External Acoustic Optimization of an Exhaust Muffler

Description of the Model

The model is for an acoustic analysis of a car muffler. A direct steady-state dynamic analysis is performed. At the inlet of the muffler, an acoustic pressure is provided as boundary condition. At the 2 outlets an acoustic impedance is specified to couple them with the air (acoustic infinite elements) on the outside. The muffler is modeled with shell elements on the outside. The Air is modeled with acoustic infinite elements and coupled to the shell with Tie constraints. Thus this is a Fully Coupled Structural-Acoustic Analysis.

The muffler is the optimization design area.

The complete FE model of the muffler with infinite acoustic elements is pictured below:

Description of the Optimization Problem

The optimization problem is to minimize the sound pressure while keeping the volume of the design area the same as before. This model does not have any damping parameters. Also thickness bounds are specified, along with clustering of elements. This is done to keep the results in a mechanically sensible range and to ensure the ease of manufacturing. The parameter file is shown below:

DRESP
  ID_NAME    = TOSCA_DRESP_1_FREQUENCY_RESPONSE_TERM_1
  LIST       = LIST
  DEF_TYPE   = SYSTEM
  NODE       = 219740
  TYPE       = FS_PRESSURE
  UPDATE     = EVER
  GROUP_OPER = Max
END_

DRESP
  ID_NAME    = TOSCA_DRESP_2_VOLUME_CONSTRAINT_1
  LIST       = LIST
  DEF_TYPE   = SYSTEM
  EL_GROUP   = ALL_SHELLS
  TYPE       = VOLUME
  UPDATE     = EVER
  GROUP_OPER = Sum
END_

OBJ_FUNC
  ID_NAME    = OBJ_FUNC_1_OBJ_FUNC_ITEM_1
  TARGET     = MIN
  DRESP      = TOSCA_DRESP_1_FREQUENCY_RESPONSE_TERM_1,
END_

...

CONSTRAINT
  ID_NAME    = CONSTRAINT_1_VOLUME_CONSTRAINT_1
  DRESP      = TOSCA_DRESP_2_VOLUME_CONSTRAINT_1
  MAGNITUDE  = REL
  LE_VALUE   = 1.
END_

...

OPTIMIZE
  ID_NAME    = OPTIMIZE_1
  DV         = DESIGN_AREA
  OBJ_FUNC   = OBJ_FUNC_1_OBJ_FUNC_ITEM_1
  CONSTRAINT = CONSTRAINT_1_VOLUME_CONSTRAINT_1
  STRATEGY   = SIZING_SENSITIVITY
  DVCON      = CLUSTER_ID
  DVCON      = BOUNDS_ID
END_

Results

The figure below shows the normalized values of the objective function and the constraints over the optimization process:

The figures below shows the vibration modes and the corresponding acoustic pressure of the muffler:

Acoustic Pressure	Shape of the vibration mode and the corresponding internal and external acoustic pressure

Acoustic Pressure	Shape of the vibration mode and the corresponding internal and external acoustic pressure

The figure below is the original design:

The thickness distribution of the original muffler

and the following figure is the optimized design:

The solution has the same volume as original design but with decrease in acoustic pressure around the muffler.

The thickness distribution of the optimized muffler