Research Article
A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
Table 8
Nondimensional frequency parameter of uniform 45 degrees spherical cap with different edge conditions.
| | n | m | Boundary conditions | | CE | SSE | Axial elastic support | Circumferential elastic support | Radial elastic support | Rotational elastic support |
| | 1 | 1 | 0.9712 | 0.9710 | 0.3044 | 0.2513 | 0.2895 | 0.0315 | | 2 | 1.0339 | 1.0246 | 0.9716 | 0.9716 | 0.9911 | 0.9752 | | 3 | 1.1508 | 1.1120 | 1.0280 | 1.0280 | 1.0860 | 1.0474 | | 4 | 1.3856 | 1.3141 | 1.1486 | 1.1486 | 1.2541 | 1.1953 | | 5 | 1.7551 | 1.6509 | 1.3861 | 1.3862 | 1.5037 | 1.4665 |
| | 2 | 1 | 1.0161 | 1.0137 | 0.1491 | 0.1494 | 0.3964 | 0.0791 | | 2 | 1.1034 | 1.0987 | 0.9928 | 0.9928 | 1.0212 | 1.0009 | | 3 | 1.2618 | 1.2123 | 1.0723 | 1.0723 | 1.1463 | 1.1014 | | 4 | 1.5552 | 1.4657 | 1.2450 | 1.2450 | 1.3556 | 1.3057 | | 5 | 1.9888 | 1.8658 | 1.5477 | 1.5477 | 1.6534 | 1.6430 |
| | 3 | 1 | 1.0441 | 1.0438 | 0.1501 | 0.1502 | 0.4852 | 0.1424 | | 2 | 1.1611 | 1.1453 | 1.0189 | 1.0189 | 1.0573 | 1.0320 | | 3 | 1.3807 | 1.3159 | 1.1357 | 1.1357 | 1.2214 | 1.1753 | | 4 | 1.7414 | 1.6371 | 1.3679 | 1.3679 | 1.4757 | 1.4420 | | 5 | 2.2385 | 2.1012 | 1.7362 | 1.7362 | 1.8292 | 1.8450 |
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