Research Article
A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges
Table 1
Frequency parameters
for the square plate of case 1 with restraining stiffness,
, , for each point support.
| | Method | Model sequence | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| | 0 | Present | 1.2897 | 1.9201 | 2.3639 | 3.2356 | 3.2356 | 5.6176 | 5.6176 | 5.6459 | | FEA | 1.2898 | 1.9212 | 2.3662 | 3.2379 | 3.2379 | 5.6231 | 5.6231 | 5.6522 | | 1 | Present | 1.2893 | 1.9204 | 2.3640 | 3.2351 | 3.2351 | 5.6176 | 5.6176 | 5.6447 | | FEA | 1.2898 | 1.9216 | 2.3663 | 3.2379 | 3.2379 | 5.6231 | 5.6231 | 5.6522 | | 101 | Present | 1.2919 | 1.9235 | 2.3650 | 3.2363 | 3.2363 | 5.6198 | 5.6198 | 5.6471 | | FEA | 1.2898 | 1.9247 | 2.3673 | 3.2385 | 3.2385 | 5.6244 | 5.6244 | 5.6547 | | 102 | Present | 1.2893 | 1.9522 | 2.3741 | 3.2415 | 3.2415 | 5.6322 | 5.6322 | 5.6697 | | FEA | 1.2898 | 1.9508 | 2.3756 | 3.2439 | 3.2439 | 5.6364 | 5.6364 | 5.6751 | | 103 | Present | 1.2893 | 2.1249 | 2.4258 | 3.2771 | 3.2771 | 5.7010 | 5.7010 | 5.8077 | | FEA | 1.2898 | 2.1093 | 2.4052 | 3.2671 | 3.2671 | 5.6817 | 5.6817 | 5.7570 | | 104 | Present | 1.2898 | 2.4948 | 2.4988 | 3.3767 | 3.3767 | 5.8271 | 5.8271 | 6.0942 | | FEA | 1.2898 | 2.4551 | 2.4870 | 3.3610 | 3.3410 | 5.8060 | 5.8060 | 6.0210 | | 106 | Present | 1.2893 | 2.4807 | 2.4889 | 3.3696 | 3.3696 | 5.8123 | 5.8123 | 6.0496 | | FEA | 1.2898 | 2.4834 | 2.5011 | 3.3787 | 3.3787 | 5.7769 | 5.7769 | 6.0209 | | 107 | Present | 1.2887 | 1.7945 | 1.7945 | 2.1151 | 2.5149 | 4.9471 | 4.9471 | 6.1398 | | 108 | Present | 1.2887 | 1.8018 | 1.8018 | 2.1325 | 2.5156 | 4.9694 | 4.9694 | 6.1398 | | 109 | Present | 1.2887 | 1.8026 | 1.8026 | 2.1342 | 2.5156 | 4.9716 | 4.9716 | 6.1398 |
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