# Total effective mass differs if using density or lumped masses

Hi all,

I use ccx to do modal vibration analysis in 3D. I’d like to understand why ccx compute a widely different total effective mass if I am using density or lumped masses.

Here is a simple example. I computed the total effective mass of a cantilever beam (1,2m long, rectangular bar section 0,05x0,20m, “density 7860kg/m3” or “density 1kg/m3 + lumped mass total 94kg”).

The expected results are :

• the mass of the cantilever beam is 94kg
• the effective modal mass should be 8/9*94=84kg since there is 1 fixed node and 9 nodes in total in this example (at least when I use lumped masses)
• the first eigen mode is 28Hz.

Example1 : If I compute the modes using a material density (7860kg/m3) for the bar and no lumped mass, the dat file show :

• the good frequency (28Hz)
• a total effective mass of 818 → it is 10 times the effective mass computed below with lumped masses
• see inp file example 1 below

Example2 : If I compute the modes using lumped mass (total lumped mass of 94kg=9 nodes x10.444kg/nodes) instead of density (1kg/m3 instead of 7860kg/m3 to neutralize density), the dat file show :

• a relatively good frequency (27Hz) → OK I use a very coarse mesh in this example
• a total effective mass of 84 → OK
• see inp file example 2 below

My final aim is not to compute the total effective mass mtot, but to compute the effective modal mass mi of each mode. Since I cannot understand CCX results for mtot for now, I am not sure if the values mi are correct or not.

Does anybody know why using density or lumped mass give so different results (factor 10) regarding modal mass ?

I initially asked the question on the Mecway forum (which use ccx as solver), but I guess the answer lies in ccx and not in Mecway (my previous message is : CCX modal mass with density / with lumped masses - Forum). I reproduce below the inp file of both examples generated by Mecway. Victor of Mecway suggested the answer might be related to the units mass*length^2 given in ccx manual for modal mass. But even so, why the widely different total masses whatever the units are ?

Example 1 with density only
** Generated by Mecway 13.0
*NODE
1,0,0,0
2,1.2,0,0
3,0.6,0,0
4,0.3,0,0
5,0.9,0,0
6,0.15,0,0
7,0.45,0,0
8,0.75,0,0
9,1.05,0,0
*ELEMENT,TYPE=B31
1,1,6
2,6,4
3,4,7
4,7,3
5,3,8
6,8,5
7,5,9
8,9,2
*NSET,NSET=fixed_support_nodes
1
*ELSET,ELSET=Default
1
2
3
4
5
6
7
8
*MATERIAL,NAME=Material
*ELASTIC,TYPE=ISOTROPIC
200000000000,0.3
*DENSITY
7860
*BEAM SECTION,ELSET=Default,MATERIAL=Material,SECTION=RECT
0.2,0.05
0,1,0
*BOUNDARY
1,1,0
1,2,0
1,3,0
1,4,0
1,5,0
1,6,0
*STEP
*FREQUENCY
4
*NODE FILE,GLOBAL=YES
U
*END STEP

Example 2 with lumped masses and very low density
** Generated by Mecway 13.0
*NODE
1,0,0,0
2,1.2,0,0
3,0.6,0,0
4,0.3,0,0
5,0.9,0,0
6,0.15,0,0
7,0.45,0,0
8,0.75,0,0
9,1.05,0,0
*ELEMENT,TYPE=B31
1,2,9
2,9,5
3,5,8
4,8,3
5,3,7
6,7,4
7,4,6
8,6,1
*ELEMENT,TYPE=MASS
9,1
10,6
11,4
12,7
13,3
14,8
15,5
16,9
17,2
*NSET,NSET=fixed_support_nodes
1
*NSET,NSET=mass_nodes
1
2
3
4
5
6
7
8
9
*ELSET,ELSET=Default
1
2
3
4
5
6
7
8
*ELSET,ELSET=Mass_1
9
10
11
12
13
14
15
16
17
*MATERIAL,NAME=Material
*ELASTIC,TYPE=ISOTROPIC
200000000000,0.3
*DENSITY
1
*BEAM SECTION,ELSET=Default,MATERIAL=Material,SECTION=RECT
0.2,0.05
0,-1,0
*BOUNDARY
1,1,0
1,2,0
1,3,0
1,4,0
1,5,0
1,6,0
*MASS,ELSET=Mass_1
10.44444444444
*STEP
*FREQUENCY
4
*NODE FILE,GLOBAL=YES
U
*END STEP

View of cantilever bar with lumped masses (example 2)

1 Like

hi, although I did not really understand why these problem occurs for B31 element. try switching to B32 element eliminate it’s condition.

1 Like

Hi xyont,

Thank you for your quick answer. Using B32 elements (line3 elements in Mecway) instead of B31 elements (line2 elements in Mecway) indeed solved the problem. Obsviously the results are not exactly the same using lumped masses and density, but they are pretty close for frequency, modal mass of individual modes and effective total mass (difference around 1%).

So I guess it is a bug and one should not use B21 elements for vibration analysis. By the way I used ccx 16 (delivered with Mecway 13), maybe it will be corrected in future versions.