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 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*	S*	C, S	S*
CONSTRAINT	S*	S*	S*	S*

*Please note that the Kreisselmaier-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 Kreisselmaier-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 Kreisselmaier-Steinhauser formulation is defined by DYN_FREQ_KREISSEL in the design response. For this design response mode tracking is not needed.

For the other optimization tasks mode tracking is often necessary because the modes and thereby the eigenfrequencies may switch during the optimization.