Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF) 2

[aouiche]

I m a new user of matlab and i have a question about how to obtain natural frequency and mode shape corresponding in the general case of system mass,sitiffness and viscous dumpinig (MDOF)

Example:

m=[40000 4000 0;0 30000 0;50000 0 20000];

c=[330 0 0;0 -8000 8000;0 -8000 8000];

k=[30000 -10000 0;-10000 20000 -10000;0 -10000 10000];

Thanks

 

[GregLocock]

c won't matter



Cheers

Greg Locock


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[aouiche]

shut your mouth
arrogant

 

[GregLocock]

...but right.

Cheers

Greg Locock


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[elogesh]

Hi aouiche,

Greg response is absolutely correct. Effect of damping on natural frequency(C won't matter) on practical structures is almost negligible....


damped natural frequency = undamped natural frequency* sqrt (1- damping ratio^2)

Think twice before commenting on others response....!

Logesh.E

 

[GregLocock]

If I might expand... you asked a question, and posted some irrelevant information. My conclusion was that you were entirely lost and therefore narrowing down your field of search would help. Your reply was quite incredibly rude, but taking a punt that you are a french speaker by choice, I ignored it. If you want me to be helpful I strongly suggest you lose the attitude and explain far better what you are trying to do and why the normal textbook approach didn't work. Alternatively, if you want a slanging match, I can do that too.




Cheers

Greg Locock


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[aouiche]

Sorry,for the misunderstanding and for ma bade language.
and i will try to explain my problem better:
I try to verify the experimental results (natural frequency of simple portale frame with semi rigid joint) obtained par SUKEO KAWASffiMA

 

[aouiche]

the first question:in the mass matrix the area A is not indicate in the doccument or in any other document I found in the net
second :My results are given in folder system ([M],[C],[K])
I use to resolve it this code RAJESKARAN(folder system)
but the results are not conform
Thanks to help

 

[aouiche]

sorry for the link
the new link containing the pdf (kawashima_dynamic experiment of portal frame) and ([M],[C],[K]) results finally the function Rajasteran
to obtain natural frequency all are in the folder in the link bellow:

 

[aouiche]

the link by item
SUKEO KAWASffiMA.pdf

 

[GregLocock]

Your links are mostly to files on your computer which we can't see. try uploading them using the attachment box just below the text box you type into.

Cheers

Greg Locock


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[amanuensis]

Actually, damping matrix has a role and even an important role on natural frequencies and modes shapes.

The C matrix, if it is not diagonal, changes the normal modes into complex modes.

Regards.

 

[aouiche]

yes i have a system where C(due to the viscous dumping in the joint) ,M (consistent e matrix) and K are not diagonal
Regards.

 

[amanuensis]

If damping is due to joints then you certainly gonna be in the presence of complex modes. It means that mode shapes will no longer be stationary waves with all points moving in phase or out of phase. The shape of the modes will evolve and change over time.

 

[GregLocock]

In that case you are going to have to define what you mean by " natural frequency and mode shape" since strictly speaking they aren't defined for that case. usually in engineering structures you can ignore the off diagonal terms.

Cheers

Greg Locock


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[aouiche]

Thanks for your answers

 

[amanuensis]

Natural frequency becomes complex : the real part reflects the oscillating motion as usual, but the imaginary part reflects the limited lifetime of the corresponding mode.

Mode shape has also an imaginary part and means that the mode is not a pure standing wave but also have a slight wave motion. The nodal points moves over time.

Actually, I think that nobody, and especially me, can really understand what complex modes are ...

 

[hacksaw]

The point raised by GL is that with damping you do not have true mode shapes or natural frequencies.

You can calculate the damped response (under forcing or initial conditions) using the mode shapes and natural frequencies.

 

[aouiche]

first i would like to verify the case where the joints are rigid in this case i get a free undeped system M(22,22)which is the sum off all consistent mass matrix of the structure.To obtain the natural frequency i uses this code:

Z=(inv(M))*K;
[V,D]=eig(Z);
Omega=(sqrt(diag(D)));
Freq=((Omega))/(2*pi);

I get Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 7.259337e-37
and the results are:

117,170734211211 + 0,00000000000000i
116,521653401816 + 0,00000000000000i
85,7477397600253 + 0,00000000000000i
84,6823425031470 + 0,00000000000000i
58,3180467468491 + 0,00000000000000i
56,7249257632524 + 0,00000000000000i
47,0648080171161 + 0,00000000000000i
37,0241025675458 + 0,00000000000000i
35,0297477617541 + 0,00000000000000i
29,9275737962262 + 0,00000000000000i
20,9725282351167 + 0,00000000000000i
18,8765032944196 + 0,00000000000000i
17,6881567071483 + 0,00000000000000i
11,5369555790805 + 0,00000000000000i
9,35018494595257 + 0,00000000000000i
8,67978551396229 + 0,00000000000000i
6,04021513571875 + 0,00000000000000i
3,40014895128681 + 0,00000000000000i
2,90681072742300 + 0,00000000000000i
2,17065617657641 + 0,00000000000000i
0,572290682070938 + 0,00000000000000i
0,00000000000000 + 4,07555137117127e-07i


but the frequency should be seem like this:

9.4
26.6
65.8
74 .9
100.4
173.1
220.2
232.7

 

[GregLocock]

Simplistically a natural frequency is a frequency where the amplitude is maximum for a given input.

However with off diaginal coupling you will find that the frequency of maximum response will vary depending on the point(s) of excitation, hence there is no such thing as a 'natural frequency' ofr the general case, you tend to get frequency bands where similar deflection shapes occur.

now, you can linearise the system in various ways and you'll have 'natural frequencies' for some of them.



Cheers

Greg Locock


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