Concepts:
A lab table of simple construction is to hold a refigeration experiment setup. The table top is 30 in. x 60 in. All around the top, just under the edge is a stiffener which is the same cross-section as the table legs. (To simplify, assume the stiffener is centered on the edge of the table top). The table legs are 36 in. long.
The table top is made of steel and is 1/4 in. thick (modulus of 30e6, poisson's ratio of 0.3, and density of 0.283 lbm/cu. in.).
The table's legs and the edge stiffener are made of aluminum (modulus of 10e6 psi, Poisson's ratio of 0.33, and denstiy of 0.1 lbm/cu. in.). The cross-section of the legs and stiffener is standard square tubing (2" x 2" x 1/4") with cross-sectional area of 1.59 in^2, moments of intertia of 0.766 in^4.
The refrigeration system causes a harmonic forced vibration on the table top. This vibration acts perpendicular to the table top and also parallel to the long dimension of the table. These two vibrations have the same amplitude and frequency, but are 90 degrees out of phase. Depending on the experiments being run, the operating frequency of the excitation may be as high as 1500 RPM. The exitation can be modeled as forces at the center of the table top acting on the base of the refrigerator unit. The amplitude of these excitation forces can be modeled as 10 lbf.
The refrigeration system weighs 120 lbm which can be modeled as a concentrated mass, centered on the table top.
Use a damping ratio which is 3% of critical. Constrain the base of each table leg in all three translation directions.