An Approach to Properly Account for Structural Damping, FrequencyDependent StiffnessDamping, and to

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An Approach to Properly Account for Structural
Damping, Frequency-Dependent Stiffness/Damping,
and to Use Complex Matrices in Transient Response

• By
• Ted Rose

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Or (more simply)Some Uses for Fourier Transforms
in Transient Analysis

• By
• Ted Rose

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Overview

• Transient Response analysis has a number of
  limitations
• It requires an approximation be used to model
  structural damping
• It does not support frequency-dependent elements
• It does not allow complex matrices
• Obtaining steady-state solutions to multiple
  rotating imbalances can take very long

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Fourier Transforms in Transient

• All of these limitations can be overcome by using
  Fourier Transforms
• In 1995 Dean Bellinger presented a paper of
  Fourier Transforms
• His paper, plus the Application Note on Fourier
  Transforms, provides the documentation on this
  approach

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Fourier Transforms in Transient

• The user interface is simple
• Set up your file for transient response
• Change the solution to 108 or 111
• Add a FREQ command to CASE CONTROL
• Add a FREQ1 entry to the BULK DATA
• Use a constant DF 1/T
• Where T the duration/period of the transient
  event
• Make sure that the duration/period of the load is
  correct (TLOAD1/2 duration is T)

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Fourier Transforms in Transient

• Verify the transformation by plotting the applied
  load (sample input in paper)
• Sample three simultaneous sine inputs (1hz,
  2hz, and 3hz) with a 1.0 second duration

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Applied Load in Transient
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Load after Fourier Transform
Duration of TLOAD2 Is 1.0, therefore, DF1./1.1.
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Load after Fourier Transform
Poorly selected Input for FREQ1 Although DF is
1.0, the Starting frequency is .5, Resulting in
a poor transformation
wrong input freq1,99,.5,1.,3 DLOAD,1,1.,1.,10,1.
,20,1.,30 T 1.0 TLOAD2,10,25,,,0.,1.,1.,-90. T
LOAD2,20,25,,,0.,1.,2.,-90. TLOAD2,30,25,,,0.,1.,3
.,-90. DAREA,25,1,1,1. TSTEP,20,100,.01,
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Compare the Results
Original Load
Good Fourier Transform
Bad Fourier Transform
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Structural Damping

• Handled correctly, it forms a complex stiffness
  matrix
• Ktotal K(1iG) iSKeGe
• Unfortunately, transient response does not allow
  complex matrices, so we must approximate
  structural damping using
• Btotal B KG/W3 SkeGe/W4
• Where w3 and w4 are the dominant frequency of
  response

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Structural Damping

• If the actual response is at a frequency less
  than w3, the results have too little damping, if
  it is at a frequency greater than w3, the results
  have too much damping
• This means that unless you are performing a
  steady-state analysis, your damping will not be
  handled correctly
• Using Fourier Transforms allows you to apply
  structural damping properly

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Multi-Frequency Steady-State

• Many structures (engines, compressors, etc) have
  multiple rotating bodies
• In many cases, they are not all rotating at the
  same frequency
• In order to handle this in conventional Transient
  analysis, it requires a very long integration
  interval to reach the steady-state response
• With Fourier transforms, it is easy to solve for
  the steady-state solution

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Multi-Frequency Steady-State

• As an example, let us look at a typical jet
  engine model with 3 rotating imbalances

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Multi-Frequency Steady-State

• All right, how about this model?

Model courtesy of Pratt and Whitney
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Multi-Frequency Steady-State

• Although rotating imbalances in jet engines occur
  at much higher frequencies, for this example, I
  will use .5hz, 1.0hz, and 2.0hz

Rotating in opposite direction
dynamic loading dload,101,1.,1.,1002,1.,1003,1
.,2002 ,1.,2003,1.,3002,1.,3003 tload2,1002,12,,
,0.,10.,1.,-90. tload2,1003,13,,,0.,10.,1.,0. forc
e,12,660001,,10.,,2., force,13,660001,,10.,,,2.
tload2,2002,22,,,0.,10.,2.,90. tload2,2003,23,,,0.
,10.,2.,0. force,22,670001,,10.,,4., force,23,6700
01,,10.,,,4.
tload2,3002,32,,,0.,10.,.5,0. tload2,3003,33,,,0.,
10.,.5,90. force,32,680001,,10.,,1., force,33,6800
01,,10.,,,1. eigrl,10,,,10 tabdmp1,1,crit ,0.,.0
1,1000.,.01,endt tstep,103,100,.02 set
delta F1/T freq1,102,.5,.5,5
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Multi-Frequency Steady-State