 6x6 stiffness matrix for the frame.

So calculating f=sqrt(eig(K*inv(m)), gives 6 numbers.

Are these numbers the 1st 6 frequencies of the framework, or the modal frequencies in x and y for each truss? Or have I calulated the wrong stiffness matrix?

Thanks,

 

[skeleton]

Your document wrote:
A=10mm dia bar (Area of strut)

Truss members would area, not diameter. So,
A = pi/4*dia^2 = 78 mm2

For structural steel,
Young's modulus: E = 200 GPa,
Shear modulus: G = 77 GPa

You wrote E=74 GPa. Your value is close to G, not E, of steel. Is that what you wanted?

The above two numerical changes would not change the "mechanics" of the equations, only the resulting values.

If you send me your MATLAB file then I'll look at it in answering your primary question.

 

[jackcolebrook]

Hi Skeleton

Apologies, should have been more clear on the document, my writing is terible!

74GPa is the young's modulas of Aluminum and area was based on a 10mm dia bar.

Attached are my MATLAB files. DSM01 set up the problem, truss2d returns a mass and stiffness matrix for a given element in global co-ordinates.

Thanks for the help,

J