Structural dynamics / tutorial
A plant platform that shakes
Decide whether a dynamic problem exists at all, then quantify it.
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesA 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.
- 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
Practice
What is the platform's natural frequency, in Hz?
Practice
The pump runs at 720 rpm. What is the frequency ratio β = ω/ωₙ?
Practice
What is the displacement magnification factor Rd at 3% damping?
Practice
The static deflection under the 8.0 kN unbalanced force would be 3.08 mm. What is the dynamic amplitude, in millimetres?
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.