Maximizing the First Eigenfrequencies

You can increase several lowest eigenfrequencies.

Note: It is important to consider more than the first natural eigenfrequency when increasing the natural frequencies using optimization. At least, the next two first natural frequencies should be considered in the optimization.

This task shows you how to:

Before you begin:
  • All natural eigenfrequencies requested in the FE model are applied in the optimization if the ALL option is applied in the LC_SET parameter.
  • During the optimization, the various natural frequencies are automatically weighted by their distance from the lowest natural frequency; that is, when the other natural frequencies approach the first natural frequency during the optimization, the more they are weighted. Generally, the first natural frequency is always maximized.
  • The design response is defined using the Kreisselmeier-Steinhauser formulation. For more information, see Overview of Eigenfrequency.
  • Any number of natural frequencies in the design response can be specified using the DRESP command.
See Also
Overview of Eigenfrequency
In this example, all calculated natural frequencies are considered for the objective function using the Kreisselmeier-Steinhauser formulation and are defined as follows: 


DRESP
 ID_NAME  = all_lowest_eigenfrequencies
 DEF_TYPE = SYSTEM
 TYPE     = DYN_FREQ_KREISSEL
 LC_SET   = MODAL, ALL, ALL
END_
  
OBJ_FUNC
 ID_NAME = maximize_eigenfrequencies
DRESP    = all_lowest_eigenfrequencies
 TARGET  = MAX
END_

If you have requested 10 eigenfrequencies in the finite element input model but only the first 5 eigenfrequencies are to be used in the optimization definition, the design response for 5 eigenfrequencies is defined as follows: 


DRESP
 ID_NAME  = all_lowest_eigenfrequencies_1_5
 DEF_TYPE = SYSTEM
 TYPE     = DYN_FREQ_KREISSEL
 LC_SET   = MODAL, ALL, 1-5
END_

OBJ_FUNC
 ID_NAME  = maximize_eigenfrequencies_1_5
 DRESP    = all_lowest_eigenfrequencies_1_5
 TARGET   = MAX
END_

Define an Eigenfrequency Design Response in Tosca Structure.gui

  1. Create a new Design Response.
  2. Set DefType = System, Category = Base and Type = DYN_FREQ_KREISSEL.
  3. Choose the load cases by clicking Add LC and setting Analysis Type to MODAL, entering the load case ID and the numbers of eigenmodes (for example, 1-5) in the Eigenmode/Subcase field.