3.5.7: Natural Vibrations

In case you want to know how and at which frequency a structure vibrates use the “NaturalVibrations”-component. Fig. 3.5.7.1 shows a simply supported steel beam IPE100 of length$10m$with a point-mass at mid-span in its 24th natural vibration mode.

The mass of beams and trusses enters the calculation of natural vibrations with the values derived from their material weight. Karamba3D uses consistent mass matrices for beam elements. For truss and shell elements a lumped approach is applied.

At nodes additional masses (see section 3.1.11) can be defined to simulate the effect of e.g. concrete slabs (these normally make up the majority of mass in high-rises) in an approximate manner. These masses are assumed to have translational inertia only.

Karamba3D scales the resulting vibration modes $\vec {v_i}$ in such a way that their largest component is 1. They get attached to a model as result-cases which can be viewed via a “ModelView”-component. The calculation of modal mass and participation factors are based on the modal displacements as scaled in the above described manner.

Fig. 3.5.7.1: Natural vibration mode of a simply supported steel beam with a point-mass at mid-span.