Natural frequency of a small platform - hand calculations

[MarioGr]

Hello,

I've been a long time lurker of this site and have found it invaluable regards many topics.

I am a structural engineer who has strayed into the area of mechanical engineering inadvertently.

I was commissioned to certify the structure which I duly did only then to have been told afterwards the platform is subject to machinery loads.

The machinery is a small sorting sluice for food processing. It operates at 50HZ, has a maximum displacement (peak to peak)of 2.5mm and the mass of the machinery is 230kg.

My understanding is that I need to calculate the natural frequency of a small platform and ensure that it exceeds the frequency of the machinery it is supporting. (I think.)

The platform consists of 4 / 150 x 5.0 SHS columns supporting a ring beam of 150 x 100 x 4.0 RHS's. There are 3 intermediate 150 x 100 x 4.0 RHS's spanning the 1.8m span at equal centres.

The columns ctrs are 4.6m x 1.8m. The platform is 2.7m high. The load is in the direction of the short axis of the platform. (The machinery is located centrally.)

My structural analysis software here does not come with the module to calculate the frequency of the platform. In any case I would not be confident of the output as I am a rank amateur at frequency analysis and would prefer to hand calc it.

Could someone please step out, or point me to, how to calculate the natural frequency of the platform and how to reconcile that with the machinery loads imparted above.

I have done some calculations based on this formula f = 1/(2 pi) * sqrt ( K / m) with K = 3EI / L^3 but am unsure if they are correct.

I apologise for the overly long post but thought it better to have too much information than not enough.

Many thanks in advance.

 

[Lion06]

I don't think I've ever analyzed a floor with a frequency even approaching 50 Hz. There is more than one consideration here.

First is resonance, in which you'll need to determine the natural frequency of the floor system and ensure it's far enough away from the operating speed of the machine to not be in resonance.

Second is determining the acceleration (or velocity) of the floor to make sure it doesn't exceed the allowable parameters set by the equipment manufacturer.

Third is to do a time history analysis with a sinusoidal load (matching the magnitude and frequency of the equipment). Pick a few points that you would expect to be the worst case for the time history analysis; this is usually a very time consuming FEA.

 

[MarioGr]

I'm not sure if this is relevant but the machinery operates at 50Hz with a 2.5mm peak to peak displacement and is placed on fibreglass dampeners mounted to the platform.

I am guessing, from 1st principles, that I have to convert the frequency of the machinery into a velocity and acceleration and then apply that somehow to the platform. I could be way off.

From your post you are saying you have to determine the natural frequency of the floor system. Correct, that is what I am asking.

 

[bljnv]

Please consider
(a) Use proper vibration isolators between the machinery and platform, so as to isolate 85~90 % of vibrations while the machine is running at normal operating conditions.
(b) The forces which are transmitted after the isolators can be accounted while doing the structural analysis of the understructure.
(c) Conduct modal analysis and determine the natural frequency of that mode which coincides with the orientation and direction of disturbing frequency. Ensure system natural frequency for that node shape does not resonate with the disturbing frequency. This will take care of vibrations in transient conditions during start up and shut downs.
Regards