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 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 *.par 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:

The figure below is the original design:

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.