Cumulative tutorial 01
A plant platform that shakes
Decide whether a dynamic problem exists at all, then quantify it.
A steel platform carries a pump in a basement plant room. The maintenance team report that the platform 'buzzes' when the pump runs, and ask whether it is dangerous. Nobody has done a dynamic calculation; the platform was designed for the pump's weight and a live load.
Before reaching for an analysis package, decide whether there is a dynamic problem, and if so, how severe.
What you are given
- Platform and pump mass 3 200 kg, lumped at the platform
- Vertical stiffness of the supporting steelwork 2.6 MN/m
- Damping ratio 3%, typical of a bolted steel frame
- Pump runs at 720 rpm with an unbalanced force of 8.0 kN
Tutorial 01
Work the problem
4 questions
Question 1
What is the platform's natural frequency, in Hz?
Question 2
The pump runs at 720 rpm. What is the frequency ratio β = ω/ωₙ?
Question 3
What is the displacement magnification factor Rd at 3% damping?
Question 4
The static deflection under the 8.0 kN unbalanced force would be 3.08 mm. What is the dynamic amplitude, in millimetres?
What this establishes
Notice what stiffening would have done. Raising the stiffness raises fₙ, which lowers β, which moves the platform TOWARDS resonance. The instinctive fix would have made it worse — and four lines of arithmetic, done before any model was built, is what reveals that.