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





RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
arrogant
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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:
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
SUKEO KAWASffiMA.pdf
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
The C matrix, if it is not diagonal, changes the normal modes into complex modes.
Regards.
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
Regards.
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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 ...
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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.
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
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
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
Natural or Eigen frequency, it's not the point.
As an engineer or researcher, the only important thing is the relationship between mathematics (here linear algebra, matrix calculation and complex numbers) and physics or nature.
Why complex numbers are so well suitable for defining damping ?
Why the fact of diagonalizing a matrix is so well suitable for finding the natural frequencies of a structure ?
This is very mysterious and reflects all the strength (and so the beauty) of mathematics for describing vibration.
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
In practice it is worse than that, the frequency of maximum response is not only affected by the location(s) of the forces exciting it but also their amplitudes.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?
RE: Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF)
"Simplicity is the ultimate sophistication." L. da Vinci
- Gian