Timoshenko Beam Theory Part 3 of 3: Equations of Motion
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- Опубликовано: 7 июл 2024
- Deriving the equations of motion for a Timoshenko beam,An introduction and discussion of the background to Timoshenko Beam Theory. Includes a brief history on beam theory and Stephen Timoshenko's accomplishments as well as a discussion of shear modeling.
A detailed derivation of the kinetic energy of a beam can be found in this video:
• Kinetic and Strain Ene...
Download notes for THIS video HERE: bit.ly/3Zi9tG0
Download notes for my other videos: bit.ly/37OH9lX
Reference: Dym & Shames, Solid Mechanics: A Variational Approach
amzn.to/468WkBp
CHAPTERS:
0:00 Continuing
0:40 Hamilton's Principle
4:46 Equations of Motion
6:03 Moment & Shear Force
11:39 Uniform Beam
14:38 Solving the Equations of Motion
16:47 Final Form
19:15 Summary & Review
This series is amazing (symptomatic of the channel as a whole i guess).
Quick note. Maybe I missed something, but shouldn't the boundary terms in eqn 25 be negative and included to the integrand of the time integral? They arise from the IBP and are positive eqn 17, then subtracted on the second (strain energy) integrand in the Hamiltonian Principle from eqn 9. Shouldn't they therefore carry the minus sign?
Thank you so much for the outstanding work.
Yes, the sign of the last 2 terms of eqn 25 should both be negative (careless error), however, since we're setting each of these terms to zero, it makes no difference in the final analysis and yes these terms should be part of the integrand of the time integral (the dt should be on the line below). Thanks for catching that.
I have just finished watching all 3 videos and took many notes. I am looking forward to next lessons.
Your explanation is awesome! Thank you very much
Ufff that was intense. Thanks for this miniseries
My pleasure!
It was amazing and very clear. Thanks!
Glad it helped!
Bravo!
Really enjoyed the little series, are you also planning on covering a higher-order beam theory like the Reddy-Bickford theory?
I will add this to my To Do list.
I've never heard of Reddy-Bickford! I'd be interested in another mini-series on it!
I found your videos really useful! Could you make a video on the deriving equations for the bifilar pendulum? I don't really understand this, and I have an exam on this coming up and would really appreciate a little help! Thanks!
I can take a look at this, but it might take me a little while.
Is there any other video that shows the Eq 46 applied for any simple example? Tube of diameter equal to length, fixed one end and point load on opposite end? Thanks!
I don't currently have a video showing an example of this. Will add it to my To Do list.
can you please do a video on deriving stiffness matrix of a timo beam with warping in it?
I'll have to add this to my ToDo list. Will need to make some videos that deal with warping first.
can someone tell me what the Timoshenko Beam Theory calculâtes or the objectif of It
i know That it's for short and Stif beams but what are we after ?
The Timoshenko beam model includes the effects of shear which become increasingly important as the beam gets shorter and thicker (ie less slender).
All your videos are excellent. Is that a New Zealand accent?
Grew up in South Africa.