Deriving the frequency in a beam equation.

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Homework Help Overview

The discussion revolves around deriving the frequency in a beam equation, specifically involving parameters such as Young's Modulus, Moment of Inertia, mass, and length. The original poster presents an equation and expresses uncertainty about the next steps in the derivation process.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants suggest assuming a form of solution and using separation of variables. Others question the correctness of the presented equation and seek clarification on the setup of the beam, including its support conditions and mass distribution.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and attempting to clarify the original poster's assumptions. Some guidance has been offered regarding references to external materials, though the original poster indicates difficulty in applying the information from those resources.

Contextual Notes

There is a lack of clarity regarding the beam's support conditions and the definition of mass in the context of the problem. The original poster acknowledges an error in their equation, which adds to the complexity of the discussion.

kezzstar
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1. Deriving frequency in a beam equation, E=Young's Modulus, I = Moment of Inertia, m=mass, L=length, f=frequency.
2. Deriving this equation: (∏/2)√(EI/mL3)
3.(EI(∂4y/∂x4 = -m(∂2y/∂x2) ≈ EI(∂4y/∂x4+ m(∂2y/∂x2 = 0
Don't know where to go from here...
 
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Maybe assume a form of solution and use separation of variables?
 
The equation in (3) looks wrong. If it is supposed to be "force = mass x acceleration", where is the derivative with respect to time?

You haven't defined the problem clearly. If this is a beam of mass m, how is it fixed? Or is it a cantilever beam (assumed to have no mass) with a mass m at the end?
 
supported at each end. m in the equation is the mass of the beam itself. Yeah 3. is wrong, just found that too. Argh I'm stumped...
 
kezzstar said:
supported at each end. m in the equation is the mass of the beam itself. Yeah 3. is wrong, just found that too. Argh I'm stumped...
See this reference: http://www.mcise.uri.edu/sadd/mce565/Ch5.pdf
 
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Chestermiller said:
See this reference: http://www.mcise.uri.edu/sadd/mce565/Ch5.pdf

Thanks for the reply. Checked that website and still no further forward.
 
kezzstar said:
Thanks for the reply. Checked that website and still no further forward.
The website gives you the exact equation you need to solve and the method of solution. What specifically are you not able to follow about the development in the reference. It's hard to help without knowing specifically what the stumbling block is.

chet
 
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Chestermiller said:
The website gives you the exact equation you need to solve and the method of solution. What specifically are you not able to follow about the development in the reference. It's hard to help without knowing specifically what the stumbling block is.

chet

Where abouts in the text am I looking?
 
kezzstar said:
Where abouts in the text am I looking?
Pages 5.1 through 5.8. Eqn. 5.5 with w = 0 is the equation you are supposed to be solving.

Chet
 
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