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Re: NATURAL FREQ OF CANTILEVER PIER

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On Dec 28, 2004, at 11:07 AM, Rich Lewis wrote:

I’m not sure what I am looking for.  Is this the equation for a pendulum since it is a concrete pier?  Would this be some kind of equation that takes into account the length and stiffness of the pier?  Does someone have this equation they could post?
You might want to check back with your dynamics text. I don't do machine beds, but I do a fair amount of dynamics, so I'll stick my next out a little bit. Vibration always involves an elastically supported mass--the simplest form is a lumped mass on a spring. Without any idea what your pier actually looks like, not a soul can tell you how to figure it. If you can think of the system as a mass hung on a cantilever beam, you can estimate the fundamental frequency by dividing the mass of the system into the stiffness of the beam, taking the square root and dividing by 2pi. This isn't an accurate estimate becasue it doesn't treat the mass of the pier or piers and it assumes that one end of the pier is clamped. Assuming clamped ends makes the system stiffer than it is and gives frequencies which are too high. Lumping the pier mass at the end of the cantilever makes the system too heavy and gives frequencies which are too low. Your mechanics text will discuss a lot of other simplifications which may apply depending on your situation.

There are lots of complicating factors, such as soil stiffness, relative mass of the pier and the machine it's supporting, other sources of stiffness such as multiple supports and location of the machine CG with respect to the pier. You probably shouldn't be doing dynamics without having done som fairly serious study, in school or on your own. Don't just go plugging into any old equation before checking the applicability to your situation. There are a lot of approximations around (of which the weightless cantilever with an end mass is only one) and if you pick the wrong one for your situation, you can find yourself in trouble.

Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw(--nospam--at)skypoint.com    | this distance" (last words of Gen.
...................................| John Sedgwick, Spotsylvania 1864)
http://www.skypoint.com/~chrisw/


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