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 ?

Thanks for your help

**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)**