HARMONICS

I/O Options EntryUsed to specify the solution harmonics to be used in cyclic symmetry analysis.

Format

HARMONICS = option

Example 1

Using SET definition in the Bulk Data section.
HARMONICS = 26
SET, 26, MODE
+, 0, 1, 2, 6, 10

Example 2

Using SET definition in the Case Control section.
HARMONICS = 26
SET 26 = 0, 1, 2, 6, 10

Definitions

Argument Options Description
option <ALL, SETID>
ALL (Default)
All harmonics will be used.
SETID
Set identification number.
The referenced SET lists the indices of the harmonics to be used.

(Integer > 0)

Comments

  1. When the HARMONICS I/O Option is not present, HARMONICS=ALL will be set by default in cyclic symmetry analysis.
  2. The SET definition referenced by HARMONICS should be a set of TYPE = MODE.
  3. The harmonic indices are supposed to be non-negative and must be no greater than (NSEG is defined in the CYSYM Bulk Data Entry).

    If NSEG is odd:

    ( N S E G − 1 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaada Wcaaqaaiaad6eacaWGtbGaamyraiaadEeacqGHsislcaaIXaaabaGa aGOmaaaaaiaawIcacaGLPaaaaaa@3D34@

    If NSEG is even:

    ( N S E G 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaada Wcaaqaaiaad6eacaWGtbGaamyraiaadEeaaeaacaaIYaaaaaGaayjk aiaawMcaaaaa@3B8C@

  4. Further remarks regarding different harmonic options for different subcase types are summarized in the table.
    Subcase Type Non-cyclic Symmetric Behavior Cyclic Symmetric Behaviour*
    Linear Static
    • Cyclic symmetry analysis can solve for non-cyclic symmetric deformation if non-cyclic symmetric loadings (including non-cyclic symmetric SPCD) exist in the input file.
    • The result is a linear superposition of all the requested harmonic solutions.
    • When all the necessary harmonics are requested, cyclic symmetry linear static analysis is capable of generating deformation identical to a regular linear static analysis which has all the segments of the structure being modelled; therefore, HARMONICS=ALL is usually recommended. In general, harmonics with lower indices contribute more to the result of in a linear static cyclic symmetry analysis, and removing some harmonics may lead to loss in accuracy.
    • If there is no non-cyclic symmetric loading (including non-cyclic symmetric SPCD), all the harmonics vanish except the 0th harmonic, which leads to cyclic symmetric deformation.
    Normal Mode
    • Each harmonic solves for a series of modal shapes of a certain pattern and the result is a collection of modes calculated from the requested harmonic solutions.
    • When all the necessary harmonics are requested, cyclic symmetry normal mode analysis is capable of generating a same number of modes identical to a regular normal mode analysis which has all the segments of the structure being modelled.
    • Removing a certain harmonic index h from the set referenced by HARMONICS would result in the absence in the corresponding mode shapes with h nodal diameters.
    • The 0th harmonic corresponds to mode shapes with cyclic symmetric mode shapes, that is, no nodal diameter.
    Nonlinear Static, Nonlinear Transient N/A
    • Only the 0th harmonic (as in, completely cyclic symmetric behaviour) is allowed due to theoretical restrictions.
    Preloading/Preloaded Subcase in Prestressed Analyses
    • Subsequent preloaded subcase can have non-cyclic symmetric deformation or modes.
    • Preloading must be completely cyclic symmetric due to theoretical restrictions.