Critical damping equation of rotational vibration

[J1D]

When calculating the damping ratio of rotational vibration of a concrete block foundation I realized that I am not sure the critical damping equation is correct.

If I use the quation: Cc=2*sqrt(K*m) (where K is the stiffness, m is the mass, Cc is the critical damping constant) and compute the damping ration using D = C/Cc, the units cannot be cancelled out! The ratio ends up having a unit (ft) left over. Apparently something wrong here.

For rotational vibration, K is in k.ft/rad, C is in k.ft.sec/rad, m is in k.sec^2/ft.

Could somebody point out the problem here? Thanks

j1d

 

[vulcanhammer]

That equation is for a single degree-of-freedom, linear system.

In that case, the spring constant k is in kips/ft and m is in kips-sec^2/ft. Multiplying that through will yield kips-sec/ft, which are certainly the units for damping. I think the problem lies in the units you have for the spring constant.

A more thorough treatment of this subject can be found in MIL-HDBK-1007/3, which is at

http://www.vulcanhammer.net/geotechnical/soil-dynamics.php

As far as rotational vibrations are concerned, unless the entire system rotates, if you have rotating machinery with eccentric loads, the load will manifest itself as a axial load which continuously changes direction. This in turn can be broken down into z- and x-components, which can usually be analysed in a linear fashion. This is similar to a vibratory pile driver, which I deal with at length at

http://www.vulcanhammer.info/vibro/vibro-technology.php

http://www.pz27.net

 

[J1D]

Thanks Vulcanhammer, you provide pretty good info on the web.

But still I don't know how to calculate the critical damping for rocking. In a specification it is required that the geometric damping ratio of pile group for rocking mode is less than 0.10.

Regards,
j1d

 

[vulcanhammer]

The only place where I could find anything approaching a direct answer to your question was here:

http://books.google.com/books?id=3e...ook_result&ct=result&resnum=2&ved=0CAsQ6AEwAQ

There's some other info (albeit theoretical) in Verruijt's book on Soil Dynamics, found at the same page as the MIL-HDBK.

http://www.pz27.net

 

[J1D]

I have this book. But I only found the critical damping equation on page 513 (Eq. 7.50). But when I used it for rocking mode, the unit problem occurred as described about. The equation looks like being for translational modes only.

Regards,
j1d