Dynamic piping analysis

Static pipe stress analysis considers loads that are applied slowly: weight, pressure, thermal expansion. If a load changes faster than the line can follow, the system responds with inertia and vibration – and may deflect considerably more than under the same load at rest.

Typical reasons for a dynamic analysis are pressure surges, the reaction forces of discharging safety valves, earthquakes, pulsation from reciprocating machinery, slug flow and unexplained vibration in service.

Every piping system has natural frequencies at which it prefers to vibrate, each with its mode shape. A modal analysis calculates both from mass and stiffness. It does not load the line – it shows how the system would vibrate if excited.

If a natural frequency lies close to an excitation frequency, such as the running speed of a machine, resonance is a risk. The aim is then sufficient separation between the two.

Which method fits depends on the type of excitation. Regularly recurring forces – pulsation, unbalance – are calculated as a harmonic analysis at the frequency concerned. Earthquakes are mostly handled with a response spectrum, which gives the maximum response for each natural frequency. One-off events such as a pressure surge call for a time history analysis that follows the system step by step.

An equivalent static load with a dynamic load factor is sometimes used as an approximation. For a suddenly applied force on a simple undamped oscillator this factor is at most 2; with repeated excitation near a natural frequency the real response can be far higher.

Dynamics depend on the distribution of mass: contents, insulation, valves including their actuators. The stiffness of supports and structure matters just as much – a beam treated as rigid in the static model may yield dynamically.

Supports that act in one direction only, have gaps or transmit friction are difficult. They behave non-linearly, whereas modal and spectrum methods assume a linear system. How such supports are represented in the model is an assumption that has to be stated in the report.

For thermal expansion a line should be flexible: few supports, long legs. For dynamics it should be stiff: short spans, guides, high natural frequencies. Every additional guide against vibration may restrain expansion.

Dynamic analysis is therefore not an appendix to the static one. Both are balanced on the same model – with restraints that allow slow movement and lock fast movement where the conflict cannot be resolved otherwise.