Research Article
Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions
Table 7
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 | 14.751 | 14.917 | 28.232 | 55.251 | 55.397 | 69.512 | (14.780b) | (14.822) | (29.252) | (55.476) | (55.505) | (70.904) | 0.1 | 11.811 | 11.910 | 23.857 | 44.462 | 45.037 | 55.453 | (11.818b) | (11.897) | (24.711) | (44.376) | (45.257) | (56.511) | 0.15 | 8.487 | 8.514 | 20.011 | 34.783 | 36.335 | 44.970 | (8.500b) | (8.544) | (20.738) | (34.404) | (36.663) | (45.625) | 0.2 | 6.073 | 6.073 | 17.431 | 28.679 | 30.805 | 38.010 | (6.096b) | (6.106) | (18.039) | (28.129) | (31.165) | (38.311) |
| 1 | 0.5 | 0.05 | 21.225 | 32.173 | 32.173 | 44.381 | 64.061 | 65.222 | (20.708b) | (32.097) | (32.285) | (45.110) | (64.182) | (65.355) | 0.1 | 8.140 | 16.878 | 16.941 | 28.100 | 48.663 | 49.015 | (7.943b) | (16.838) | (16.970) | (28.888) | (48.700) | (49.171) | 0.15 | 4.493 | 11.859 | 11.878 | 22.429 | 38.352 | 39.247 | (4.383b) | (11.867) | (11.891) | (23.125) | (38.177) | (39.488) | 0.2 | 2.932 | 8.690 | 8.691 | 18.919 | 31.108 | 32.600 | (3.540b) | (8.791) | (8.791) | (16.229) | (27.520) | (27.889) |
| 1.5 | 1 | 0.05 | 27.819 | 40.919 | 41.430 | 54.595 | 70.792 | 72.896 | (27.146b) | (41.008) | (41.434) | (55.256) | (70.895) | (73.051) | 0.1 | 11.285 | 20.068 | 20.230 | 31.101 | 51.046 | 51.429 | (11.012b) | (20.025) | (20.270) | (31.849) | (51.126) | (51.569) | 0.15 | 6.292 | 13.912 | 13.922 | 24.132 | 40.500 | 41.120 | (6.139b) | (13.912) | (13.934) | (24.808) | (40.426) | (41.316) | 0.2 | 4.121 | 10.321 | 10.331 | 20.051 | 32.796 | 33.921 | (4.021b) | (10.329) | (10.357) | (20.635) | (32.540) | (34.178) |
| 2 | 2 | 0.05 | 34.615 | 51.972 | 53.088 | 68.255 | 81.344 | 84.510 | (33.806b) | (52.100) | (53.157) | (68.891) | (81.433) | (84.761) | 0.1 | 15.416 | 24.659 | 24.829 | 35.615 | 53.879 | 54.494 | (15.045b) | (24.625) | (24.888) | (36.303) | (53.970) | (54.626) | 0.15 | 8.740 | 16.420 | 16.481 | 26.353 | 42.417 | 42.946 | (8.529b) | (16.414) | (16.499) | (26.996) | (42.398) | (43.114) | 0.2 | 5.761 | 12.127 | 12.127 | 21.434 | 34.286 | 35.192 | (5.622b) | (12.134) | (12.148) | (21.998) | (34.110) | (35.415) |
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, , ). Results in parentheses are taken from FEM.
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