modes & its significance

[kk10CAE]

What is mean by modes & its significance in structural analysis?
why i need to perform mode based structural analysis?

 

[csk62]

A) eigenvectors - eigenmodes - modes/ mode shapes

B) mode based methods significantly reduce the computational effort, due to uncoupling/orthogonality

 

[msquared48]

A structure will go through several standard deflected shape patterns, where each shape is characteristic of a certain natural frequency of that particular structure.

Mike McCann, PE, SE (WA)

 

[kk10CAE]

Thanks for your replies

@csk62- mathematically modes means eigenvectors but what is its physical meaning. Imaginary of stiffness & mass distribution in the entire structure is my interpretation of modes.How it will reduce computational costs?

@msquared48- If my excitation has same frequency as natural frequency of the structure also direction of application is same as mode shape then it will leads to resonance & uncontrolled vibration will occur so whether direct frequency analysis without considering modes is senseless?

Once againg thanks for spare your time, please through some light on above mentioned queries.
Regards
Krishna

 

[rob768]

Knowing modes shapes will help in determing if a natural frequency will create a problem due to resonance, if excitation source (frequency and direction) is known. Also, if a problem exists, knowing the mode of vibration will help you find a solution, for instance the maximum effect of an added stiffener or alteration of overall stiffness or mass distribution.

 

[kk10CAE]

@rob768- Thanks rob. Yes, you are right idetifing mode shapes & natural frequency will help us to avoid resonance. I want to know the physical meaning of modes.

 

[electricpete]

Each mode has a shape and a frequency.

The free (unforced) motion of a linear system can always be descrigbed as a linear combination of its modes. That is a pretty basic physical significance of a mode. It describes the way the system vibrates when no external forcing remains.

While above paragraph focused on free behavior, these same modes are remarkably helpful for predicting forced behavior.

Additionally a modal model of a system provides more physical insight than other models for example state space model. (knowing the frequencies and modeshapes we can often qualitatively guess the responses much better than if we knew the state space coefficients… example: you said yourself a system will have high vibration near resonance).


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(2B)+(2B)' ?

 

[csk62]

@csk62- mathematically modes means eigenvectors but what is its physical meaning. Imaginary of stiffness & mass distribution in the entire structure is my interpretation of modes.How it will reduce computational costs?

A) I would say the physical meaning of a mode is the displacement behaviour of the structure at a particular natural frequency. Modes are usually normalized by disp when showing a plot, for ease of understanding. I believe they need to be mass normalized to calculate participation factors (how much each mode participates).

B) As electric pete mentioned, any system can be described as a linear combination of its modes. If we say that 90% of the structure can be represented by a reduced number of modes (say three for example), then you can accurately estimate forced analyses using only these three modes, since the remaining modes are less important. Analyzing the structure by using just these three modes will probably be much more practical computationally than a time-marching solution for the entire structure.


Aside:
One professor once told me: Never say "N factorial", just scream "N" at the top of your lungs.

 

[Tmoose]

if I have an idea of the requencies of the forcing functions that may exist, and some may be higher than the first three, I increase the range of the solution to include them.

It is embarrasing to design a housing with a large panel eager to sing a song at gear mesh frequency.

 

[csk62]

@Tmoose

Good Point. The rule of thumb the good people at Abaqus told me was that the maximum frequency extraction range should be twice the maximum frequency sweep range in SSD. (if you want to do a sweep from 50-100Hz, you should probably extract all eigenvalues between 50-200Hz)

 

[IRstuff]

A mode describes how a system is actually resonating at a particular resonance frequency. Wikipedia has a some good GIFs of different vibration modes of a membrane:

http://commons.wikimedia.org/wiki/Category:Drum_vibration_animations

here are a couple:

TTFN
faq731-376

Need help writing a question or understanding a reply? forum1529

Of course I can. I can do anything. I can do absolutely anything. I'm an expert!

 

[electricpete]

If my excitation has same frequency as natural frequency of the structure also direction of application is same as mode shape then it will leads to resonance & uncontrolled vibration will occur so whether direct frequency analysis without considering modes is senseless?

If you don't know the modeshape, you don't have the whole picture. It may be that a system excited near resonant frequency will not vibrate excessively if the spatial distribution of of the exciting force compared to the modeshape.

Example look at the two modes in IRStuff's link.
One the left is the first natural frequency.
On the right is the 2nd natural frequency.
If you were to apply that excitation at that 2nd natural frequency but located spatially at the exact middle of the disk, then you would not excite the resonance. The reason is that you are applying excitation at the node of the 2nd mode.
So it is not just relationship between excitation frequency and system mode frequency that leads to resonance response, it is also relationship between excitation spatial distribution and system mode shape.


=====================================
(2B)+(2B)' ?

 

[Tmoose]

Or, an anti-node at a mode of interest is a pretty good place to apply a stiffener or damper.

Those new Koni shocks sitting in their boxes on the back seat can not contribute much to wheel control.