Modal Dynamic And Ritz Analysis Cases

For dynamic tasks there is the option of Local or Global response.

Local

If the mode is predominantly local it may be more appropriate to consider the boundary of the sub model as fixed and to carry out a modal analysis of the sub-model. In this case the model extraction is straightforward. In this case the analysis task is copied directly

Global

It is not possible to carry out a sub-model model analysis when the mode is global. In this case the modal results are used to create a set of static loads

The modal analysis of the full model gives us eigenvalues and eigenvectors which satisfy

$$K\phi_{i} - \lambda_{i}M\phi_{i} = 0$$

This can be rearranged in the form

$$K\phi_{i} = \lambda_{i}M\phi_{i}$$

Which we can consider as a static (pseudo modal) analysis of

$$K\phi_{i} = p_{i}$$

where

$$p_{i} = \lambda_{i}M\phi_{i}$$

When extracting the sub-model the frequency (eigenvalue) and mode shape (eigenvector) can be used to create a set of node loads:

$$\begin{aligned} ^{n}{p}_{i} &= \lambda_{i}^{n} M^{n}\phi_{i} \\ ^{n}p_{i} &= \left( 2\pi f_{i} \right)^{2}.^{n}M^{n}\phi_{i} \end{aligned}$$

The modal task in the full model is mapped to a static task in the sub-model. As for the static analysis the displacements at the boundary nodes are used to determine settlements at the boundary nodes and the inertia loads are saved as node loads. The static analysis of these loads will then recover the mode shapes of the original model.