Find natural frequencies and mode shapes

Natural Vibration finds the modes of a structure, with their periods and frequencies, and Model View shows each mode move. Run it first on a new model: a first period far from what you expect means the mass or the stiffness is wrong.

A footbridge's first mode, 2.03 Hz, coloured by how far it moves.

You need

• An assembled model from Assemble, with its supports.
• Mass: from the material's density, through the section, or from Mass Point. A Gravity Load gives force, not mass.
• The Grasshopper file saved: the component writes its files beside it.

Steps

1. Wire the model from Assemble into the AlpacaModel input of Natural Vibration Analysis (Alpaca4d ▸ 07_Analysis). It needs no Analysis Settings.
2. Set Vibration Modes to the number of modes you want. The default is 1.
3. Plug Frequencies, in Hz, and Period, in s, into panels: one value per mode.
4. Wire its AlpacaModel output into Model View, with a slider on Step. Step 0 is the first mode.
5. In Model View's Results menu, tick Deformed shape, then Animate to swing the mode through its rest and out the other side. Tick Displacement as well to colour it.
6. Open the Modal Report menu under Natural Vibration, and plug ModalParticipationMassesRatio(%)_Cumulative into a panel.

Check

• TotalMassOfStructure, in the Modal Report menu, should match a hand calculation of the mass. It catches a missing density or a mis-scaled Mass Point.
• Most codes ask for 90 % of the mass in each direction in the cumulative ratios. Raise Vibration Modes until you get there.

Good to know

• A mode has no size of its own. Alpaca4d reads each mode with its largest translation 1, and Model View draws it at Deformation scale 1 with its largest movement 8 % of the model's diagonal. Its displacements and colours are relative only.
• An analysed model, from Run Analysis or Section Optimiser, can be connected too. Its modes are those of the model unloaded.
• The default Solver, -genBandArpack, suits a few modes of a large model. -fullGenLapack extracts all of them, but only on a small model.
• Unsaved, the component stops with "Have you saved the Grasshopper script?".

See also

• Natural Vibration — the inputs, the Modal Report and the solvers
• Model View — Deformed shape, Deformation scale and Animate
• Nodal Displacements — a mode shape as numbers
• Natural Vibration example — a concrete tank's first hundred modes, all drawn at once
• The Rebellious Slave — the modes of a marble statue in tetrahedra
• Response Spectrum from Sticks — a period from Natural Vibration for each of thirty models