ansys

what is cumulative mass fraction?

i am doing modal analysis of a cantilever using ANSYS 19.R2, in the result tables (effective mass & participation factor) there is a column called (cumulative mass fraction) , what is cumulative mass fraction and how to be calculated ? .Also when i tried to find the ratio between effective mass to total mass (by dividing effective mass/total mass) it didn't match the mentioned ratio in the last column, what is wrong with that ?

    TOTAL MASS = 0.16200

    


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          ***** PARTICIPATION FACTOR CALCULATION *****ROTY DIRECTION
                                                                                  CUMULATIVE     RATIO EFF.MASS
  MODE   FREQUENCY       PERIOD      PARTIC.FACTOR     RATIO    EFFECTIVE MASS   MASS FRACTION   TO TOTAL MASS
     1     9.87449       0.10127      -0.42882E-01    0.623472    0.183887E-02    0.169375        0.136208    
     2     61.8617       0.16165E-01   0.68780E-01    1.000000    0.473062E-02    0.605105        0.350404    
     3     130.200       0.76805E-02    0.0000        0.000000     0.00000        0.605105         0.00000    
     4     173.265       0.57715E-02  -0.44597E-01    0.648408    0.198891E-02    0.788299        0.147321    
     5     231.543       0.43189E-02  -0.71107E-08    0.000000    0.505616E-16    0.788299        0.374517E-14
     6     339.795       0.29430E-02   0.33295E-01    0.484079    0.110854E-02    0.890405        0.821111E-01
     7     562.331       0.17783E-02  -0.26529E-01    0.385710    0.703786E-03    0.955229        0.521304E-01
     8     697.127       0.14345E-02   0.83584E-08    0.000000    0.698636E-16    0.955229        0.517490E-14
     9     792.583       0.12617E-02    0.0000        0.000000     0.00000        0.955229         0.00000    
    10     841.121       0.11889E-02   0.22047E-01    0.320544    0.486065E-03     1.00000        0.360035E-01
Solution

  • Cards on the table, I am citing the ansys documentation here. The cumulative mass fraction for the i-th mode is:

    enter image description here

    So for example the cumulative mass fraction of your 4-th mode is

    (0.00183887 + 0.00473062 + 0 + 0.00198891) / 0.1085679 =

    78.8299%