Research Article
Behaviour and Optimization Aids of Composite Stiffened Hypar Shell Roofs with Cutout under Free Vibration
Table 7
Values of “” for 0/90/0/90 hypar shells.
| Edge condition | | | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 |
| CCCC | 0.2 | 97.52 | 98.19 | 99.14 | 99.69 | 99.12 | 98.17 | 97.49 | 0.3 | 98.23 | 98.83 | 99.51 | 99.87 | 99.51 | 98.81 | 98.22 | 0.4 | 99.25 | 99.61 | 99.86 | 99.96 | 99.86 | 99.6 | 99.23 | 0.5 | 99.86 | 100.03 | 100.03 | 100 | 100.03 | 100.03 | 99.86 | 0.6 | 99.23 | 99.6 | 99.86 | 99.97 | 99.86 | 99.61 | 99.25 | 0.7 | 98.22 | 98.81 | 99.51 | 99.86 | 99.51 | 98.83 | 98.23 | 0.8 | 97.49 | 98.16 | 99.09 | 99.68 | 99.1 | 98.16 | 97.51 |
| CSCC | 0.2 | 99.53 | 99.69 | 100.03 | 100.24 | 100.03 | 99.68 | 99.47 | 0.3 | 100.24 | 100.15 | 100.25 | 100.35 | 100.26 | 100.16 | 100.21 | 0.4 | 100.09 | 99.84 | 100 | 100.19 | 100.02 | 99.86 | 100.1 | 0.5 | 97.94 | 98.62 | 99.33 | 100 | 99.34 | 98.63 | 98.79 | 0.6 | 97.34 | 97.15 | 98.3 | 99.78 | 98.29 | 97.16 | 97.35 | 0.7 | 96.37 | 95.99 | 96.98 | 99.42 | 96.98 | 96 | 96.38 | 0.8 | 95.87 | 95.29 | 95.69 | 96.68 | 95.7 | 95.3 | 95.89 |
| CCSC | 0.2 | 96.21 | 96.77 | 97.75 | 99.07 | 100.12 | 100.13 | 99.48 | 0.3 | 95.57 | 96.35 | 97.51 | 98.83 | 99.83 | 100.09 | 99.72 | 0.4 | 95.66 | 97.17 | 98.52 | 99.42 | 99.96 | 100.24 | 100.13 | 0.5 | 95.95 | 99.59 | 99.9 | 100 | 100.13 | 100.35 | 100.38 | 0.6 | 95.58 | 97.08 | 98.46 | 99.39 | 99.96 | 100.24 | 100.13 | 0.7 | 95.52 | 96.3 | 97.46 | 98.8 | 99.83 | 100.1 | 99.72 | 0.8 | 96.21 | 96.75 | 97.68 | 98.99 | 100.1 | 100.12 | 99.49 |
| CCCS | 0.2 | 95.89 | 95.31 | 95.71 | 96.64 | 95.67 | 95.29 | 95.87 | 0.3 | 96.38 | 96 | 96.97 | 99.41 | 96.96 | 95.99 | 96.37 | 0.4 | 97.35 | 97.16 | 98.29 | 99.78 | 98.29 | 97.15 | 97.34 | 0.5 | 98.79 | 98.63 | 99.34 | 100 | 99.33 | 98.62 | 98.78 | 0.6 | 100.1 | 99.86 | 100.02 | 100.19 | 100 | 99.84 | 100.08 | 0.7 | 100.21 | 100.16 | 100.26 | 100.35 | 100.25 | 100.15 | 100.21 | 0.8 | 99.32 | 99.49 | 99.83 | 100.05 | 99.83 | 99.47 | 99.31 |
| CSSC | 0.2 | 98.79 | 98.82 | 99.2 | 99.86 | 100.55 | 100.89 | 100.79 | 0.3 | 98.95 | 99.27 | 99.66 | 100.08 | 100.48 | 100.8 | 100.95 | 0.4 | 98.27 | 100.33 | 100.3 | 100.38 | 100.43 | 100.46 | 100.57 | 0.5 | 96.25 | 97.59 | 98.9 | 100 | 100.32 | 99.93 | 99.75 | 0.6 | 96.09 | 96.3 | 97.29 | 99.15 | 100.22 | 99.4 | 99.01 | 0.7 | 96.62 | 96.19 | 96.67 | 98.31 | 100.17 | 98.95 | 98.66 | 0.8 | 97.57 | 96.83 | 96.72 | 97.23 | 98.56 | 98.61 | 98.7 |
| CCSS | 0.2 | 97.54 | 96.8 | 96.73 | 97.24 | 98.51 | 98.56 | 98.64 | 0.3 | 96.61 | 96.18 | 96.66 | 98.3 | 100.13 | 98.91 | 98.62 | 0.4 | 96.14 | 96.34 | 97.32 | 99.15 | 100.2 | 99.37 | 98.99 | 0.5 | 96.32 | 97.69 | 98.95 | 100 | 100.29 | 99.9 | 99.73 | 0.6 | 98.28 | 100.3 | 100.27 | 100.34 | 100.38 | 100.41 | 100.53 | 0.7 | 98.84 | 99.19 | 99.6 | 100.03 | 100.44 | 100.76 | 100.91 | 0.8 | 98.65 | 98.67 | 98.92 | 99.56 | 100.32 | 100.69 | 100.63 |
| CSCS | 0.2 | 86.53 | 86.51 | 86.95 | 86.16 | 86.97 | 86.49 | 86.48 | 0.3 | 92.9 | 92.77 | 92.84 | 92.87 | 92.84 | 92.75 | 92.84 | 0.4 | 96.52 | 96.4 | 97.17 | 97.7 | 97.17 | 96.38 | 96.47 | 0.5 | 97.17 | 97.41 | 98.85 | 100 | 98.84 | 97.41 | 97.17 | 0.6 | 96.47 | 96.39 | 97.17 | 97.7 | 97.17 | 96.4 | 96.5 | 0.7 | 92.84 | 92.75 | 92.84 | 92.88 | 92.84 | 92.77 | 92.9 | 0.8 | 86.17 | 86.18 | 86.66 | 87.02 | 86.73 | 86.33 | 86.33 |
| SCSC | 0.2 | 86.38 | 92.89 | 97.14 | 98.25 | 97.12 | 92.87 | 86.36 | 0.3 | 86.43 | 92.92 | 96.97 | 98.23 | 96.93 | 92.87 | 85.96 | 0.4 | 86.9 | 92.92 | 97.45 | 99.25 | 97.39 | 92.87 | 86.84 | 0.5 | 87.13 | 92.85 | 97.71 | 100 | 97.71 | 92.85 | 87.13 | 0.6 | 86.84 | 92.87 | 97.39 | 99.25 | 97.45 | 92.92 | 86.9 | 0.7 | 86.39 | 92.87 | 96.93 | 98.22 | 96.95 | 92.92 | 86.43 | 0.8 | 86.27 | 92.76 | 97.09 | 98.14 | 97.05 | 92.8 | 86.31 |
| CSSS | 0.2 | 87.55 | 87.4 | 87.57 | 88.03 | 88.73 | 89.14 | 88.85 | 0.3 | 94.37 | 94.44 | 94.06 | 94.01 | 95.18 | 96.65 | 96.62 | 0.4 | 98.85 | 98.84 | 98.33 | 98.33 | 99.99 | 101.94 | 101.87 | 0.5 | 100.37 | 100.28 | 99.82 | 100 | 101.89 | 103.9 | 103.68 | 0.6 | 98.76 | 98.77 | 98.29 | 98.31 | 99.99 | 101.94 | 101.87 | 0.7 | 94.28 | 94.37 | 94.02 | 93.98 | 95.16 | 96.63 | 96.59 | 0.8 | 87.17 | 87.1 | 87.29 | 87.74 | 88.4 | 88.85 | 88.6 |
| SSSC | 0.2 | 89.01 | 96.86 | 102.03 | 103.78 | 102.03 | 96.86 | 88.99 | 0.3 | 89.2 | 96.84 | 102.06 | 103.95 | 102.06 | 96.82 | 89.16 | 0.4 | 88.7 | 95.26 | 100.02 | 101.88 | 100.03 | 95.26 | 88.7 | 0.5 | 87.94 | 94.02 | 98.32 | 100 | 98.39 | 94.1 | 88 | 0.6 | 87.47 | 94.07 | 98.36 | 99.88 | 98.44 | 94.18 | 87.55 | 0.7 | 87.29 | 94.47 | 98.9 | 100.4 | 98.98 | 94.56 | 87.38 | 0.8 | 87.34 | 94.26 | 98.78 | 100.33 | 98.84 | 94.35 | 87.42 |
| SSCS | 0.2 | 88.83 | 89.09 | 88.68 | 88 | 87.53 | 87.34 | 87.45 | 0.3 | 96.58 | 96.62 | 95.15 | 93.97 | 94.01 | 94.37 | 94.27 | 0.4 | 101.85 | 101.94 | 99.98 | 98.3 | 98.27 | 98.77 | 98.78 | 0.5 | 103.67 | 103.9 | 101.89 | 100 | 99.82 | 100.28 | 100.36 | 0.6 | 101.87 | 101.94 | 99.98 | 98.33 | 98.32 | 98.83 | 98.83 | 0.7 | 96.61 | 96.65 | 95.17 | 94 | 94.05 | 94.44 | 94.37 | 0.8 | 88.43 | 88.7 | 88.33 | 87.77 | 87.26 | 87.21 | 87.22 |
| SSSS | 0.2 | 83.79 | 86.96 | 87.85 | 88.06 | 87.93 | 87.06 | 83.88 | 0.3 | 87.24 | 93.04 | 94.61 | 94.75 | 94.7 | 93.12 | 87.28 | 0.4 | 88.2 | 94.89 | 98.09 | 98.78 | 98.2 | 94.94 | 88.2 | 0.5 | 88.38 | 95.08 | 99.09 | 100 | 99.09 | 95.08 | 88.38 | 0.6 | 88.21 | 94.95 | 98.2 | 98.78 | 98.09 | 94.89 | 88.2 | 0.7 | 87.28 | 93.12 | 94.68 | 94.75 | 94.61 | 93.04 | 87.24 | 0.8 | 83.72 | 86.9 | 87.65 | 87.76 | 87.44 | 86.79 | 83.43 |
|
|
, , , ; , , , , , . Each stiffener has a single lamina with fibres along its length.
|