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# Experimentale Modal Analysis Results Interpretation?

04/11/2017 3:48 AM

Hello everyone,

Is it possible to estimate the stiffness properties of a system knowing that all we have as input isthe mass of the system and accelerations mesured by accelerometres at 3 points.

thank you.

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#1

### Re: experimentale Modal Analysis results interpretation?

04/11/2017 4:33 AM

Probably not; you would need to know the forces involved.

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#2

### Re: experimentale Modal Analysis results interpretation?

04/11/2017 9:00 AM

I don't know what background you have and whats the reason you would study finite element.

Yes if it has to be vertically constrained with its weight on it.

Begin with the equation of force =mg equate this with the force of a spring. F=-kx

You sounded like a psychiatrist though.

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#9

### Re: experimentale Modal Analysis results interpretation?

04/12/2017 4:34 AM

yes but the problem is that i'm trying to calculate radial stiffness

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#11

### Re: experimentale Modal Analysis results interpretation?

04/12/2017 6:17 AM

O, there are lots of reference on the world wide web. Here are some. Have some good read, alright?

So what's your set up? Do you have a sketch?

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#3

### Re: experimentale Modal Analysis results interpretation?

04/11/2017 10:09 AM
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#4

### Re: Experimentale Modal Analysis Results Interpretation?

04/11/2017 10:30 AM

stiffness is defined as

k = F/γ, where k is stiffness (basically the Hooke's law constant), F is Force applied, and γ is the displacement.

So please do tell me how you can get that from masses and accelerations, without measuring displacement. If you can, then you are performing miracles.

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#5

### Re: Experimentale Modal Analysis Results Interpretation?

04/11/2017 1:44 PM

You can get there without being told force or displacement explicitly.

You would have to know the distribution of mass, not merely the magnitude.

The accelerations would need to be nonzero.

The forces applied to obtain the accelerations must not act uniformly on the structure...one point would be best.

The using the known mass and the indications of acceleration, you can get force.

Using indications of acceleration at three points, you can get relative displacement.

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#6

### Re: Experimentale Modal Analysis Results Interpretation?

04/11/2017 2:15 PM

I suppose you are correct in that the displacement function is the second time integral of the acceleration equations. That is strictly because we can impose the boundary condition of γ=0 at all three points at t=0, right?

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#7

### Re: Experimentale Modal Analysis Results Interpretation?

04/11/2017 4:19 PM

Yeah.

As long as stress remains below the proportional limit, arbitrarily assigning a zero point for displacement shouldn't be a problem, even with some stress(therefore strain) in the original static condition....as long as that component of stress isn't meaningfully altered during measurement/application of force.

Of course, if the response is nonlinear and not otherwise well modeled, all bets are off.

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#8

### Re: Experimentale Modal Analysis Results Interpretation?

04/11/2017 4:25 PM

Then OP should have his answer: Move along now, nothing to see here, except my blood trail as I limp off wounded into the foggy distance.

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#10

### Re: Experimentale Modal Analysis Results Interpretation?

04/12/2017 4:36 AM

truth is not a compromise

but how i get mass destrubution, PS i'm a noob in experimental analysis, i don't know the tricks

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#12

### Re: Experimentale Modal Analysis Results Interpretation?

04/12/2017 11:52 AM

Measure.

Use a few scales to support the structure at points. Reposition the piece and measure at three more support points. Repeat.

Then consider the density of the material and the physical dimensions of the piece. Calculate a distribution of mass and check how closely it matches the measurements you have taken.

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#13

### Re: Experimentale Modal Analysis Results Interpretation?

04/12/2017 1:57 PM

If your system can be dropped suddenly, the force on the system will be 1 G. Your tri-axial accelerometer will then record the natural resonances of the system. You could then use modal analysis software to compute the LaPlace transform, obtaining the Frequencies, Mass, Stiffness, and Damping of each mode. A software program such as Star Modal (see Spectral Dynamics Corp) could be used to get these results.

You may need to use a load cell to actually measure the 1 G force in order to get a true frequency response function for the LaPlace curve fitting. Place it under the load; the release will un-compress it to generate a force signal.

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#16

### Re: Experimentale Modal Analysis Results Interpretation?

04/13/2017 2:24 PM

A few problems in your comment.

.

'...the force on the system will be 1 G...."

'1 G' describes an acceleration (due to gravity), not a force.

.

'...If your system can be dropped suddenly....'

Dropping suddenly or dropping slowly or even not dropping will have no meaningful effect on the force that brings about acceleration in freefall of 1 G....a force commonly described as weight.

.

One problem with trying to use just gravity and normal forces for this investigation is that gravity is distributed with mass. Without knowing something about the geometry, we can't know if it is feasible to support (and the drop) the item at a point that will cause displacement oriented usefully for determining stiffness in the desired dimension.

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#17

### Re: Experimentale Modal Analysis Results Interpretation?

04/14/2017 1:00 PM

A load cell placed directly under the CG would allow measurement of the 1 G force. Accelerometers have been calibrated by this method many times.

Since we have decided to use a load cell, a far more convenient way to get the data is to use a hammer with the load cell attached. The user would need to collect tri-ax acceleration data from many points on the structure after each hammer hit. This allows the test to be done "in situ". Software like Star Modal, or MODAMS can calculate the mode shapes, frequencies of resonance, damping, and phase of each mode.

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#14

### Re: Experimentale Modal Analysis Results Interpretation?

04/12/2017 6:55 PM

Yes, it is possible to ''WAG'' an estimate of most any physical thing...

The issue only gets more complicated as you want that estimate to be more and more accurate...

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#15

### Re: Experimentale Modal Analysis Results Interpretation?

04/13/2017 10:32 AM

That is why prototypes are "first-order approximations" in so many instances.

You build it, you run it, gather data, see what happens, and then learn how to correct or compensate the data so that the next operation of data collection is flat linear, etc.

OR you have something take down numbers, and then learn what affects the results mathematically, that are independent variables not isolated. Measure the independent variables separately, and compensate for their effects. Plain, simple, effective, Tylenol for physics.

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