×
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

Den Hartog: equivalence of angle/force and displacement/moment

Den Hartog: equivalence of angle/force and displacement/moment

Den Hartog: equivalence of angle/force and displacement/moment

(OP)
This is more a statics question than a vib question, but the context is Den Hartog's "Mechanical Vibrations", so I figure I'd try ask it here.

Page 261:

Quote:

Alpha12 is the angle theta at the disk from 1 lb force
Alpha12 is also the y at the disk from 1 in-lb moment.

Are these two quantities always the same? It seems like he's assuming they are.  Seems plausible that there is some kind of reciprocity/duality that causes this in a linear system.  There alpha's would be the off-diagnoal elements in a stiffness matrix K such that:
[Displacment, angle]' = K * [Force,moment]'

I'm a little foggy on the related question: Are stiffness matrices always symmetric for simple linear systems?

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

RE: Den Hartog: equivalence of angle/force and displacement/moment

Yes, any linear system has a symmetrical stiffness matrix and obeys reciprocity for force vs displacement and moment vs angle

M

--
Dr Michael F Platten

RE: Den Hartog: equivalence of angle/force and displacement/moment

(OP)
Thanks Mike.  

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

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