Harmonic Analysis

1
Harmonic Analysis

• Appendix Ten

2
Background on Harmonic Analysis

• Separation of real and imaginary terms can be
  performed for not just the force loading but also
  the response
• If the harmonic loading and response are
  substituted back in the equation of motion, the
  following is obtained

3
Loads and Supports (ANSYS)

• Internally, loads are applied slightly
  differently than in an equivalent static
  analysis
• Forces on vertices and edges are applied as real
  imaginary nodal loads via F,,FX/FY/FZ,REAL,IMAG
• Pressures and Forces on surfaces are applied on
  surface effect elements SURF154 with KEYOPT(11)2
• For Pressure Load, input is via
  SF,,PRES,REAL,IMAG
• For Force Load on surface, input via
  SFE,,5,PRES,0 for real and SFE,,5,PRES,2 for
  imaginary components
• Given Displacement Support is via
  D,,UX/UY/UZ,REAL,IMAG
• Acceleration, Bearing, and Moment Loads are used
  as normal
• Bearing loads are applied as SFE on face 5 of
  SURF154. Two sets are created for axial and
  radial components of bearing load Axial uses
  KEYOPT(11)2, Radial uses KEYOPT(11)0
• Moments on vertices or edges of shells are
  applied as nodal loads via F,,MX/MY/MZ while
  moments on surfaces are applied via CONTA174
  surface-based constraint (see Ch. 4)

4
Mode Superposition Method

• The previous two equations can be combined and
  pre-multiplied by the mode shape fiT
• Although outside of the scope of the discussion,
  the above equation reduces to the following
• The resulting equation is uncoupled and is easier
  to solve
• The total degrees of freedom are not dictated by
  the number of nodes in the mesh. Instead, it is
  determined by the number of modes n used in the
  equation.
• The equation is simplified because of the
  following properties
• Normalization of M
• Natural frequency wi for mode i
• Damping ratio xi for mode i

5
Mode Superposition (ANSYS)

• The ANSYS mode superposition method is run
  internally
• A modal analysis is run first with Block Lanczos
  eigenvalue extraction method (MODOPT,LANB,200,FREQ
  B/2,2FREQE)
• A maximum of 200 modes between ½ of the beginning
  frequency FREQB to 2 times the ending frequency
  FREQE is solved for
• A load vector is automatically created at this
  time
• A harmonic analysis using mode superposition
  method (HROPT,MSUP) is then performed
• Frequency range specified with HARFRQ,FREQB,FREQE
• If clustering is requested, HROUT,,ON is issued
• All loads are step-applied in the frequency range
  (KBC,1)
• Number of intervals (or cluster number) specified
  with NSUBST
• Load vector of 1.0 is issued with LVSCALE,1
• OUTRES with nodal and element components used
• An expansion pass is also performed for contour
  results
• EXPASS,ON and HREXP,ALL are used

6
Full Method (ANSYS)

• Internally, the Full method is used in ANSYS
• Frequency range specified with HARFRQ,FREQB,FREQE
• HROPT,FULL is used
• Number of intervals specified with NSUBST
• Loads are step applied in frequency range with
  KBC,1
• The equation solver is the default sparse solver.
  The Details view of the Solution branch has no
  effect on full harmonic analyses, as no solver
  command (EQSLV) is issued
• OUTRES with nodal and element components used