×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Timoshenko Beam Theory

Timoshenko Beam Theory

Timoshenko Beam Theory

(OP)
Does anyone have a good reference for solving Timoshenko Beam Theory?

RE: Timoshenko Beam Theory

Er, Timoshenko?

RE: Timoshenko Beam Theory

Sorry, to be more precise:  Theory of Elasticity by Stephen P. Timoshenko and J.N. Goodier

Various versions/editions available, typically used.  See Amazon.com

RE: Timoshenko Beam Theory

What do you want to do with it?  That would really help.  If you are just interested in capturing shear deformations (and not so interested in the non-neglect of rotary inertia of differential elements), then just see the virtual forces part of any classical structural analysis book.

RE: Timoshenko Beam Theory

(OP)
Sorry to be vague.  What I am after is the time response of a beam after given an input.  I have the 2 PDEs, but am having trouble solving for them in finite form (been a while since my last PDE class).

RE: Timoshenko Beam Theory

Sorry, no help from here then.  My vibrations book has the solution for beams, but it neglects shear deformations and rotary inertia of the differential element.  I assume you've taken those into account and your PDEs somehow can't be solved using the typical separation of variables route.  What PDEs are you coming up with?  Perhaps if you can post them, I can find a solution in one of my books.  I have Timoshenko's book and a math book that is often very helpful for problems like this.

RE: Timoshenko Beam Theory

Do you need help finding the modes (eigenvectors) and frequencies (eigenvalues)?  

Or how to use that info to find time-domain response for a given input disturbance?

Somehow, I was given a link to the following paper, which gives the solutions for Timoshenko beams in all of the classical end-fixity conditions:

DYNAMICS OF TRANSVERSELY VIBRATING BEAMS USING FOUR ENGINEERING THEORIES, SEON M. HAN, HAYM BENAROYA AND TIMOTHY WEI, Mechanical and Aerospace Engineering, Rutgers, the State University of New Jersey,
Journal of Sound and Vibration (1999) 225(5), 935-988
Article No. jsvi.1999.2257, available online at http://www.idealibrary.com

I can't get to the link anymore, but you may find other web access to the above article, or could find it at a local university engineering library.

RE: Timoshenko Beam Theory

(OP)
Thanks for your help everyone.  After muttering over this with a couple co-workers I think we have come to a closed-form solution (quite lengthy!).

RE: Timoshenko Beam Theory

If you still need help try this:

Wave Motion in Elastic Solids By Karl F. Graff

Check out page 180 or so.

RE: Timoshenko Beam Theory

of course the solution is manageable, it is only the undetermined constants that cause the grief...



Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources