7.2. HBM Cyclic Analysis: Superelements Use Pass

  1. Determine the spatial harmonic index corresponding to each of the NH+1 time harmonics (NH on the HROPT command).

  2. Starting from the 0th time harmonic, load one cyclic stage SE per time harmonic, h, by copying the proper SE generated in step 4 of the generation pass, offsetting its node number and renaming it to Sname_NH_ using the SETRAN command (Sname will be the stage SE prefix used in the HBMOPT,CYCLIC command in step 6 below).

  3. Create the nonlinear elements and connect them only to the primary stage nodes (the nonlinear elements must not be duplicated for higher harmonic stages).

  4. Apply boundary conditions to primary stage only (they will be automatically duplicated on higher harmonic stages during solution).

  5. Apply loading in either of the following two ways:

    • Define a table with primary variable NHINDEX, define load values corresponding to the time harmonics of the external load, and apply this tabular load to the primary stage master nodes.

      With this method, the real part of the loading must be applied as a tabular real component and the imaginary part must be applied as a tabular imaginary component.

    • Apply the load to the proper time harmonic stage (for example, for a time harmonic 1 load, select nodes/elements belonging to Sname_NH_1 superelement to apply the load).

      With this method, the real part of the loading must be applied to the base sector nodes/elements and the imaginary part of the loading must be applied to the duplicate sector nodes/elements as a real component.

      For a superelement load vector (SFE,,,SELV), only the second load specification method above applies—applying the load to the proper time harmonic stage.

    Note:  The direct definition (no NHINDEX-based table) of the traveling wave load is summarized in Harmonic Traveling Wave Load in the Multistage Cyclic Symmetry Analysis Guide.

  6. In addition to standard HBM options (HBMOPT), the command HBMOPT,CYCLIC,ON,EO,Sname, must be defined to trigger an HBM cyclic analysis, with Sname as the name of the stage SE prefix and EO the engine order of excitation.

  7. Run the HBM analysis.

Macros are available to simplify the setup of an HBM cyclic use pass. See the example below.

  • Use the HBMCYCHIGET macro to perform step 1.

  • Use the HBMCYCSEIMPORT macro to perform step 2.

Example

The following example snippet and selected output show the HBM cyclic use pass for the same example as above.

!!! HBM CYCLIC USE PASS

/clear,nostart
		
Sname  = 'stage'             ! stage name

HBMCYCHIGET,Nsec,EO,NH,'USE' ! step 1.
HBMCYCSEIMPORT,Sname         ! step 2.

! create nonlinear elements linked to primary stage (h=0) – step 3.
/prep7
[...]
finish

/solu
antype,harmonic

hropt,hbm,NH
harfrq,fmin,fmax

! HBM cyclic options
hbmopt,cyclic,1,EO,stage

! other HBM options
[...]

! use pass loading and boundary conditions
[...]

solve

finish

The spatial harmonics corresponding to each time harmonic computed in step 1 by the HBMCYCHIGET macro are:

 ________________________ HBMCYCHIGET MACRO _______________________
 *
 * CYCLIC HARMONIC INDICES REQUIRED FOR AN HBM ANALYSIS USE PASS
 * WITH ENGINE ORDER 3 AND 11 TIME HARMONICS ARE WRITTEN
 * IN VECTOR ARRAY 'HBMCYCHIarray'
 *
 * LIST OF HARMONIC INDICES/ALIASED ENGINE ORDERS (IF EXPA)
 *            0
 *            3
 *            6
 *            9
 *            12
 *            9
 *            6
 *            3
 *            0
 *            3
 *            6
 *            9
 *
 *