# In Release 10.0, why are the modal participation factors different for a model with a doubly symmetric cross-section as opposed to an equivalent model with a slightly non-doubly symmetric cross-section?

 Below are two examples of an open box modeled with SHELL elements. In one model, the cross-section is doubly symmetric (i.e., square cross-section). In the other model, the width of cross-section is 0.1% larger than the height (i.e., rectangular cross-section). The calculated frequencies and total effective mass for each mode are almost identical for both models. However, the participation factors for individual modes are different. For the single symmetry model, the effective mass for the first mode acts entirely along the Y axis, and the effective mass for the second mode acts entirely along the Y axis. For the double symmetry model, the effective mass along the X and Y axes are distributed between the first and second modes. The sum of the effective masses for mode 1 and 2 are almost identical for both models.The reason for this discrepancy is that the double symmetry model does not have one distinct set of solutions. It has a range of possible solutions. The single symmetry model has one distinct set of solutions. In the doubly symmetric model, the first mode could act entirely along the X axis, entirely along the Y axis, or at some angle in the XY plane. Small perturbations in the solution process can produce different results. In the example below, the calculated modes are rotated in the XY plane.This behavior is not an issue in the frequency calculation. However, it could be an issue in subsequent analyses that use the effective mass (e.g., SPECTRUM). To avoid any potential problems, you should include all the appropriate modes that have effective masses in a particular direction. For this example, if modes 1 and 2 are included in a SPECTRUM analysis, then the results will be equivalent for both models. However, if only mode 1 is included, the SPECTRUM results will be different. The results for the doubly symmetric model will be incorrect.! double symmetry modeldel = 1e-6wid = 1hgt = 1len = 5thk = 0.1/prep7et,1,181,,,2sectype,1,shellsecdata,.1mp,ex,1,2e11mp,prxy,1,0.3mp,dens,1,7850block,-wid/2,wid,-hgt/1,hgt/2,0,lenesize,.2amesh,allnsel,s,loc,z,-del,deld,all,all,0alls/soluantype,modalmodop,lanb,2solve ***** PARTICIPATION FACTOR CALCULATION ***** X DIRECTION CUMULATIVE MODE FREQUENCY PERIOD PARTIC.FACTOR RATIO EFFECTIVE MASS MASS FRACTION 1 50.5841 0.19769E-01 71.738 0.667703 5146.33 0.308355 2 50.5841 0.19769E-01 107.44 1.000000 11543.3 1.00000 SUM OF EFFECTIVE MASSES= 16689.7 ***** PARTICIPATION FACTOR CALCULATION ***** Y DIRECTION CUMULATIVE MODE FREQUENCY PERIOD PARTIC.FACTOR RATIO EFFECTIVE MASS MASS FRACTION 1 50.5841 0.19769E-01 107.44 1.000000 11543.3 0.691645 2 50.5841 0.19769E-01 -71.738 0.667703 5146.33 1.00000 SUM OF EFFECTIVE MASSES= 16689.7! single symmetry modeldel = 1e-6wid = 1.0001hgt = 1len = 5thk = 0.1/prep7et,1,181,,,2sectype,1,shellsecdata,.1mp,ex,1,2e11mp,prxy,1,0.3mp,dens,1,7850block,-wid/2,wid,-hgt/1,hgt/2,0,lenesize,.2amesh,allnsel,s,loc,z,-del,deld,all,all,0alls/soluantype,modalmodop,lanb,2solve***** PARTICIPATION FACTOR CALCULATION ***** X DIRECTION CUMULATIVE MODE FREQUENCY PERIOD PARTIC.FACTOR RATIO EFFECTIVE MASS MASS FRACTION 1 50.5837 0.19769E-01 -0.22894E-07 0.000000 0.524113E-15 0.314017E-19 2 50.5873 0.19768E-01 129.19 1.000000 16690.6 1.00000 SUM OF EFFECTIVE MASSES= 16690.6 ***** PARTICIPATION FACTOR CALCULATION ***** Y DIRECTION CUMULATIVE MODE FREQUENCY PERIOD PARTIC.FACTOR RATIO EFFECTIVE MASS MASS FRACTION 1 50.5837 0.19769E-01 129.19 1.000000 16690.7 1.00000 2 50.5873 0.19768E-01 0.22466E-07 0.000000 0.504722E-15 1.00000 SUM OF EFFECTIVE MASSES= 16690.7