Research Article
Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions
Table 5
Frequencies (Hz) of
cylindrical shell with FFCF boundary constraints and varying gradient power-law exponent
(
GPa,
GPa,
,
kg/m
3,
kg/m
3,
,
,
,
).
| | Method | Mode number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 0 | Present | 61.03 | 94.83 | 153.13 | 241.67 | 276.26 | 291.68 | 355.13 | 450.74 | 512.49 | [58] | 61.02 | 94.82 | 153.13 | 241.39 | 275.83 | 291.45 | 355.14 | 450.76 | 511.92 | [26] | 61.06 | 94.92 | 153.11 | 241.75 | 276.37 | 291.94 | 355.07 | 450.82 | 512.48 |
| 0.6 | Present | 59.11 | 92.94 | 148.16 | 234.52 | 266.87 | 287.37 | 342.44 | 442.01 | 495.33 | [58] | 59.24 | 93.14 | 148.51 | 234.79 | 267.06 | 287.85 | 343.22 | 443.06 | 495.89 | [26] | 59.13 | 93.03 | 148.14 | 234.60 | 266.97 | 287.63 | 342.38 | 442.09 | 495.31 |
| 1 | Present | 58.79 | 92.39 | 147.51 | 233.23 | 265.51 | 285.52 | 341.09 | 439.41 | 492.81 | [58] | 58.96 | 92.65 | 147.94 | 233.64 | 265.86 | 286.16 | 342.08 | 440.72 | 493.67 | [26] | 58.82 | 92.48 | 147.49 | 233.31 | 265.61 | 285.77 | 341.04 | 439.49 | 492.80 |
| 5 | Present | 59.93 | 91.45 | 151.59 | 236.35 | 272.08 | 278.81 | 353.89 | 435.11 | 504.54 | [58] | 60.09 | 91.69 | 152.02 | 236.75 | 272.42 | 279.34 | 354.89 | 436.34 | 505.35 | [26] | 59.96 | 91.54 | 151.57 | 236.42 | 272.19 | 279.06 | 353.83 | 435.18 | 504.56 |
| 20 | Present | 59.13 | 90.21 | 149.31 | 233.26 | 268.47 | 275.15 | 348.37 | 429.12 | 497.85 | [58] | 59.19 | 90.29 | 149.49 | 233.27 | 268.37 | 275.23 | 348.80 | 429.63 | 497.87 | [26] | 59.16 | 90.30 | 149.29 | 233.32 | 268.57 | 275.41 | 348.32 | 429.19 | 497.87 |
| 50 | Present | 58.18 | 89.52 | 146.47 | 229.93 | 263.84 | 274.07 | 340.84 | 425.59 | 489.36 | [58] | 58.20 | 89.55 | 146.55 | 229.79 | 263.58 | 273.98 | 341.04 | 425.83 | 489.06 | [26] | 58.21 | 89.60 | 146.45 | 230.00 | 263.95 | 274.32 | 340.79 | 425.66 | 489.36 |
| 100 | Present | 57.72 | 89.21 | 145.09 | 228.32 | 261.56 | 273.66 | 337.14 | 424.02 | 485.17 | [58] | 57.73 | 89.21 | 145.14 | 228.12 | 261.23 | 273.51 | 337.25 | 424.15 | 484.75 | [26] | 57.75 | 89.29 | 145.08 | 228.39 | 261.66 | 273.90 | 337.09 | 424.10 | 485.16 |
| ∞ | Present | 57.17 | 88.83 | 143.43 | 226.37 | 258.77 | 273.21 | 332.64 | 422.20 | 480.04 | [58] | 57.16 | 88.81 | 143.43 | 226.11 | 258.36 | 273.00 | 332.65 | 422.21 | 479.49 | [26] | 57.19 | 88.91 | 143.41 | 226.44 | 258.87 | 273.46 | 332.59 | 422.27 | 480.02 |
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