What is the difference between 'Uncoupled' vs. 'coupled' natural period in a MDOF system ? 1

[DimzK]

I have been trying to google this and I am getting some ideas, but if someone can explain this difference between coupled vs. uncoupled natural period in MDOF analysis for 3D models, that would be great. Just to add some context to this, I am trying to understand the seismic analysis of building and reading the below excerpt from a book:

 

[GregLocock]

In general mode shapes include a little bit in all 3 coordinates, at each response point. That may be what he means by coupling. It's not a great use of terminology, more generally modes are coupled when excitation at the resonant frequency of one mode causes some excitation of a mode shape with a different frequency, and of course, is used to understand responses at intermediate frequencies between the two.

Cheers

Greg Locock


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[chris3eb]

Uncoupled modes are completely orthogonal meaning that they don't share any component of movement (think perpendicular vectors).

You generally think of the fundamental modes as being the two modes with the largest periods. But you can have cases where the first few modes all have some component in the same direction before you get to one that is completely in the other direction - in which case, the fundamental modes would correspond to the largest period and the 4th or 5th largest period (for example).

 

[JoshPlumSE]

Well, I think of this as a difference between equivalent lateral force methods of seismic loading vs the response spectra method of seismic analysis.

When you have a "regular" structure with clearing defined and distinct orthogonal modes in each direction then you can use the equivalent lateral force methods. I'm specifically talking about the US codes / IBC. However, it is likely similar for the Euro Codes.

Now, the equivalent lateral force method falls apart when the first mode can't be solely counted on to really capture the seismic behavior. This may be due to modes that have components in both lateral directions... maybe due to torsional irregularity. This could be called coupling I suppose. Though I wouldn't personally use that term.

It could be also due to having multiple modes in one direction. You can get this when you have a mass or stiffness irregularity. Let's say you've got a braced frames at some levels and a portal frame at another. Then you wouldn't have a single mode in that direction that really represents the seismic response. I wouldn't really call this coupling.

Another thing you might have is interaction between modes with similar natural frequencies. Let's say the primary mode in the N-S direction is pretty close to in frequency to a E-W mode that has some torsional response. When they're closely spaced like that, the Response Spectra analysis must account for "modal coupling" when doing the statistical combination of the various individual modal responses.

 

[DimzK]

All, thank you for your response. I have some idea on it now! Cheers.