Maximizing the Band Gap

Sometimes it is desirable that the first eigenfrequencies are as far away as possible from a certain value. For example, if an engine mainly works at 150 Hz, there should be an as large as possible interval called a band gap around 150 Hz in the eigenfrequency spectrum containing no eigenfrequencies. You can maximize the band gap to decrease some eigenfrequencies and increase others.

This task shows you how to:

Context:

In the following optimization definition, the structure should be designed so that the first four eigenfrequencies are as far away as possible from 150 Hz to avoid the resonance at this frequency.

This is done by defining the first four eigenfrequencies as single design responses with TYPE = DYN_FREQ and applying the eigenfrequencies in the objective function using a min-max-formulation as follows: 


DRESP
  ID_NAME  = eigenfrequency_1
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 1
END_
  
DRESP
  ID_NAME  = eigenfrequency_2
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 2
END_
  
DRESP
  ID_NAME  = eigenfrequency_3
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 3
END_
  
DRESP
  ID_NAME  = eigenfrequency_4
  DEF_TYPE = SYSTEM
  TYPE     = DYN_FREQ
  LC_SET   = MODAL, ALL, 4
END_
  
OBJ_FUNC
  DRESP    = eigenfrequency_1, 1.0, 150.0
  DRESP    = eigenfrequency_2, 1.0, 150.0
  DRESP    = eigenfrequency_3, 1.0, 150.0
  DRESP    = eigenfrequency_4, 1.0, 150.0
  TARGET   = MINMAX
END_

Define an Objective Function for a Band Gap Maximization in Tosca Structure.gui

  1. Create four design responses: Choose Command > DRESP.
  2. Set DefType = System, Category = Base and Type = DYN_FREQ.
  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 (1 for the first term, 2 for the second one, etc.) in the Eigenmode/Subcase field.

  4. When the design responses are defined, create an OBJ_FUNC and choose the design responses and their reference values (set RefValue = 150 for each design response).