Research Article
Natural Frequencies of Shear Deformable Plates by Polyharmonic Splines
Table 7
Comparison study of frequency parameters,
for square isotropic plates with SSSS boundaries.
| | Method of solution |
Mode | | (1, 1) | (1, 2) | (2, 1) | (2, 2) | (1, 3) | (3, 1) |
| | 0.01 | Classical theory [4] | 2.000 | 5.000 | 5.000 | 8.000 | 10.000 | 10.000 | | FSDT, Ritz method [5] | 1.999 | 4.995 | 4.995 | 7.998 | 9.981 | 9.981 | | Orthogonal polynomials [3] | 1.999 | 4.995 | 4.995 | 7.998 | 9.981 | 9.981 | | Present, grid | 1.9695 | 5.1285 | 5.1286 | 7.9350 | 10.4481 | 10.4689 | | Present, grid | 1.9950 | 5.0563 | 5.0563 | 8.0279 | 10.1396 | 10.1719 | | Present, grid | 1.9997 | 5.0189 | 5.0189 | 8.0180 | 10.0261 | 10.0464 |
| | 0.1 | Classical theory [4] | 2.000 | 5.000 | 5.000 | 8.000 | 10.000 | 10.000 | | 3D analysis [6] | 1.934 | 4.662 | 4.622 | 7.103 | 8.662 | 8.662 | | FSDT, Ritz method [5] | 1.931 | 4.605 | 4.605 | 7.064 | 8.605 | 8.605 | | Orthogonal polynomials [3] | 1.931 | 4.605 | 4.605 | 7.064 | 8.605 | 8.605 | | Present, grid | 1.9387 | 4.6608 | 4.6608 | 7.1929 | 8.7181 | 8.7134 | | Present, grid | 1.9386 | 4.6448 | 4.6448 | 7.1589 | 8.7070 | 8.7134 | | Present, grid | 1.9376 | 4.6394 | 4.6394 | 7.1449 | 8.7091 | 8.7110 |
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