Deriving the frequency in a beam equation.

[kezzstar]

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...

 

[SteamKing]

Maybe assume a form of solution and use separation of variables?

 

[AlephZero]

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?

 

[kezzstar]

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...

 

[Chestermiller]

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

 

[kezzstar]

See this reference: http://www.mcise.uri.edu/sadd/mce565/Ch5.pdf

Thanks for the reply. Checked that website and still no further forward.

 

[Chestermiller]

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

 

[kezzstar]

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?

 

[Chestermiller]

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