Beam With Mixed (Non-Classical) Boundary Conditions

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Beam With Mixed (Non-Classical) Boundary Conditions

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Good Vibrations with Freeball

Күн бұрын

Пікірлер: 22

@mByyurt 8 ай бұрын

INTEGRATION BY PARTS! had to say that.

@mcastanonf 5 ай бұрын

Nice having you back I have run many of your excercices I would like to have a video solving vibrations for tapered shaft rotating with 2 symmetric loads at center and cantilever load as the gearbox to modelate a pulley shaft Is it possible?

@Freeball99 5 ай бұрын

I can add it to my To Do list, but this will likely take some time. Probably requires more than one video.

@sohampinemath1086 Жыл бұрын

Sir why did you stop uploading?, your videos are gold

@Freeball99 Жыл бұрын

New ones coming soon. Busy putting the final touches on my series on Timoshenko Beam Theory (3 parts). Will be out soon. If you subscribe to the channel, you'll be notified upon release.

@spazmoidectomorf6209 Жыл бұрын

Hello there, I've been watching all you videos on variational calculus and am keen to tackle some problems myself. Could you recommend any nice books or books which have questions and solutions? Thanks on advance

@Freeball99 Жыл бұрын

Take a look at Solid Mechanics: A Variational Approach by Dym & Shames. It doesn't contain solutions, but you can probably find a solutions manual for it somewhere online.

@wernhervonbraun4222 9 ай бұрын

You are godsend! Can you please guide me on how to do the same with a Timoshenko beam? And how to find the natural frequency of the system? Thanks!

@Freeball99 9 ай бұрын

I'll add it to my to-do list.

@HAN_Dynamic Жыл бұрын

Hi, What would it be like if we added TMD to this system? In addition, if the position of the TMD was variable, what would be its effect on damping the vibration in the system?

@Freeball99 Жыл бұрын

This is a very general question. I don't know that I can answer it entirely without using any equations... In order to add the TMD to the tip, I would attach the tip spring to a mass instead of the ground. This mass would have its own displacement coordinate. The effects of the tip mass would then be added to the kinetic energy for the system and then the equations of motion can be generated. For an arbitrary placement of the TMD along the span of the beam, this will require breaking the problem into two separate pieces (domains) since the TMD will produce a discontinuity in the shear force in the beam at that point. The solution to the problem is then divided into two separate piece-wise solutions and continuity conditions are applied to the boundary between the two solutions. I haven't worked a problem like this yet (where we need to split solution into two domains), but will be making a video on this soon.

@mByyurt 8 ай бұрын

Here is a question: do we need to solve the eqn of motion by imposing the boundary conditions to get the frequency of the system? [also, if so, how? numerically?] If I had a single dof system K and M would yield the frequency. Boundary conditions would be implicitly included in the eqn of motion. Think of a masless column with a lumped mass at the top. then we would have k=3EI/L. the boundary condition is already inside the stiffness. Here it is a bit confusing because there are stiffness and mass values in the boundary conditions. That means if I were to use the eqn of motion given in this video to get a frequency, I would end up with something irrelevant because I miss the spring and the mass at the end I know this is not a sdof system but a continuous system meaning it has infinite frequency modes. But I was curious if we can somehow go to the major frency modes aside from spatial discretization and calculating stiffness and mass matrices. Similar to what we do in rayleighs quotient. anyway, I got covid last week and had to stay home. discovered the channel around Wednesday and been watching this play list ever since. great stuff. thanks for sharing.

@Freeball99 8 ай бұрын

If you replace the beam with an equivalent mass and and equivalent spring, as you have suggested, then you can turn it into a single degree of freedom system as you have suggested. The natural frequency for the equivalent system will be the same as the fundamental frequency of the original system. So, if all you were interested in finding was the fundamental frequency, then you could use this method. However, if any of the higher modes were important to the problem you're studying, then you'd have to use the beam equation and substitute the boundary conditions.

@mcastanonf 4 ай бұрын

Sr, about a beam supported in three points of it, can we run one of those please?

@Freeball99 4 ай бұрын

Good suggestion. I will add it to my To Do list.

@hesammortazavi9371 4 ай бұрын

Thank you very much. could you please introduce me a reference to find why the boundary terms (in integral by part) are zero? I did not find anywhere, I mean I understand either force or displacement have to be zero but you mentioned many times there is another reason that it must be zero anyway.

@Freeball99 4 ай бұрын

Dym & Shames, "Solid Mechanics: A Variational Approach". Take a look at sections 2.3 & 2.9

@hesammortazavi9371 4 ай бұрын

@@Freeball99 great, thank you