Fig. 3.6.6.1: Left: 8th eigen-mode with strain display enabled. Right: EigenMode-component in action
Karamba3D's **“EigenMode”** component allows the calculation of eigenmodes and corresponding eigenvalues of structures (see Fig. 3.6.6.1). The input parameters include a model, the index of the first eigenmode to be computed, and the number of desired eigenmodes. By setting the **“ThII?”** input to **“true”** (default is **“false”**), the effect of second-order forces can be considered. The **“LCasesNII”** input defines the load cases from which the most compressive second-order theory force is selected. If **“ThII?”** is **“true”** and **“LCasesNII”** is empty, all calculated load cases are considered. If there are no calculated load cases, user-defined $$N^{II}$$-values are used.
The inputs **"MaxIter"** and **"Eps"** control the accuracy of the Eigen Modes calculation. The default values work in most cases.
The output model lists the computed eigenmodes as result cases of load-case combination **“EigenModes”**. These can be superimposed using the **“ModelView”** component for form-finding or structural optimization. The determination of eigenshapes can be time-consuming for large structures or many modes.
The number of different eigenmodes in a structure equals the number of degrees of freedom. For beams, there are six degrees of freedom per node; for nodes with only trusses attached, there are three degrees of freedom. Fig. 3.6.6.2 shows the first nine eigenmodes of a triangular beam mesh fixed at its lower corners, with the undeformed shape in the upper left corner. Higher-index eigenmodes exhibit more folds.
Eigenvalues represent a measure of the structure's resistance to deformation into the corresponding eigenform. Values of zero or nearly zero indicate rigid body modes. If the **“Analyze”** or **“AnalyzeThII”** components report a kinematic structure, the eigenforms can help detect these kinematic modes. The displacements of the eigenmodes are scaled such that the largest displacement component corresponds to 1.
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