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Rahul Ponginan

How do we interpret Normal Modal Analysis results?

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Sir,
I never understood the significance of modal analysis. I know the
theory of resonance that whenever actuating frequency matches the
natural frequency of the body, it starts vibrating with maximum
amplitude. I edited the card edit panel with V1= 1.00 and V2=200.00
and ND=10 as per our webinar videos. But what ND=10 actually
interpret?
Also in the result panel, on left side in results tab, under `subcase`
toggle option, where we can change different modes by toggling
up-down, I`m getting different values e.g. it shows for mode 2,
F=97.65 and in model view `Staic Max. value`= 28.662.

What do this `F=97.65` and` Static Max=28.662` indicate?

I `m giving you this particular case through which I think I `ll be cleared more easily.

Thank You.
wd05j-Modal-Analysis-query.png

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Hi,


-->Modal analysis determines the mode shapes (vibration shapes) and frequencies for that particular mode shape of a structure for a free vibration analysis.


-->ND defines the root numbers or mode shapes that should be known starting from V1 frequency till v2 frequency


--> the F which you are seeing is the frequency of the strucutre for that particular mode (in your case it is the 3rd mode)


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I`m sorry sir,
I`m still not getting.
How the mode shape or the corresponding frequency is determined?
And if the F indicates the natural frequency (does it?) then what the static max value in the graphic area represent?
What should be the criteria to check our structures safety?

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the governing equation for free-free (normal) modal analysis is dependent on mass and stiffness of the structure.


Eigenvalues are calculated based on these parameters and corresponding vectors are calculated based on the eigevalues (these vectors are also called as eigenvectors)


From this Eigenvalue the frequency is caculated and the frequency is directly proportional to this value.


The static value is the static displacement (relative displacement) and it is recommended not to reply on these displacement values.


it is important to know these frequencies. for instance if the loads are applied on the structure whose natural frequency matches with the applied load frequency, this will result in resonance and thus failure in the structure


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Soumitra,

Did you see Altair OptiStruct > User's Guide > Structural Finite Element Analysis > Solution Sequences:
Normal Modes Analysis

Normal Modes Analysis, also called eigenvalue analysis or eigenvalue extraction, is a technique used to calculate the vibration shapes and associated frequencies that a structure will exhibit. It is important to know these frequencies because if cyclic loads are applied at these frequencies, the structure can go into a resonance condition that will lead to catastrophic failure. It is also important to know the shapes in order to make sure that loads are not applied at points that will cause the resonance condition.

I would say, the mode shapes are useful because they represent the shape that the object will vibrate in free motion, you can then design accordingly so that nothing obstruct this object etc i.e. the neighboring components can be of such a shape as to not get in the way of this shape.

 

Perhaps you will be interested in learning (from textbooks, library , internet etc) about mode shapes and also ODS (operating deflection shape), I think mode shape cannot be given any displacement value or any number, however just like the mode (natural frequency) of an object, the shape of vibration is unique, the relative motion of one point in the resonating object with another is unique and this information helps us design better.

Rahul

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2 hours ago, KALIMUTHU said:

hi

Am a beginner Any give the answer, what is Eigenvalue? and how its used in normal mode analysis?

 

 

Hi,

in algebra math, with a given square matrix A, and a vector V not equal zero

if you found a value "e" satisfy:

 

A.V = e.V  => then "e" call eigen value. a matrix may have some "e" values

 

math meaning of "e" is essence of matrix A, if A has one eigen value equal 0 => rank of A is down and its determination is 0 (not invertible)

 

also, vector V is a special vector, that do not change direction when transformed by matrix A, called eigen vector

 

 

In normal mode, below problem is solved:  M.x'' + K.x = 0   or  M.x'' = -K.x

x'' proportional to x, mean:    M.e.x = -K.x or  K.(1/M).x = -e.x

K.(1/M) is matrix A, so "-e" is eigenvalue of A

 

x = V.sin(wt+phi) => x'' = -w².x

 

so "e" is w²

 

w is called eigen frequency, but not eigen value of matrix A  K.(1/M)

 

 

 

 

 

 

 

 

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The natural frequencies of a structure are the frequencies at which the structure naturally tends to vibrate if it is subjected to a disturbance. The deformed shape of the structure at a specific natural frequency of vibration is  termed its normal mode of vibration. The other term to represent normal mode is mode shape.Each mode shape is associated with a natural frequency.  In many engineering applications, the natural frequencies of vibration are of interest. This is probably the most common type of dynamic analysis and is referred to as an ‘eigenvalue analysis’. In addition to the frequencies, the mode shapes of vibration which arise at the natural frequencies are also of interest.

If the displacement vector {D} has the form {D} = {A}sin(wt) and from this the velocity and acceleration vector can be derived and substituting these into the general equation of motion yields the eigenvalue equation, ([K] - X[M]){A} = {0} and X is eigenvalue which is w2 ( w is the frequency of vibration ). The total number of eigenvalues or natural frequencies is equal to the total number of degrees of freedom in the model. Each eigenvalue or frequency has a corresponding eigenvector or mode shape  

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Hello Experts,

 

I have done a normal modes analysis. I am looking for my first frequency and it looks as I had expected it to be (meeting the target). My problem is, the mode shape I have for that frequency is pretty distorted.

1. Such huge deformation at the right expected frequency is looking weird to me. Am I doing something wrong?

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I have 3D tets and 1D elements in my model with an average mesh size of 2 for all the parts. All my 3D elements are 2nd order elements with FREEZE type of contacts wherever it was necessary.

 

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