An instrument cabinet having a mass of 250 kg is restrained

An instrument cabinet having a mass of 250 kg is restrained by a mounting that has a lateral stiffness of 1000 kN/meter. The term lateral stiffness means an equivalent spring constant resulting from the mounting details. Earthquakes impose a lateral acceleration within a frequency range of 0.5 to 12 Hz. Does this cabinet have a natural oscillation frequency that places it at risk for resonant failure in an earthquake? If so, what change to either the mass or the stiffness, or both, would you recommend?

Solution

k = 1000 kN/m = 10^6 N/m

omega, w = sqrt(k/m) = 63.24 rad/s2

Frequency range of earthquake, 0.5 to 12 hz

Angular frequency range = 0.5*2pi to 12*2pi = 3.14 to 75.36 rad/s2

Since, the naturat frequency lies in the range of earthquake frequency, the resonance may be introduced.

So, since, the cabinet is the requirement, so increasing the lateral stiffness by adding additional mounting coloumns.

for f = 12 Hz, w = 75.36 rad/s2

k = m*w*w = 1420 kN/m

So, the stiffness should be greater than this value