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

Mindlin-Herrmann Rod Theory

Mindlin-Herrmann Rod Theory

Mindlin-Herrmann Rod Theory


I don’t know if this is the right forum for this……but we’ve discussed elastic wave propagation theory here in the past and it wasn’t a issue. Lately I’ve been reading this text on wave propagation that discussed the Mindlin-Herrmann Rod Theory. This theory predicts transverse motions from longitudinal waves (due to Poisson’s ratio). But reading this theory……it appears that the wave is dilatational, i.e. there is no net motion laterally.

For those of you familiar with this theory…..is that accurate or am I misunderstanding something?

RE: Mindlin-Herrmann Rod Theory

Never heard this - I spent time doing research on waves so here is a small summary of my conclusions from this research :).

The full set of modes that can propagate in a finite structure are given by the superposition of the fundamental longitudinal and transverse waves (in infinite domain).

With finite boundaries we get (due to reflections) Lamb Waves - this can be for plates and then also for cylinders. In plates these are the Symmetric (S modes - S0 is a longitudinal type of mode) and Anti symmetric (A modes - A0 is a bending mode), similar theory and names are given for waves in cylindrical structure. I would suggest books on wave motion by Graaf and Achnebach if you are interested.

The motion you mention is a longitudinal mode or a quasi-long. mode (e.g., S0) which will as you say due to Poisson's effect have a contract/expansion of the cross section, but the wave is a longitudinal type of wave (S0 type, thus the main in plane displacements are in the same direction as the wave propagation along the rod), and not a bending wave where the main disp. is transverse to the wave propagation direction.

This is a video if this:

RE: Mindlin-Herrmann Rod Theory

Thanks Erik.

RE: Mindlin-Herrmann Rod Theory

Glad to help - good to be able to share this and perhaps help a bit otherwise it sits there for nothing taking up space (have not used this for 10 over years) :).

RE: Mindlin-Herrmann Rod Theory

One thing that occurred to me today: since the strains developed under compression and tension (in steel for example) are typically not identical (and since this lateral displacement under these longitudinal waves is proportional to longitudinal strains)......I would think a net effect would develop along the length of a rod that would give a net lateral displacement.

Food for thought.

RE: Mindlin-Herrmann Rod Theory

Ok, I think I've figured this out: There is no net lateral motion via this theory. Looking at one of the texts you mention ('Wave Motion in Elastic Solids', by; Graff, p.511), it appears it is a pure dilatational wave.

Ergo, lateral vibration should be expected only when the equations of motion take into account initial imperfections, other (antisymmetric) wave types (including those from boundary reflections), etc.

In other words what you said was quite right Erik. Thanks again.

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! Already a Member? Login


White Paper - How ESI is Helping Move New Medical Device Product to Market Quicker & More Cost Effic
Early Supplier Involvement has long been a strategy employed by manufacturers to produce innovative products. Now, it almost seems like a necessity. Because decisions made in the design phase can positively affect product quality and costs, this can help add value to OEM bottom lines. This white paper will discuss many facets of ESI, including why it’s so valuable today, what challenges limit the benefits of ESI, how cost is impacted, and more. Download Now
White Paper - Moving to a Driverless Future
This white paper describes what we see as the best practices to support a sustainable engineering process for autonomous vehicle design. It exposes how to use simulation and testing in common frameworks to enable design exploration, verification and validation for the development of autonomous cars at a system, software and full-vehicle level to drive a mature product development process for automated driving. Download Now
Research Report - How Engineers are Using Remote Access
Remote access enables engineers to work from anywhere provided they have an internet connection. We surveyed our audience of engineers, designers and product managers to learn how they use remote access within their organizations. We wanted to know which industries have adopted remote access, which software they are using, and what features matter most. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close