Research Article
Free Vibration Analysis of Moderately Thick Rectangular Plates with Variable Thickness and Arbitrary Boundary Conditions
Table 3
Frequency parameters
for S-S-S-S moderately thick plates (
) with uniform thickness and elastic rotation support (
).
| | | Model sequence | | 1 | 2 | 3 | 4 | 5 | 6 |
| | 0 | 0.05 | 1.945 | 4.834 | 4.834 | 7.591 | 9.515 | 9.519 | | (1.942b) | (4.836) | (4.836) | (7.584) | (9.547) | (9.552) | | 0.1 | 1.856 | 4.500 | 4.500 | 6.829 | 8.499 | 8.513 | | (1.858b) | (4.510) | (4.510) | (6.843) | (8.539) | (8.554) | | 0.15 | 1.758 | 4.114 | 4.114 | 6.040 | 7.421 | 7.445 | | (1.761b) | (4.126) | (4.126) | (6.060) | (7.462) | (7.486) | | 0.2 | 1.656 | 3.733 | 3.733 | 5.335 | 6.468 | 6.499 | | (1.660b) | (3.747) | (3.747) | (5.357) | (6.508) | (6.538) |
| | 0.5 | 0.05 | 3.541 | 7.071 | 7.071 | 10.227 | 12.318 | 12.399 | | (3.546b) | (7.091) | (7.091) | (10.253) | (12.386) | (12.468) | | 0.1 | 3.274 | 6.242 | 6.242 | 8.719 | 10.302 | 10.421 | | (3.282b) | (6.267) | (6.267) | (8.754) | (10.370) | (10.488) | | 0.15 | 2.947 | 5.361 | 5.361 | 7.290 | 8.465 | 8.606 | | (2.956b) | (5.387) | (5.387) | (7.327) | (8.524) | (8.666) | | 0.2 | 2.624 | 4.599 | 4.599 | 6.148 | 7.057 | 7.199 | | (2.634b) | (4.624) | (4.624) | (6.182) | (7.107) | (7.250) |
| | 1 | 0.05 | 3.541 | 7.072 | 7.072 | 10.228 | 12.320 | 12.401 | | (3.547b) | (7.093) | (7.093) | (10.254) | (12.388) | (12.470) | | 0.1 | 3.278 | 6.248 | 6.248 | 8.727 | 10.311 | 10.429 | | (3.286b) | (6.274) | (6.274) | (8.762) | (10.378) | (10.497) | | 0.15 | 2.957 | 5.374 | 5.374 | 7.305 | 8.478 | 8.620 | | (2.966b) | (5.400) | (5.400) | (7.341) | (8.537) | (8.680) | | 0.2 | 2.641 | 4.617 | 4.617 | 6.166 | 7.070 | 7.215 | | (2.651b) | (4.643) | (4.643) | (6.200) | (7.121) | (7.268) |
| | 1.5 | 0.05 | 3.542 | 7.073 | 7.073 | 10.229 | 12.320 | 12.401 | | (3.547b) | (7.093) | (7.093) | (10.254) | (12.388) | (12.471) | | 0.1 | 3.280 | 6.251 | 6.251 | 8.729 | 10.313 | 10.432 | | (3.287b) | (6.276) | (6.276) | (8.765) | (10.381) | (10.500) | | 0.15 | 2.960 | 5.379 | 5.379 | 7.309 | 8.482 | 8.625 | | (2.969b) | (5.405) | (5.405) | (7.346) | (8.541) | (8.685) | | 0.2 | 2.647 | 4.623 | 4.623 | 6.172 | 7.074 | 7.221 | | (2.657b) | (4.649) | (4.649) | (6.206) | (7.125) | (7.274) |
| | 2 | 0.05 | 3.542 | 7.073 | 7.073 | 10.229 | 12.321 | 12.402 | | (3.547b) | (7.093) | (7.093) | (10.255) | (12.389) | (12.471) | | 0.1 | 3.280 | 6.252 | 6.252 | 8.730 | 10.315 | 10.434 | | (3.288b) | (6.277) | (6.277) | (8.766) | (10.382) | (10.501) | | 0.15 | 2.962 | 5.381 | 5.381 | 7.312 | 8.484 | 8.628 | | (2.971b) | (5.407) | (5.407) | (7.348) | (8.543) | (8.688) | | 0.2 | 2.650 | 4.627 | 4.627 | 6.175 | 7.076 | 7.224 | | (2.660b) | (4.652) | (4.652) | (6.210) | (7.128 | (7.277) |
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, ).
bResults in parentheses are taken from FEM.
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