Research Article
Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions
Table 2
Frequency parameters
for uniform thickness moderately thick plates with different classical boundaries and structure parameters.
| | Boundary condition | a/b | Model sequence | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| | S-S-S-S | 1 | 1.931 | 4.605 | 4.605 | 7.064 | 8.605 | 8.605 | 10.792 | 10.792 | | (1.933a) | (4.611) | (4.611) | (7.067) | (8.607) | (8.607) | (10.799) | (10.780) | | (1.931b) | (4.605) | (4.605) | (7.064) | (8.605) | (8.605) | (10.792) | (10.792) | | 3/2 | 1.408 | 2.648 | 4.127 | 4.605 | 5.261 | 7.064 | 7.153 | 8.184 | | (1.410a) | (2.651) | (4.128) | (4.608) | (5.267) | (7.074) | (7.155) | (8.188) | | (1.408b) | (2.648) | (4.127) | (4.605) | (5.261) | (7.064) | (7.151) | (8.184) |
| | C-F-F-F | 1 | 0.348 | 0.817 | 2.035 | 2.583 | 2.862 | 4.816 | 5.478 | 5.774 | | (0.348a) | (0.817) | (2.038) | (2.586) | (2.865) | (4.821) | (5.504) | (5.793) | | (0.348b) | (0.816) | (2.034) | (2.582) | (2.860) | (4.811) | (5.477) | (5.772) | | 3/2 | 0.155 | 0.502 | 0.941 | 1.665 | 2.292 | 2.613 | 3.303 | 3.498 | | (0.154a) | (0.502) | (0.941) | (1.663) | (2.295) | (2.618) | (3.305) | (3.500) | | (0.154b) | (0.501) | (0.940) | (1.662) | (2.292) | (2.612) | (3.298) | (3.494) |
| | S-S-F-F | 1 | 0.333 | 1.678 | 1.875 | 3.559 | 4.720 | 4.946 | 6.474 | 6.632 | | (0.335a) | (1.680) | (1.878) | (3.600) | (4.721) | (4.949) | (6.478) | (6.642) | | (0.333b) | (1.677) | (1.874) | (3.557) | (4.718) | (4.945) | (6.472) | (6.631) | | 3/2 | 0.222 | 0.938 | 1.631 | 2.363 | 2.573 | 4.082 | 4.482 | 4.753 | | (0.223a) | (0.940) | (1.632) | (2.364) | (2.575) | (4.092) | (4.483) | (4.759) | | (0.222b) | (0.938) | (1.631) | (2.361) | (2.571) | (4.077) | (4.479) | (4.752) |
| | F-F-F-F | 1 | 1.290 | 1.919 | 2.363 | 3.235 | 3.235 | 5.605 | 5.605 | 5.646 | | (1.291a) | (1.920) | (2.365) | (3.239) | (3.239) | (5.607) | (5.607) | (6.648) | | 3/2 | 0.865 | 0.948 | 1.961 | 2.166 | 2.461 | 2.843 | 3.551 | 4.026 | | (0.865a) | (0.949) | (1.963) | (2.168) | (2.465) | (2.844) | (3.556) | (4.034) |
| | S-C-S-C | 1 | 2.700 | 4.971 | 5.990 | 7.973 | 8.787 | 10.250 | 11.334 | 12.024 | | (2.701a) | (4.971) | (5.993) | (7.975) | (8.788) | (10.253) | (11.335) | (12.028) | | 3/2 | 2.348 | 3.253 | 4.972 | 5.646 | 6.489 | 7.381 | 7.974 | 9.930 | | (2.348a) | (3.255) | (4.974) | (5.647) | (6.590) | (7.384) | (7.801) | (9.932) |
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Results in parentheses are taken from FEM.
Results in parentheses are taken from [11].
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