PSI - Issue 47

Yaroslav Dubyk et al. / Procedia Structural Integrity 47 (2023) 863–872 Yaroslav Dubyk et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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Table 2. Frequency parameter comparison for F-F boundary conditions. For parameters definition see Table 1. Model n 3 6 9 12 15 18 21 24 - Cone as cylinders 0.8268 3.4991 7.2334 12.0982 18.1964 25.5623 34.1957 44.0625 Cone 0.8380 3.5551 7.2199 12.0149 18.1000 25.4637 34.0833 43.9587 0.6688 2.8256 6.1622 10.2578 15.2928 21.4174 28.6693 - Cone as cylinders 0.6564 2.7873 6.1293 10.1218 14.8993 20.5964 27.2580 34.8841 Cone 0.7387 2.9068 6.3309 10.3532 15.0633 20.7602 27.4291 35.0549 1 Experiment 0.7976 3.4427 7.0575 12.1354 18.3035 26.3077 - 2 Experiment

Experiment

0.6352 2.5705 5.7170 9.5283

14.1019 19.5224 25.7476 33.4549 13.5817 18.6123 24.5023 31.2266 14.1963 19.2352 25.1503 31.9081 13.0447 18.0546 23.7262 30.2958 12.2521 16.7945 22.0704 28.1645 13.4367 18.0823 23.4239 29.5366

3

Cone as cylinders 0.6134 2.4841 5.5176 9.2842

Cone

0.7145 2.6694 5.7871 9.7979 0.6002 2.3726 5.1990 8.7910

Experiment

4

Cone as cylinders 0.5718 2.2646 5.0013 8.4151

Cone

0.6846 2.5090 5.3491 9.1296

The effect of initial stresses in a simple supported conical shell was compared with the Ansys code solution for 9600 surface elements. Cylindrical shell is one of the cases of a conical shell in which side surface inclination angle is 0 0 , so to study effect of initial stresses was chosen scheme where conical shell is represented by sets of cylinders. On fig. 4-5 our solution is marked with a solid line, Ansys solution marked with markers. Figure 4a shows a comparison frequency parameter  with circumferential number n for 0.2 MPa internal pressure, and figure 4b for external pressure 0.2 MPa. Figures 5a and 5b show a comparison frequency parameter  with n for compression force 86942 N and compression force 86942 N with external pressure 0.2 MPa, respectively.

Fig. 4. S-S conical shell: α=20 0 , x

2 /x 1 =1,78, h/R=0,0041, R=123,7 mm, E=207 GPa, ρ=8200 kg/m P external =0.2 MPa. ( ○ ) m=1; ( □ ) m=2; ( Δ ) m = 3; ( ◊ ) m = 4: Ansys results,

3 , µ=0,3; (a) with P

internal =0.2 MPa (b) with

our results.