natural frequency of foundation

huangyhg

natural frequency of foundation
hi, i'm working in a foundation design for some kind of machinery, i was reading the requirements, and based on them you shall have a concrete floor system (on grade) with a first natural frequency  higher than 200 hz, i'm trying a 24-inch thick foundation, the dimensions of the foundation are 16'-6" wide by 31'-6" long.  i try hand calculations based on soil spring values, and also risa3d to calculate the natural frequency but i only get around 30 hz.  has anyone done similar calculations.  
thank you for all your help
   
try adding either piles around the perimeter to encase a large mass of soil or a hollow box shape to use the soil mass enclosed.  the greater the mass the better.
my dynamic machinery support experience has been limited to far above grade (steel structures) so i do not have a direct solution to draw advice from.
if the natural frequency (fn) needs to be > 200 hz, i believe you need to lower your mass (do not contain soil) and increase your foundation stiffness. i believe a typical 12" x 40' concrete pile in granular soil may have a vertical fn between 25 and 50 hz and a lateral fn much lower, so it may not help much in this situation.
it will be interesting to see the solution with regards to the dynamic soil interaction.