3.6.6: Eigen Modes
Last updated
Last updated
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 -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.
