Measuring the deflection of a beam

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Discussion Overview

The discussion revolves around the normalization of a set of 2-D data representing the deflection of a beam, specifically focusing on transforming Y values to achieve zero endpoints at X=±200. Participants explore the mathematical and graphical implications of this transformation, as well as its connection to beam deflection theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks guidance on normalizing Y values in a dataset to achieve specific boundary conditions at X=±200, indicating a lack of familiarity with the required transformations.
  • Another participant questions the graphical representation of the data and the meaning of having Y values equal to zero at the specified X values, prompting further clarification.
  • A participant suggests that simply setting all Y values to zero would not achieve the desired outcome and asks for the purpose of the transformation.
  • One participant explains that the transformation is necessary to match the boundary conditions derived from a differential equation related to beam deflection.
  • Concerns are raised about the compatibility of the measured displacement values with the expected zero slope at the endpoints, suggesting potential measurement errors.
  • Another participant proposes that a 2D conformal transformation might be applicable, while also noting that a zero offset could be achieved by subtracting a constant from the Y values.
  • Discussion includes the idea that there are infinite mathematical transformations, but not all will accurately reflect the beam deflection, emphasizing the importance of maintaining the shape of the data.
  • One participant expresses uncertainty about whether the transformation can maintain the same shape while meeting the boundary conditions.
  • Another participant mentions successfully applying a rotation and linear transformation to the data, although they did not have time to assess the results fully.
  • Questions arise regarding the specifics of the equation derived from the beam theory and how it relates to the measured data.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility and implications of the proposed transformations. There is no consensus on the best approach to achieve the desired normalization of the data, and several competing perspectives on the underlying theory and practical application remain unresolved.

Contextual Notes

Participants note the potential for measurement errors and the need for clarity on the relationship between the measured values and the theoretical model. The discussion highlights the complexity of transforming data while preserving its integrity and the challenges posed by the specific boundary conditions.

Who May Find This Useful

Individuals interested in data normalization techniques, beam deflection theory, and those working with experimental data in engineering contexts may find this discussion relevant.

saybrook1
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Hi guys, I have a set of 2-D data in excel, an X and Y column. The X column ranges from ±200 and the Y column is a Gaussian distribution ranging from about 6 to 12. In total there are about 500 data points. I need to normalize the data so that the Y column values have endpoints at 0 for X=±200. I know this requires a rotation of the data or a linear transformation but I'm really pretty foreign to that process. If anyone could point me in the direction of being able to do this either on paper or within excel or other software, I would really appreciate it. Please let me know if you need any more information or pictures. Thanks!
 
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saybrook1 said:
so that the Y column values have endpoints at 0 for X=±200
What does that mean?
How would that look graphically?
 
mfb said:
What does that mean?
How would that look graphically?
What I mean is that Y currently has values at approximately 6.7 and 6.8 at X=±200. Since I need the values of Y to be zero at X=±200, I believe that I need to transform/rotate the entire set of data in order to keep the shape/integrity. Did this clear it up at all? I can try to explain further or attach a graph of what I mean if that helps. Thanks for the quick reply.
 
Well, set all Y values to zero, and you achieved your goal. I'm sure that is not what you want. Which brings me back to the question: What do you want to do? What is the purpose of the transformation you are looking for? What should it preserve, what can it change, and how exactly do the Y values have to be zero "at X=+-200" (given that you have a discrete dataset)?
 
mfb said:
Well, set all Y values to zero, and you achieved your goal. I'm sure that is not what you want. Which brings me back to the question: What do you want to do? What is the purpose of the transformation you are looking for? What should it preserve, what can it change, and how exactly do the Y values have to be zero "at X=+-200" (given that you have a discrete dataset)?

Okay, right, so the Y values(slope/displacement) need to be zero at the endpoints of +- a given length(say L) because I am trying to reproduce the curve based on an equation that I derived from a differential equation of a bent beam (Bernouilli-Euler eqn). In deriving the equation I set the boundaries to be zero at +-L/2. So in order to match the curve from the data to the curve that I'm producing from my closed-form equations, I need the boundary conditions of the data to be the same.

The data currently looks like the attached plot.
 

Attachments

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Do you think that this thread might be more appropriate elsewhere?
 
saybrook1 said:
The data currently looks like the attached plot.
Ah, that's not what I expected. I expected a Gaussian distribution of your y-values.

If those values are measured displacement values, then I don't see how they would be compatible with zero slope. You must have some weird source of measurement error that you have to identify first before you can correct it.
Zero offset is easy - subtract 6.8 from all values.

Let's try the mechanical engineering forum. This is first a question about measuring the deflection.
 
mfb said:
Ah, that's not what I expected. I expected a Gaussian distribution of your y-values.

If those values are measured displacement values, then I don't see how they would be compatible with zero slope. You must have some weird source of measurement error that you have to identify first before you can correct it.
Zero offset is easy - subtract 6.8 from all values.

Let's try the mechanical engineering forum. This is first a question about measuring the deflection.

I did some research and it looks like a 2D conformal transformation might work? I understand the subtraction will work to bring us down to zero but only for one point, they are not both at 6.8. Also, they won't be compatible with zero slope - it's the case that my equation contains variables for the moments C_1 and C_2 and I intend to make a small application that will find the best ratio of C_1 by C_2 to give the smallest slope error when combined with the data. There also shouldn't be a measurement error - it's from a really well put together FEA model - the asymmetry comes from an asymmetric heat load deposited on the beam. Let me know if you need more details.

Thanks a ton for your help; I'm really excited to make progress on this.
 
There is an infinite set of mathematical transformations that will work, but most of them won't accurately reflect your beam deflection.

If your models are really good, they shouldn't have a non-zero slope where you have exactly zero slope.
 
  • #10
mfb said:
There is an infinite set of mathematical transformations that will work, but most of them won't accurately reflect your beam deflection.

If your models are really good, they shouldn't have a non-zero slope where you have exactly zero slope.

Hmmm... are you saying that I can't rotate this data so that the endpoints respect my boundary conditions while maintaining the same shape? I'll attach a short derivation of the equation for deformation(y) with respect to beam/mirror length(x). I may not have explained it properly.
 

Attachments

  • #11
Currently the shape is parabola-like. The two ends point in different directions. You cannot make them point in the same direction (well, 180° apart) without changing the shape.
 
  • #12
mfb said:
Currently the shape is parabola-like. The two ends point in different directions. You cannot make them point in the same direction (well, 180° apart) without changing the shape.

Okay, right; I don't want them to point in the same direction, it's just that one end is slightly lower than the other so after a linear translation, I should be able to rotate them a bit so that the ends are at y=0 for x=±L/2. I guess the x-coordinates will transform as well in this case. I understand that once I add the my own analytical(and opposite) curve, I will not be able to get it completely flat.
 
  • #13
I still don't see the physical motivation behind it, and how you expect anything useful from transforming the parabola to a shape that has to look completely different.
 
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  • #14
I'm just leaving the place where I have that data and forgot to put it on the web although I think I figured it out. I just did a rotation and a linear transformation on both sets of coordinates which I got from defining a new origin where the endpoints equal zero. The shape appeared the same although I didn't have time to properly see how much different it is. I know people have done this sort of thing before in this type of application. If you'd like, I can explain it to you in more detail on Tuesday. I really appreciate your help/input today.
 
  • #15
saybrook1 said:
the Y values(slope/displacement) need to be zero at the endpoints of +- a given length(say L) because I am trying to reproduce the curve based on an equation that I derived from a differential equation of a bent beam (Bernouilli-Euler eqn).

Your question is too vague.

What specifically is the equation?

How do the variables in the equation relate to the measured values of X and Y?

(Presumably the measured values of X and Y are not exactly the same quantities as the variables in the equation since you are looking for some way to modify the measured values so they fit the variables in the equation.)
 
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  • #16
I may be waaay of the mark, but this looks like you are taking the data from a LIDAR and are trying to normalize it's values into usable distance data?
 

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