Overview of Eigenfrequency


Parameter Name	Formula
DYN_FREQ	$f_{j}$
DYN_FREQ_KREISSEL	$- \frac{1}{k} ln (\sum_{j} e^{- k f_{j}})$ by default $k = \frac{30}{f_{min}}$

Analysis Types: Modal Analysis


$(4 π^{2} f^{2} M - K) φ = 0$

For eigenvalues, the following table shows the allowed combinations between the strategy and the items OBJ_FUNC and CONSTRAINT with C for controller and S for sensitivity-based optimization.


	TOPO	SHAPE	BEAD	SIZING
OBJ_FUNC	S*	C, S	C, S*	S*
CONSTRAINT	S	S	S	S

*The Kreisselmeier-Steinhauser formulation is only allowed in objective function.

Eigenvalues are the simplest dynamic responses in structural mechanics. Typical optimization tasks for modal analysis would be to:

Maximize the first eigenfrequency (first natural mode)
Constrain an eigenfrequency to be higher or lower than a given value
Maximize or minimize an eigenfrequency at a certain mode
Bandgap optimization: Force modes away from a certain frequency

It is recommended to use the Kreisselmeier-Steinhauser formulation when maximizing the first eigenfrequencies (especially for multiple eigenfrequencies) given by


$- \frac{1}{k} ln (\sum_{j} e^{- k f_{j}}) , by default: k = \frac{30}{f_{min}}$

The Kreisselmeier-Steinhauser formulation is defined by DYN_FREQ_KREISSEL in the design response. For this design response, mode tracking is not required.

For the other optimization tasks, mode tracking is often required because the modes and the eigenfrequencies might switch during the optimization.