Negative eigen values in frequency analysis

1

What I am trying to do

I am trying to do a frequency analysis of a flap due to particle impact. There are two parts to do:

  • I run a coupled simulation between CalculiX and XDEM using preCICE coupling library. From this, I get the impact forces.
  • Using the *SUBMODEL card, I used the forces captured in the coupling to do an eigenvalue analysis

The files of the flap can be found on the preCICE tutorials.

Particle_impact_Crop

t=1574
t=15741478×829 59.9 KB

Input Deck

** ---------------------------- Mesh Files ----------------------------
*INCLUDE, INPUT=all.msh
*INCLUDE, INPUT=fix1_beam.nam
*INCLUDE, INPUT=interface_beam.nam
** ---------------------------- Material Data ----------------------------
*MATERIAL, Name=EL
*ELASTIC
2100000.,0.3
*DENSITY
7850
*SOLID SECTION, Elset=Eall, Material=EL
** ---------------------------- Input File ----------------------------
*SUBMODEL,TYPE=NODE,INPUT=flap.frd.ref
Nall
** ---------------------------- STEP ----------------------------
** --------------------------- Static ----------------------------
*STEP
*STATIC
** ---------------------------- Cant. Beam end fix ----------------------------
** fix on the lower boundary from x to z.  
*BOUNDARY
Nfix1, 1, 3
** ---------------------------- Read Force ----------------------------
*CLOAD,SUBMODEL,DATA SET=1574
Nall,1,3
** ---------------------------- OUTPUT ---------------------------- 
*NODE FILE
U, RF
*END STEP
** ---------------------------- STEP ----------------------------
** ------------------ Frequency Calc ------------------
*STEP, PERTURBATION
*FREQUENCY, STORAGE=YES
10
*NODE FILE
PU
*END STEP
** ---------------------------- STEP ----------------------------
** ------------------ Complex Frequency Calc ------------------
** *STEP, PERTURBATION
** *COMPLEX FREQUENCY, FLUTTER
** 10
** *END STEP

Results & Problem

I am able to run everything properly and I have a negative eigenvalue. flap.dat.

  • Is the Problem setup correct for frequency analysis? (After going through the various examples and correcting for errors, I have arrived at the Input deck you see above)
  • How do we interpret the physical meaning of this result?
  • What should I do with such values when considering my results? I.e I tried to do a *COMPLEX FREQUENCY as suggested in the CCX manual but I get errors. (I know I don’t understand the functionality of a complex frequency card fully, but I tried to perform it just in case. From the CCX manual, section 5.3, we see the rotor problem with negative eigenvalues. But in that case, we have a rotating disc, whereas for the current problem we have a cantilever beam. I used FLUTTER instead of CORIOLIS as it seemed appropriate for the case. I could not find any examples for this.)

(Sorry I could not upload the result and log file)

     E I G E N V A L U E   O U T P U T

 MODE NO    EIGENVALUE                       FREQUENCY   
                                     REAL PART            IMAGINARY PART
                           (RAD/TIME)      (CYCLES/TIME     (RAD/TIME)

      1  -0.5975806E+02   0.0000000E+00   0.0000000E+00   0.7730334E+01
      2   0.1543140E+01   0.1242232E+01   0.1977073E+00   0.0000000E+00
      3   0.1124300E+02   0.3353058E+01   0.5336558E+00   0.0000000E+00
      4   0.5469685E+03   0.2338736E+02   0.3722214E+01   0.0000000E+00
      5   0.6146888E+03   0.2479292E+02   0.3945916E+01   0.0000000E+00
      6   0.1537126E+04   0.3920620E+02   0.6239861E+01   0.0000000E+00
      7   0.2934439E+04   0.5417046E+02   0.8621497E+01   0.0000000E+00
      8   0.3338533E+04   0.5778004E+02   0.9195979E+01   0.0000000E+00
      9   0.5054865E+04   0.7109758E+02   0.1131553E+02   0.0000000E+00
     10   0.8141709E+04   0.9023142E+02   0.1436078E+02   0.0000000E+00

     P A R T I C I P A T I O N   F A C T O R S

MODE NO.   X-COMPONENT     Y-COMPONENT     Z-COMPONENT     X-ROTATION      Y-ROTATION      Z-ROTATION

      1   0.9447008E-01   0.1858602E+01   0.6256283E-01  -0.2205057E+01  -0.1720052E-01  -0.6232727E+00
      2  -0.5235674E+01   0.9764268E+00   0.1107465E+02   0.9895292E+00  -0.3646000E+01   0.7962989E+00
      3   0.5250772E+00   0.1198690E+02  -0.8757844E+00  -0.8642642E+01   0.3615266E+00   0.9492632E-01
      4   0.8356452E+01   0.4557903E+00  -0.3139760E+01  -0.4881141E+00   0.3715997E+01  -0.1258870E+01
      5   0.7306408E+00  -0.6925246E+01  -0.1591927E+00   0.1181296E+01   0.3582107E+00  -0.4303149E-01
      6  -0.1091750E+02  -0.4631987E-02  -0.6606001E+01  -0.1017033E+01  -0.6216500E+01   0.1633013E+01
      7   0.3917344E+00   0.2363007E+01   0.4983027E+00  -0.8927839E-01   0.2692057E+00   0.5433820E-01
      8  -0.5492709E+00   0.3328634E+01  -0.9331235E+00  -0.5772504E+00  -0.4287974E+00   0.2946158E-01
      9  -0.1792303E+01  -0.4600129E+00  -0.5500685E+01  -0.7715543E+00  -0.2050516E+01   0.2830800E+00
     10  -0.1682093E-01  -0.2604448E+01   0.4173555E+00   0.2158936E+00   0.1412961E+00   0.8915518E-01

     E F F E C T I V E   M O D A L   M A S S

MODE NO.   X-COMPONENT     Y-COMPONENT     Z-COMPONENT     X-ROTATION      Y-ROTATION      Z-ROTATION

      1   0.8924596E-02   0.3454401E+01   0.3914108E-02   0.4862277E+01   0.2958580E-03   0.3884689E+00
      2   0.2741228E+02   0.9534093E+00   0.1226478E+03   0.9791681E+00   0.1329332E+02   0.6340920E+00
      3   0.2757061E+00   0.1436857E+03   0.7669982E+00   0.7469527E+02   0.1307015E+00   0.9011006E-02
      4   0.6983028E+02   0.2077448E+00   0.9858090E+01   0.2382553E+00   0.1380863E+02   0.1584754E+01
      5   0.5338360E+00   0.4795904E+02   0.2534232E-01   0.1395461E+01   0.1283149E+00   0.1851709E-02
      6   0.1191919E+03   0.2145530E-04   0.4363924E+02   0.1034356E+01   0.3864487E+02   0.2666730E+01
      7   0.1534558E+00   0.5583804E+01   0.2483056E+00   0.7970630E-02   0.7247168E-01   0.2952640E-02
      8   0.3016986E+00   0.1107980E+02   0.8707195E+00   0.3332181E+00   0.1838672E+00   0.8679849E-03
      9   0.3212350E+01   0.2116119E+00   0.3025754E+02   0.5952961E+00   0.4204617E+01   0.8013430E-01
     10   0.2829437E-03   0.6783148E+01   0.1741856E+00   0.4661006E-01   0.1996457E-01   0.7948646E-02
TOTAL     0.2209207E+03   0.2199186E+03   0.2084921E+03   0.8418788E+02   0.7048705E+02   0.5376811E+01

     T O T A L   E F F E C T I V E   M A S S

MODE NO.   X-COMPONENT     Y-COMPONENT     Z-COMPONENT     X-ROTATION      Y-ROTATION      Z-ROTATION

          0.2276500E+03   0.2276500E+03   0.2276500E+03   0.8532950E+02   0.7868971E+02   0.7019208E+01

Error for *COMPLEX FREQUENCY card

 *INFO reading *STEP: nonlinear geometric
       effects are turned on

 *WARNING reading *COMPLEX FREQUENCY:
          for this keyword
          STORAGE=YES is deactivated
          in the CalculiX code

 STEP            3


 Perturbation parameter is active

 Determining the structure of the matrix:
 number of equations
 360
 number of nonzero lower triangular matrix elements
 7128

 Composing the complex eigenmodes from the real eigenmodes

 *INFO in complexfreq: if there are problems reading the .eig file this may be due to:
       1) the nonexistence of the .eig file
       2) other boundary conditions than in the input deck
          which created the .eig file

 *ERROR in readforce: neither a force file
        nor a generalized force file exists
2

Negative eigenvalues mean that the stiffness matrix is not positive definite. They can occur due to many different reasons but in natural frequency extraction analyses they are caused by instabilities and initial stress effects. In this case there’s only one negative eigenvalue and it occurs for 0 Hz so I wouldn’t worry about that as long as other results look correct.

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3

Negative eigenvalues mean that the stiffness matrix is not positive definite. They can occur due to many different reasons but in natural frequency extraction analyses they are caused by instabilities and initial stress effects.

So in the present case, we can consider the forces acting as initial stress effects? (I assume initial stress is the same/similar as the pre-stress concept), and hence the results.

In this case there’s only one negative eigenvalue and it occurs for 0 Hz so I wouldn’t worry about that as long as other results look correct.

Yes looking at the results they look fine, nothing out of the ordinary.

4

Not in this particular case because such effects are considered in frequency analyses only when Nlgeom is used. But still, I would treat this as a numerical error with no significant impact on the results.

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