3.5.6: Eigen Modes

Fig. 3.5.6.1: Left: 14th eigen-mode with strain display enabled. Right: EigenMode-component in action

Karamba3D’s “EigenMode”-component allows to calculate eigenmodes and corresponding eigenvalues of structures (see fig. 3.5.6.1).

The input parameters are a model, the index of the first eigenmode to be computed and the number of desired eigenmodes. The model which comes out on the right side lists the computed eigenmodes as result-cases. Thus they can be superimposed using the “ModelView”-component for form-finding or structural optimization. All loads which were defined on the input model get discarded. The determination of eigenshapes can take some time in case of large structures or many modes to be calculated. Grasshopper has no “Cancel”-button. Therefore you should save your model before activating the component.

The number of different eigenmodes in a structure equals the number of degrees of freedom. In case of beams there are six degrees of freedom per node, with only trusses attached, a node possesses three degrees of freedom. Fig. 3.5.6.2 shows the first nine eigenmodes of a triangular beam mesh that is fixed at its lower corners. In the upper left corner of fig. 3.5.6.2 one sees the undeformed shape. The higher the index of an eigenmode the more folds it exhibits.

The eigenvalues represent a measure for the resistance of a structure against being deformed to the corresponding eigenform. Values of zero or nearly zero signal rigid body modes. In case that the “Analyze”- or “AnalyzeThII”-components complain about a kinematic structure the eigenforms can be used to detect those kinematic modes.

Again the displacements of the eigenmodes get scaled such that the largest displacement-component corresponds to 1.

Fig. 3.5.6.2: Undeformed geometry (upper left corner) and the first nine eigen-modes of the structure