Kinetic and Strain Energy for Common Structural Members

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Kinetic and Strain Energy for Common Structural Members

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Good Vibrations with Freeball

Күн бұрын

Пікірлер: 12

@moaqirahmad5948 3 жыл бұрын

seems like you we going for something big. this was basic but extraordinarily done. thank you very much

@miro.s 3 жыл бұрын

It is awesome!

@ziaee62 3 жыл бұрын

Everything is great, just in one part you mentioned that M=EI(W,xx)^2, I think that the square must be eliminated, M=EIW,xx

@Alliban59 Жыл бұрын

At 10:21 it should be M=EIw,xx (w,xx is not squared, it is just the second derivative) acc. to my understanding. The right side might be negative, depending on the orientation of the coordinate system. However, under the integral it is correct.

@Freeball99 Жыл бұрын

Correct. It should not be squared - this is a typo. The strain energy is what contains w, xx squared.

@chopinscriabin 3 ай бұрын

Does taking the variation of strain energy del U and kinetic energy del T, and plug to hamilton will result in equation of motion of Bernoulli beam in this case? I watched your Timoshenko part 2, and more or less that's what you did to result in equation of motion for Timoshenko beam. Then I was wondering if we can do the same for this simpler case for Bernoulli. Thank you

@Freeball99 2 ай бұрын

Yes, it is exactly the same. When deriving things in this video, I glossed over some of the formality in deriving it because I wanted to keep it simple, but then in the Timoshenko video, I wanted to lay it all out since I expect viewers of that video to be a little more familiar with the material. The only difference between the 2 theories is in the strain energies, since the strain energy for the Timoshenko beam includes shear and the EB beam does not. This is consistent with the EB assumption that cross-sections that are normal to the elastic axis before deformation remain normal to the elastic axis after deformation.

@chopinscriabin 2 ай бұрын

@@Freeball99 thank you for your reply. I found your video that actually did it (deriving Bernoulli equation of motion from Hamilton), so actually it already answered my original question. Thanks again anyway for explaining it again. Your videos are really awesome.

@hesammortazavi9371 4 ай бұрын

could somebody explain why we did not consider sigma21depsilon21 in flexural member?

@Freeball99 4 ай бұрын

I explained at 10:30 that for the case of an Euler-Bernouli beam (slender beam), the shear effects are negligible. However, in the case of shorter, stubbier beams, the shear effects become important in which case, we cannot use the Euler-Bernoulli Theory and must use the Timoshenko Beam Theory instead. That process is described here: kzfaq.info/get/bejne/or92qpaIl9qyY30.html

@hesammortazavi9371 4 ай бұрын

@@Freeball99 Thank you, understood