12.2. Postprocessing a Harmonic Acoustic Analysis

For additional information, see Acoustic Output Quantities in the Mechanical APDL Theory Reference.

12.2.1. Reviewing Analysis Results

Results from an acoustic analysis are written to the results file Jobname.rst. Results include the following:

Primary data: Nodal DOFs (UX, UY, UZ, PRES, VX, VY, VZ, TEMP, ENKE)

Derived data:

  • Nodal sound pressure level (SPL) or A-weighted sound pressure level (dBA)

  • Nodal velocity, sound intensity, or energy density flux (room acoustics)

  • Element velocity, sound intensity, or energy density flux (room acoustics)

  • Element average pressure amplitude

  • Square of the L2 norm of pressure over element volume

  • Element effective complex mass density (if possible)

  • Element effective complex sound speed (if possible)

  • Element input power (if required)

  • Element output power (if required)

  • Acoustic potential energy in element (MENE)

  • Acoustic kinetic energy in element (KENE)

Many harmonic acoustic analysis results vary harmonically at the operating frequency (or frequencies) for which the measurable quantities can be calculated as the real solution times cosine(ωt) minus the imaginary solution times sine(ωt), where ω is the angular frequency. (See Harmonic Analysis Using Complex Formalism in the Mechanical APDL Theory Reference.) In harmonic analysis, the time-average root mean square quantities are calculated over one period of sinusoidal function.

For more information, see Elements for Acoustic Analysis in the Element Reference.

Review analysis results via the POST1 general postprocessor (/POST1). Typically, the results are out-of-phase with the input loads. The solution is calculated and stored in terms of real and imaginary components.

Use POST1 to review results over the entire model at specific frequencies. For viewing results over a range of frequencies, use the POST26 time-history postprocessor (/POST26).

The SPL and the dBA of the octave band can be calculated (PRAS or PLAS) on the selected nodes. The calculated values can be monitored and stored by issuing the following command:

*GET,Par,ACUS,0,Item1

To obtain the SPL and dBA of the octave band via the *GET command, issue the PRAS or PLAS command at specified positions prior to issuing the *GET command. For multiple load and substeps cases, the results are obtained at the last position and band.

For more information, see Acoustic Output Quantities in the Mechanical APDL Theory Reference.

For a complete description of all postprocessing functions, see An Overview of Postprocessing in the Basic Analysis Guide.

The following topics discuss some typical POST1 operations for calculating the near- and far-fields and parameters for acoustic devices.

    12.2.2. Calculating Near Fields, Far Fields, and Far-Field Parameters

    Postprocessing commands are available for calculating the near or far sound pressure field beyond the FEA computational domain.

    The commands PRNEAR, PLNEAR, PRFAR, and PLFAR use the surface equivalence principle to determine the sound pressure field. The surface equivalence principle states that equivalent sources can exactly represent the pressure field exterior to the surface. Use the PRFAR or PLFAR command to print or plot the far-field parameters based on the defined load steps, substeps, or frequency range. For more information, see Acoustic Output Quantities in the Mechanical APDL Theory Reference.

    Before issuing the postprocessing commands:

    1. Flag an equivalent source surface (Lab = MXWF on the SF command) in the preprocessor before solution. For more information, see Equivalent Surface Source.

    2. If a symmetry plane exists in the modeled region, indicate its presence (HFSYM). For more information, see Accounting for Model Symmetry.

    3. If the radiation space when calculating radiation parameters is not the entire spherical domain, define the spatial angles (HFANG).

    12.2.2.1. Accounting for Model Symmetry

    You must account for symmetry planes in the modeled domain for postprocessing near or far sound pressure field beyond the computational domain.

    The HFSYM command accounts for the sound-soft or sound-hard symmetry planes that coincide with the X-Y, Y-Z or Z-X planes of the global or local Cartesian coordinate system. It applies the image principle on the symmetric part of the computational domain to represent the radiation effect of the partial equivalent source beyond the modeled domain so that the radiation from the entire structure is modeled.

    If sound-soft or sound-hard symmetry planes exist, issue the HFSYM command before issuing a postprocessing command (PRNEAR, PLNEAR, PRFAR, or PLFAR). Although a sound-hard symmetry plane is a natural boundary condition in a finite element analysis, it must be defined via the HFSYM command.

    Example 12.1: Defining the Symmetric Planes for a Far-Field Calculation

    /post1
    hfsym,,shb,shb,ssb ! y-z, x-z plane as sound hard and x-y as sound soft
    plfar,pres,sump,,  ! plot far-field pressure in polar coordinate
    

    12.2.2.2. Radiation Solid Angle

    When calculating radiation parameters, the radiation space can be specified.

    The HFANG command defines the radiation space of a sound radiator in terms of the type of radiator. For example, the solid angle of a sound dipole is determined by φϵ[0,360°] and θϵ[0,180°], and the solid angle of a piston above an infinite baffle is associated with φϵ[0,360°] and θϵ[0,90°].

    If the sound pressure wave is not radiated into the entire space, issue the HFANG command before issuing a postprocessing command (PRNEAR, PLNEAR, PRFAR, or PLFAR).

    12.2.2.3. Near Sound Pressure Field

    The maximum sound pressure can be printed or plotted beyond the FEA computational domain.

    To print the near sound pressure field, issue the PRNEAR command.

    To plot the sound pressure along a path:

    1. Define a path (PATH and PPATH).

    2. Issue either the PRNEAR or PLNEAR command to map the sound pressure onto the path.

    3. Issue the PLPAGM or PLPATH command.

    12.2.2.4. Far Sound Pressure Field and Far-Field Parameters

    The far sound pressure field and far-field parameters (for example, radiation patterns, directivity, radiated power, radiation efficiency, and target strength) are essential for sound radiation or sound scattering analysis.

    The far sound pressure field and far-field parameters can be printed (PRFAR command) or plotted (PLFAR command) beyond the FEA computational domain.

    To print or plot the 2D far-field parameters in a 3D computational model, extrude the 2D plane model for a distance Δz in the Z-direction to generate a 3D numerical model. For an axisymmetric model that is equivalent to the y-rotated extrusion 3D model, the far field parameters are calculated on the plane defined in global spherical coordinates (PLFAR or PRFAR with Lab = PROT). The theta angles (input as VAR2B and VAR2E) default to 90 degrees for the 2D extrusion model, so you would typically input only the phi angles (VAR1B and VAR1E) in order to report values on the X-Y plane. The HFSYM,,,SHB,, command may be used for symmetry on the y = 0 plane.

    The 2D far-field parameters can also be calculated from a 2D planar or axisymmetric model in which the 2D acoustic elements are utilized without any extrusion. Note that Lab = PROT and Lab = PLAT on PLFAR and PRFAR are invalid when 2D acoustic elements are used to calculate far-field parameters.

    A maximum of ten far-field curves can be plotted on a chart (PLFAR) for multiple angles or frequencies. The waterfall diagram for far-field parameters is available with both frequency and angle as variables. The waterfall diagram for radiated sound power level can be generated with variables of frequency and revolutions per minute (RPM), if RPM is defined (see the MRPM command).

    A contour of far-field pressure, sound pressure level, weighted sound pressure level, acoustic directivity, scattered pressure, or target strength can be plotted on a defined X-Y, Y-Z, or X-Z plane of the global Cartesian coordinate system or on a defined spherical surface (PLFAR). Alternatively, the same quantities can be printed using PRFAR.

    For more information, see Acoustic Output Quantities in the Mechanical APDL Theory Reference.

    12.2.2.5. Far-Field Microphone

    The far field and far-field parameters at a given frequency can be monitored and stored. To do so, issue this command:

    *GET,par,0,ACUS,Item1

    To obtain a far field or a far-field parameter with the parameter par via the *GET command, issue the PRFAR or PLFAR command at a specified position prior to issuing the *GET command.

    Example 12.2: Storing a Far-Field Parameter at a Given Frequency

    /post1
    hfsym,1,ssb,shb,ssb                    ! set symmetric planes
    set,1,1
    plfar,pres,splp,0,0,1,0,360,5,10,2.e-5 ! spl in polar plot
    plfar,pres,splc,0,0,1,0,0,1,10         ! spatial point
    *get,par,0,acus,spl                    ! store spl
    fini
    

    The far-field SPL or a-weighted SPL over octave bands can be obtained by defining the LogOpt argument on the PRFAR or PLFAR command.

    12.2.2.6. Radiated Far-Field of a Vibrating Panel

    Assuming that the sound waves do not affect the structural motion, the vibration of a flat or slightly curved panel can be solved very efficiently without involving any acoustic mesh. The far field and far-field parameters can be directly calculated from structural results based on the Rayleigh integral in which the modified Green's function is used.

    The vibrating surface on the structural model must be identified by the equivalent source surface flag (SF,,MXWF) before the far-field calculation. Use the PRFAR or PLFAR command with Lab = PLAT to perform the far-field calculation for a vibrating panel. The HFSYM command should be issued if planar symmetry is used in the model. Use the PRAS or PLAS command to calculate and print or plot the transmission loss and radiated power of a panel with an incident diffuse sound field.

    The HFANG command is invalid for the vibrating panel radiation, since the hemispherical radiation space is assumed.

    For more information, see Acoustic Output Quantities in the Mechanical APDL Theory Reference.

    12.2.3. Calculating Acoustic Propagation Parameters

    After solving an acoustic problem, it may be desirable to calculate some parameters for the underlying acoustic system. The following parameters can be calculated:

    • Input power

    • Output power

    • Return loss

    • Attenuation coefficient

    • Transmission loss

    Perform the calculation in the POST1 general postprocessor (/POST1) by first reading in the solution for a given frequency, and then performing postprocessing tasks based on the corresponding definition of the parameter. Use the PRAS or PLAS command to print or plot the propagation parameters based on the defined load steps, substeps, or frequency range.

    To calculate the acoustic propagation parameters for two ports of a network, issue the PRAS or PLAS command after defining the port numbers (SF) in the preprocessor.

    If VAL2 (output port) is defined via PRAS or PLAS, VAL1 is the excitation port and should be defined. The impedance boundaries are applied to the excitation port surfaces to absorb the outgoing pressure waves without reflection.

    To plot the power data, issue the PLAS command.

    Example 12.3: Calculating Acoustic Propagation Parameters

    nsel,s,loc,z,0      ! select nodes on inlet
    sf,all,port,3       ! define port 3 on inlet 
    sf,all,impd,z01     ! define impedance on inlet
    sf,all,shld,-vn     ! define normal velocity on inlet
    …
    nsel,s,loc,l        ! select nodes on outlet
    sf,all,port,1       ! define port 1 on outlet
    sf,all,impd,z02     ! define impedance on outlet
    …
    /solu
    antype,harm
    harfrq,0,300
    nsub,3
    solve
    fini
    /post1
    plas,tl,1,all,,,,,3,1
    fini
    

    12.2.4. Calculating Acoustic Surface Quantities

    After solving an acoustic problem, the following quantities can be calculated on the selected surface for a 3D model or on the selected line for a 2D model:

    • Specific acoustic impedance

    • Acoustic impedance

    • Mechanical impedance

    • Pressure

    • Force

    • Equivalent radiated power (ERP) from the structural surface

    • Normal velocity on the structural surface nodes

    The calculation occurs in the POST1 general postprocessor (/POST1) based on the corresponding definition of the quantities. Use the PRAS or PLAS command to print or plot the surface quantities based on the defined load steps, substeps, or frequency range.

    Select the surface nodes for which the acoustic quantities will be calculated. Perform the calculation by issuing the PRAS or PLAS command. The subset number (SUBSTEP argument) specified on the command corresponds to the solving frequency. The acoustic quantities are the average values on the surface.

    Example 12.4: Calculating Acoustic Surface Quantities

    …
    /solu
    antype,harmic
    hropt,full
    harfrq,0,1000
    nsubst,2	 ! two substeps
    solve
    finish 
    /post1
    nsel,s,loc,z,l   ! select surface nodes
    pras,simpd       ! list specific acoustic impedance at default load/substep 
    pras,aimpd,1,2   ! list acoustic impedance at load step 1 and substep 2
    pras,mimpd       ! list mechanical impedance at default load/substep
    pras,pres        ! list pressure at default load/substep
    pras,force       ! list force at default load/substep
    pras,power       ! list sound power at default load/substep
    alls
    finish 
    

    The acoustic surface quantities can be monitored and stored by issuing this command:

    *GET,Par,ACUS,0,Item1

    To obtain an acoustic surface quantity via the *GET command, issue the PRAS or PLAS command at a specified position prior to issuing the *GET command.

    The equivalent radiated power (ERP) from the selected structural surface is calculated for the structure-borne sound via the PRAS or PLAS command. The waterfall diagram of the equivalent radiated power can be generated if the RPM is defined via the MRPM command.

    The normal velocities on the structural surface nodes (VNS) are printed or plotted via the PRNSOL or PLNSOL command.

    For more information, see Acoustic Output Quantities in the Mechanical APDL Theory Reference.

    12.2.5. Calculating Acoustic Volumetric Quantities

    After solving an acoustic problem, the following quantities can be calculated on the selected elements:

    • Sum of acoustic potential energy

    • Sum of acoustic kinetic energy

    • Sum of acoustic total energy (potential energy + kinetic energy)

    • Average square of the L2 norm of pressure

    In the POST1 general postprocessor (/POST1), select the elements for which the acoustic quantities will be calculated. Perform the calculation by issuing the PRAS or PLAS command; specify the frequency via the corresponding substep number (SUBSTEP argument). These two commands print (PRAS) or plot (PLAS) the volumetric quantities based on the defined load steps, substeps, or frequency range.

    Example 12.5: Calculating Acoustic Volumetric Quantities

    ...
    /solu
    antype,harmic
    hropt,full
    harfrq,0,1000
    nsubst,2	 ! two substeps
    solve
    finish 
    /post1
    esel,s,,,1       ! select surface nodes
    pras,kene        ! list kinetic energy at default load/substep 
    pras,kene,1,2    ! list kinetic energy at load step 1 and substep 2
    pras,mene        ! list potential energy at default load/substep
    pras,tene        ! list total energy at default load/substep
    pras,pl2v        ! list average square of the L2 norm of pressure at default load/substep
    alls
    finish