Research Article
Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method
Table 9
Nondimensional fundamental natural transverse frequencies
for axially FG beams with respect to the gradient index.
| | | P-P | C-C | C-P | C-F | | Case 1 | Case 2 | Case 1 | Case 2 | Case 1 | Case 2 | Case 1 | Case 2 |
| −10 | Reference [14] | 11.4532 | 9.9358 | 24.0576 | 24.7949 | 16.4775 | 17.2993 | 3.5656 | 4.1800 | SFPM | 11.4560 | 9.9366 | 24.0660 | 24.8068 | 16.4111 | 17.3037 | 3.5340 | 4.1801 |
| −3 | Reference [14] | 11.2443 | 10.3669 | 23.9456 | 24.9375 | 16.0307 | 17.8701 | 3.1421 | 4.8317 | SFPM | 11.2443 | 10.3669 | 23.9446 | 24.9366 | 16.0262 | 17.8701 | 3.1410 | 4.8317 |
| 0 | Reference [14] | 10.8663 | 10.8663 | 24.3752 | 24.3752 | 15.8734 | 17.9147 | 2.9256 | 5.0156 | SFPM | 10.8664 | 10.8664 | 24.3756 | 24.3756 | 15.8735 | 17.9148 | 2.9256 | 5.0156 |
| 3 | Reference [14] | 10.3669 | 11.2443 | 24.9375 | 23.9456 | 15.7171 | 17.8867 | 2.8544 | 4.8466 | SFPM | 10.3669 | 11.2443 | 24.9366 | 23.9446 | 15.7169 | 17.8874 | 2.8545 | 4.8466 |
| 10 | Reference [14] | 9.9358 | 11.4532 | 24.7949 | 23.9456 | 15.4930 | 17.9050 | 3.0431 | 4.4629 | SFPM | 9.9366 | 11.4560 | 24.8068 | 24.0660 | 15.4958 | 17.9155 | 3.0431 | 4.4629 |
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