Research Article
Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions
Table 11
Frequency parameter
for moderately thick plates (
) with linearly varying thickness and elastic rotation and translation support (
,
, and
).
| | | | Model sequence | | 1 | 2 | 3 | 4 | 5 | 6 |
| | 0.5 | 0 | 0.05 | 12.926 | 13.041 | 25.090 | 47.935 | 47.943 | 61.761 | | (12.931b) | (13.053) | 25.099 | (47.947) | (47.952) | (61.788) | | 0.1 | 10.900 | 10.988 | 21.545 | 39.980 | 40.147 | 50.322 | | (10.904b) | (10.992) | (21.557) | (39.984) | (40.166) | (50.334) | | 0.15 | 8.245 | 8.298 | 18.081 | 31.503 | 32.617 | 40.950 | | (8.247b) | (8.230) | (18.092) | (31.508) | (32.622) | (40.955) | | 0.2 | 6.106 | 6.124 | 15.639 | 25.631 | 27.601 | 34.458 | | (6.110b) | (6.125) | (15.642) | (25.637) | (27.617) | (34.462) |
| | 1 | 0.5 | 0.05 | 21.575 | 31.615 | 31.644 | 42.573 | 57.889 | 58.607 | | (21.580b) | (31.617) | (31.644) | (42.581) | (57.893) | (58.610) | | 0.1 | 8.451 | 16.024 | 16.210 | 25.969 | 43.839 | 43.867 | | (8.451b) | (16.025) | (16.217) | (25.972) | (43.844) | (43.870) | | 0.15 | 4.682 | 11.479 | 11.480 | 20.642 | 35.172 | 35.598 | | (4.684b) | (11.480) | (11.481) | (20.644) | (35.178) | (35.604) | | 0.2 | 3.059 | 8.621 | 8.648 | 17.320 | 28.487 | 29.638 | | (3.062b) | (8.619) | (8.644) | (17.327) | (28.492) | (29.641) |
| | 1.5 | 1 | 0.05 | 27.713 | 40.203 | 40.978 | 52.951 | 65.352 | 66.815 | | (27.714b) | (40.207) | (40.988) | (52.972) | (65.368) | (66.822) | | 0.1 | 11.667 | 19.322 | 19.615 | 29.122 | 46.115 | 46.183 | | (11.674b) | (19.327) | (19.619) | (29.137) | (46.120) | (46.188) | | 0.15 | 6.544 | 13.416 | 13.481 | 22.405 | 37.238 | 37.430 | | (6.547b) | (13.420) | (13.488) | (22.410) | (37.241) | (37.434) | | 0.2 | 4.295 | 10.175 | 10.190 | 18.543 | 30.330 | 31.056 | | (4.296b) | (10.177) | (10.194) | (18.544) | (30.336) | (31.060) |
| | 2 | 2 | 0.05 | 33.453 | 50.854 | 52.088 | 66.311 | 76.610 | 78.947 | | (33.455b) | (50.852) | (50.097) | (66.321) | (76.627) | (78.971) | | 0.1 | 15.832 | 24.130 | 24.372 | 33.924 | 49.118 | 49.362 | | (15.830b) | (24.127) | (24.374) | (33.931) | (49.147) | (49.382) | | 0.15 | 9.060 | 15.956 | 16.099 | 24.754 | 39.134 | 39.249 | | (9.064b) | (15.961) | (16.102) | (24.755) | (39.138) | (39.452) | | 0.2 | 5.992 | 11.955 | 11.971 | 20.034 | 31.908 | 32.392 | | (5.991b) | (11.957) | (11.978) | (20.042) | (31.910) | (32.398) |
|
|
, ), , ).
Results in parentheses are taken from FEM.
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